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004 Valuing Payment Streams We can now determine the present value of a stream of payments over time. For example, consider the two payment streams in Table 15.2. Stream A comes to $200: $100 paid now and $100 a year from now. Stream B comes to $220: $20 paid now, $100 a year from now, and $100 two years from now. Which payment stream would you prefer to receive? The answer depends on the interest rate. To calculate the present discounted value of these two streams, we compute and add the present values of each year’s payment: PDV of Stream A = $100 + $100 (1 + R) PDV of Stream B = $20 + $100 (1 + R) + $100 (1 + R)2 Table 15.3 shows the present values of the two streams for interest rates of 5, 10, 15, and 20 percent. As the table shows, the preferred stream depends on the interest rate. For interest rates of 10 percent or less, Stream B is worth more; for interest rates of 15 percent or more, Stream A is worth more. Why? Because even though less is paid out in Stream A, it is paid out sooner. TABLE 15.2 TWO PAYMENT STREAMS Payment Stream A: Payment Stream B: TODAY $100 $ 20 1 YEAR $100 $100 2 YEARS $ 0 $100 CHAPTER 15 • Investment, Time, and Capital Markets 563 TABLE 15.3 PDV OF PAYMENT STREAMS R.05 R.10 R.15 R.20 PDV of Stream A: PDV of Stream B: $195.24 205.94 $190.91 193.55 $186.96 182.57 $183.33 172.78 This simple example shown in Tables 15.2 and 15.3 illustrates an important principle. The present value of a stream of payments depends on three things: (1) the amount of each payment, (2) the timing of the payments, and (3) the interest rate used to discount payments made in the future. As we will see, this principle applies to a wide variety of problems. E X AM PLE 15.1 THE VALUE OF LOST EARNINGS In legal cases involving accidents, victims or their heirs (if the victim is killed) sue the injuring party (or an insurance company) to recover damages. In addition to compensating for pain and suffering, those damages include the future income
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that the injured or deceased person would have earned had the accident not occurred. To see how the present value of lost earnings can be calculated, let’s examine an actual 1996 accident case. (The names and some of the data have been changed to preserve anonymity.) Harold Jennings died in an automobile accident on January 1, 1996, at the age of 53. His family sued the driver of the other car for negligence. A major part of the damages they asked to be awarded was the present value of the earnings that Jennings would have received from his job as an airline pilot had he not been killed. The calculation of present value is typical of cases like this. Had he worked in 1996, Jennings’ salary would have been $85,000. The normal age of retirement for an airline pilot is 60. To calculate the present value of Jennings’ lost earnings, we must take several things into account. First, Jennings’ salary would probably have increased over the years. Second, we cannot be sure that he would have lived to retirement had the accident not occurred; he might have died from some other cause. Therefore, the PDV of his lost earnings until retirement at the end of 2003 is PDV = W0 + W0(1 + g)(1 - m1) (1 + R) + W0(1 + g)2(1 - m2) (1 + R)2 + g + W0(1 + g)7(1 - m7) (1 + R)7 where W0 is his salary in 1996, g is the annual percentage rate at which his salary is likely to have grown (so that W0(1 + g) would be his salary in 1997, W0(1 + g)2 his salary in 1998, etc.), and m1, m2,…, m7 are mortality rates, i.e., 564 PART 3 • Market Structure and Competitive Strategy TABLE 15.4 CALCULATING LOST WAGES YEAR 1996 1997 1998 1999 2000 2001 2002 2003 W0(1 + g)t (1 – mt) 1/(1 + R)t W0(1 + g)t (1 – mt)/(1 + R)t $ 85,000 91,800 99,144 107,076 115,642 124,893 134,884 145,675.991.990.989.988.987.986.985.984 1.000 $84,235.917
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.842.772.708.650.596.547 83,339 82,561 81,671 80,810 80,044 79,185 78,409 the probabilities that he would have died from some other cause by 1997, 1998,…, 2003. To calculate this PDV, we need to know the mortality rates m1,…, m7, the expected rate of growth of Jennings’ salary g, and the interest rate R. Mortality data are available from insurance tables that provide death rates for men of similar age and race.2 As a value for g, we can use 8 percent, the average rate of growth of wages for airline pilots over the period 1985–1995. Finally, for the interest rate we can use the rate on government bonds, which at the time was about 9 percent. (We will say more about how one chooses the correct interest rate to discount future cash flows in Sections 15.4 and 15.5.) Table 15.4 shows the details of the present value calculation. By summing the last column, we obtain a PDV of $650,254. If Jennings’ family was successful in proving that the defendant was at fault, and if there were no other damage issues involved in the case, they could recover this amount as compensation.3 15.3 The Value of a Bond • bond Contract in which a borrower agrees to pay the bondholder (the lender) a stream of money. A bond is a contract in which a borrower agrees to pay the bondholder (the lender) a stream of money. For example, a corporate bond (a bond issued by a corporation) might make “coupon” payments of $100 per year for the next ten years, and then a principal payment of $1000 at the end of the ten-year period.4 How much would you pay for such a bond? To find out how much 2Mortality data can be found in the Statistical Abstract of the United States (Table 105 in the 2011 Edition). 3Actually, this sum should be reduced by the amount of Jennings’ wages which would have been spent on his own consumption and which would not therefore have benefited his wife or children. 4In the United States, the coupon payments on most corporate bonds are made in semiannual installments. To keep the arithmetic simple, we will assume that they are made annually. CHAPTER 15 • Investment, Time, and Capital Markets 565 PDV of cash flow (thousands of dollars) 2.0
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1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0 0.05 0.10 0.15 0.20 Interest rate FIGURE 15.1 PRESENT VALUE OF THE CASH FLOW FROM A BOND Because most of the bond’s payments occur in the future, the present discounted value declines as the interest rate increases. For example, if the interest rate is 5 percent, the PDV of a 10-year bond paying $100 per year on a principal of $1000 is $1386. At an interest rate of 15 percent, the PDV is $749. the bond is worth, we simply compute the present value of the payment stream: PDV = $100 (1 + R) + $100 (1 + R)2 + g + $100 (1 + R)10 + $1000 (1 + R)10 (15.1) Again, the present value depends on the interest rate. Figure 15.1 shows the value of the bond—the present value of its payment stream—for interest rates up to 20 percent. Note that the higher the interest rate, the lower the value of the bond. At an interest rate of 5 percent, the bond is worth about $1386, but at an interest rate of 15 percent, its value is only $749. Perpetuities A perpetuity is a bond that pays out a fixed amount of money each year, forever. How much is a perpetuity that pays $100 per year worth? The present value of the payment stream is given by the infinite summation: • perpetuity Bond paying out a fixed amount of money each year, forever. PDV = $100 (1 + R) + $100 (1 + R)2 + $100 (1 + R)3 + $100 (1 + R)4 + g 566 PART 3 • Market Structure and Competitive Strategy • effective yield (or rate of return) Percentage return that one receives by investing in a bond. Fortunately, it isn’t necessary to calculate and add up all these terms to find the value of this perpetuity; the summation can be expressed in terms of a simple formula.5 PDV = $100/R (15.2) So if the interest rate is 5 percent, the perpetuity is worth $100/(.05
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) = $2000, but if the interest rate is 20 percent, the perpetuity is worth only $500. The Effective Yield on a Bond Many corporate and most government bonds are traded on the bond market. The value of a traded bond can be determined directly by looking at its market price—the value placed on it by buyers and sellers.6 Thus we usually know the value of a bond, but to compare the bond with other investment opportunities, we would like to determine the interest rate consistent with that value. EFFECTIVE YIELD Equations (15.1) and (15.2) show how the values of two different bonds depend on the interest rate used to discount future payments. These equations can be “turned around” to relate the interest rate to the bond’s value. This is particularly easy to do for the perpetuity. Suppose the market price—and thus the value—of the perpetuity is P. Then from equation (15.2), P = $100/R, and R = $100/P. Thus, if the price of the perpetuity is $1000, we know that the interest rate is R = $100/$1000 = 0.10, or 10 percent. This interest rate is called the effective yield, or rate of return: the percentage return that one receives by investing in a bond. For the ten-year coupon bond in equation (15.1), calculating the effective yield is a bit more complicated. If the price of the bond is P, we write equation (15.1) as P = $100 (1 + R) + $100 (1 + R)2 + $100 (1 + R)3 + g + $100 (1 + R)10 + $1000 (1 + R)10 Given the price P, this equation must be solved for R. Although there is no simple formula to express R in terms of P in this case, there are methods (sometimes available on calculators and spreadsheet programs such as Excel) for calculating R numerically. Figure 15.2, which plots the same curve as that in Figure 15.1, shows how R depends on P for this ten-year coupon bond. Note that if the price of the bond is $1000, the effective yield is 10 percent. If the price rises to $1300, the effective yield drops to about 6 percent. If the price falls to $700, the effective yield rises to over 16 percent. Yields can differ considerably among different
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bonds. Corporate bonds generally yield more than government bonds, and as Example 15.2 shows, the bonds of some corporations yield much more than the bonds of others. One of the most important reasons for this is that different bonds carry different degrees of risk. The U.S. government is less likely to default (fail to make interest or principal 5Let x be the PDV of $1 per year in perpetuity, so x = 1/(1 + R) + 1/(1 + R)2 + …. Then x(1 + R) = 1 + 1/(1 + R) + 1/(1 + R)2 + …, so x(1 + R) = 1 + x, xR = 1, and x = 1/R. 6The prices of actively traded corporate and U.S. government bonds are shown on financial market Web sites such as www.yahoo.com, www.bloomberg.com, and www.schwab.com. CHAPTER 15 • Investment, Time, and Capital Markets 567 PDV of payments (value of bond) (thousands of dollars) 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0 0.05 0.10 0.15 0.20 Interest rate FIGURE 15.2 EFFECTIVE YIELD ON A BOND The effective yield is the interest rate that equates the present value of the bond’s payment stream with the bond’s market price. The figure shows the present value of the payment stream as a function of the interest rate. The effective yield is found by drawing a horizontal line at the level of the bond’s price. For example, if the price of this bond were $1000, its effective yield would be 10 percent. If the price were $1300, the effective yield would be about 6 percent; if the price were $700, it would be 16.2 percent. payments) on its bonds than is a private corporation. And some corporations are financially stronger and therefore less likely to default than others. As we saw in Chapter 5, the more risky an investment, the greater the return that an investor demands. As a result, riskier bonds have higher yields. EXAM PLE 15.2 THE YIELDS ON CORPORATE BONDS To
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see how corporate bond yields are calculated—and how they can differ from one corporation to another—let’s examine the yields for two coupon bonds: one issued by Microsoft and the other by the drug store chain Rite Aid. Each has a face value of $100, which means that when the bond matures, the holder receives a principal payment of that amount. Each bond makes a “coupon” (i.e., interest) payment every six months.7 7These bonds actually have a face value of $1000, not $100. The prices and coupon payments are listed as though the face value were $100; to get the actual prices and payments, just multiply by 10 the numbers that appear on financial Web sites or in the newspaper. 568 PART 3 • Market Structure and Competitive Strategy We calculate the bond yields using the closing prices on August 1, 2011. The following information was downloaded from the Yahoo! Finance Web site: Price ($): Coupon ($): Microsoft Rite Aid 106.60 5.300 93.00 9.500 Maturity Date: Feb. 8, 2041 Jun. 15, 2017 Yield to Maturity (%): Current Yield (%): Rating: 4.877 4.972 AAA 11.099 10.215 CCC What do these numbers mean? For Microsoft, the price of $106.60 was the closing price on August 1, 2011, based on a face value for the bond of $100. The coupon of $5.30 means that $2.65 is paid to the owner of the bond every six months. The maturity date is the date at which the bond comes due and the owner receives the $100 face value. The 4.877 percent yield to maturity, discussed further below, is the effective yield (i.e., rate of return) on the bond. The current yield is simply the coupon divided by the price, i.e., 5.300/106.60 = 4.972 percent. (The current yield is of limited relevance because it doesn’t tell us the actual rate of return on the bond.) Finally, the Microsoft bond is rated AAA, which is the highest rating possible for a corporate bond, indicating that the likelihood of default is very low. How does one determine the effective yield (i.e., rate of return, or yield to maturity) on this bond? For simplicity, we’ll assume that the coupon payments are made annually instead of every six months.
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(The error that this introduces is small.) Because the Microsoft bond matures in 2041, coupon payments will be made for 2041 – 2011 = 30 years. Thus the yield is given by the following equation: 106.60 = 5.3 (1 + R) + 5.3 (1 + R)2 + 5.3 (1 + R)3 + g + 5.3 (1 + R )29 + 5.3 (1 + R)30 To find the effective yield, we must solve this equation for R.8 You can check (by substituting to see whether the equation is satisfied) that the solution is approximately R* = 4.877 percent. The effective yield on the Rite Aid bond is found the same way. The bond had a price of $93.00, made coupon payments of $9.50 per year, and had 2017 – 2011 = 6 years to mature. Thus the equation for its yield is: 93.00 = 9.5 (1 + R) + 9.5 (1 + R)2 + 9.5 (1 + R)3 + 9.5 (1 + R)4 + 9.5 (1 + R)5 + 9.5 (1 + R)6 8Solving the equation for R can be done in Excel by using Solver. CHAPTER 15 • Investment, Time, and Capital Markets 569 The solution to this equation is R* = 11.099 percent. Why was the yield on the Rite Aid bond so much higher than on the Microsoft bond? Because the Rite Aid bond was much riskier. By 2011, the drug store chain was suffering large losses due to increasing competition from larger chains like Wal-Mart, which were able to use their scale to undercut prices on everything from toiletries to prescription drugs. Between 2007 and 2011, Rite Aid turned a profit for only one quarter, leading many analysts to predict bankruptcy. Consistent with this, Rite Aid’s bond was rated CCC (the lowest ranking). Because investors knew that there was a significant possibility that Rite Aid would default on its bond payments, they were prepared to buy the bond only if the expected return was high enough to compensate them for the risk. 15.4 The Net Present Value Criterion for Capital Investment Decisions One of the most common and important decisions that firms make is to invest in new capital. Millions of dollars may be invested in a factory or machines that will last—and affect profits—for many years. The
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future cash flows that the investment will generate are often uncertain. And once the factory has been built, the firm usually cannot disassemble and resell it to recoup its investment—it becomes a sunk cost. How should a firm decide whether a particular capital investment is worthwhile? It should calculate the present value of the future cash flows that it expects to receive from the investment and compare it with the cost of the investment. This method is known as the net present value (NPV) criterion: NPV criterion: Invest if the present value of the expected future cash flows from an investment is larger than the cost of the investment. In §7.1, we explain that a sunk cost is an expenditure that has been made and cannot be recovered. • net present value (NPV) criterion Rule holding that one should invest if the present value of the expected future cash flow from an investment is larger than the cost of the investment. Suppose a capital investment costs C and is expected to generate profits over the next 10 years of amounts p 10. We then write the net present value as 2,…, p 1, p NPV = -C + p 1 (1 + R) + p 2 (1 + R)2 + g + 10 p (1 + R)10 (15.3) where R is the discount rate that we use to discount the future stream of profits. (R might be a market interest rate or some other rate; we will discuss how to choose it shortly.) Equation (15.3) describes the net benefit to the firm from the investment. The firm should make the investment only if that net benefit is positive—i.e., only if NPV > 0. • discount rate Rate used to determine the value today of a dollar received in the future. DETERMINING THE DISCOUNT RATE What discount rate should the firm use? The answer depends on the alternative ways that the firm could use its money. For example, instead of this investment, the firm might invest 570 PART 3 • Market Structure and Competitive Strategy • opportunity cost of capital Rate of return that one could earn by investing in an alternate project with similar risk. in another piece of capital that generates a different stream of profits. Or it might invest in a bond that yields a different return. As a result, we can think of R as the firm’s opportunity cost of capital. Had the firm not invested in this project, it could have earned a return by investing in something else. The correct value for
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R is therefore the return that the firm could earn on a “similar” investment. By “similar” investment, we mean one with the same risk. As we saw in Chapter 5, the more risky an investment, the greater the return one expects to receive from it. Therefore, the opportunity cost of investing in this project is the return that one could earn from another project or asset of similar riskiness. We’ll see how to evaluate the riskiness of an investment in the next section. For now, let’s assume that this project has no risk (i.e., the firm is sure that the future profit flows will be p 1, p 2, etc.). In that case, the opportunity cost of the investment is the risk-free return—e.g., the return one could earn on a government bond. If the project is expected to last for 10 years, the firm could use the annual interest rate on a 10-year government bond to compute the NPV of the project, as in equation (15.3).9 If the NPV is zero, the benefit from the investment would just equal the opportunity cost, so the firm should be indifferent between investing and not investing. If the NPV is greater than zero, the benefit exceeds the opportunity cost, so the investment should be made.10 The Electric Motor Factory In Section 15.1, we discussed a decision to invest $10 million in a factory to produce electric motors. This factory would enable the firm to use labor and copper to produce 8000 motors per month for 20 years at a cost of $42.50 each. The motors could be sold for $52.50 each, for a profit of $10 per unit, or $80,000 per month. We will assume that after 20 years, the factory will be obsolete but can be sold for scrap for $1 million. Is this a good investment? To find out, we must calculate its net present value. We will assume for now that the $42.50 production cost and the $52.50 price at which the motors can be sold are certain, so that the firm is sure that it will receive $80,000 per month, or $960,000 per year, in profit. We also assume that the $1 million scrap value of the factory is certain. The firm should therefore use a risk-free interest rate to discount future profits. Writing the cash flows in millions of dollars, the NPV is NPV = - 10 +.
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96 (1 + R) +.96 (1 + R)2 +.96 (1 + R)3 (15.4) + c +.96 (1 + R)20 + 1 (1 + R)20 9This is an approximation. To be precise, the firm should use the rate on a one-year bond to discount 1, the rate on a two-year bond to discount p p 2, etc. 10This NPV rule is incorrect when the investment is irreversible, subject to uncertainty, and can be delayed. For a treatment of irreversible investment, see Avinash Dixit and Robert Pindyck, Investment under Uncertainty (Princeton, NJ: Princeton University Press, 1994). Net present value (millions of dollars) 10 1 –2 – 3 –4 – 5 –6 CHAPTER 15 • Investment, Time, and Capital Markets 571 FIGURE 15.3 NET PRESENT VALUE OF A FACTORY The NPV of a factory is the present discounted value of all the cash flows involved in building and operating it. Here it is the PDV of the flow of future profits less the current cost of construction. The NPV declines as the discount rate increases. At discount rate R*, the NPV is zero. 0 0.05 R* 0.10 0.15 0.20 Discount rate, R Figure 15.3 shows the NPV as a function of the discount rate R. Note that at the rate R*, which is about 7.5 percent, the NPV is equal to zero. (The rate R* is sometimes referred to as the internal rate of return on the investment.) For discount rates below 7.5 percent, the NPV is positive, so the firm should invest in the factory. For discount rates above 7.5 percent, the NPV is negative, and the firm should not invest. Real versus Nominal Discount Rates In the example above, we assumed that future cash flows are certain, so that the discount rate R should be a risk-free interest rate, such as the rate on U.S. government bonds. Suppose that rate happened to be 9 percent. Does that mean the NPV is negative and the firm should not invest? To answer this question, we must distinguish between real and nominal discount rates, and between real and nominal cash flows. Let’s begin with the cash flows. In Chapter 1, we discussed real versus nominal prices. We explained that whereas the real price is net of
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inflation, the nominal price includes inflation. In our example, we assumed that the electric motors coming out of our factory could be sold for $52.50 each over the next 20 years. We said nothing, however, about the effect of inflation. Is the $52.50 a real price, i.e., net of inflation, or does it include inflation? As we will see, the answer to this question can be critical. Let’s assume that the $52.50 price—and the $42.50 production cost—are in real terms. This means that if we expect a 5-percent annual rate of inflation, the nominal price of the motors will increase from $52.50 in the first year to (1.05)(52.50) = $55.13 in the second year, to (1.05)(55.13) = $57.88 in the third year, and so on. Therefore, our profit of $960,000 per year is also in real terms. 572 PART 3 • Market Structure and Competitive Strategy Opportunity cost is discussed in §7.1. Now let’s turn to the discount rate. If the cash flows are in real terms, the discount rate must also be in real terms. Why? Because the discount rate is the opportunity cost of the investment. If inflation is not included in the cash flows, it should not be included in the opportunity cost either. In our example, the discount rate should therefore be the real interest rate on government bonds. The nominal interest rate (9 percent) is the rate that we see in the newspapers; it includes inflation. The real interest rate is the nominal rate minus the expected rate of inflation.11 If we expect inflation to be 5 percent per year on average, the real interest rate would be 9 - 5 = 4 percent. This is the discount rate that should be used to calculate the NPV of the investment in the electric motor factory. Note from Figure 15.3 that at this rate the NPV is clearly positive, so the investment should be undertaken. When the NPV rule is used to evaluate investments, the numbers in the calculations may be in real or in nominal terms, as long as they are consistent. If cash flows are in real terms, the discount rate should also be in real terms. If a nominal discount rate is used, the effect of future inflation must also be included in the cash flows. Negative Future Cash Flows Factories and other production facilities can take several years
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to build and equip. The cost of the investment will also be spread out over several years, instead of occurring only at the outset. In addition, some investments are expected to result in losses, rather than profits, for the first few years. (For example, demand may be low until consumers learn about the product, or costs may start high and fall only when managers and workers have moved down the learning curve.) Negative future cash flows create no problem for the NPV rule; they are simply discounted, just like positive cash flows. For example, suppose that our electric motor factory will take a year to build: $5 million is spent right away, and another $5 million is spent next year. Also, suppose the factory is expected to lose $1 million in its first year of operation and $0.5 million in its second year. Afterward, it will earn $0.96 million a year until year 20, when it will be scrapped for $1 million, as before. (All these cash flows are in real terms.) Now the net present value is NPV = -5 - 5 (1 + R) - 1 (1 + R)2 -.5 (1 + R)3 +.96 (1 + R)4 +.96 (1 + R)5 (15.5) + g +.96 (1 + R)20 + 1 (1 + R)20 Suppose the real interest rate is 4 percent. Should the firm build this factory? You can confirm that the NPV is negative, so this project is not a good investment. 11People may have different views about future inflation and may therefore have different estimates of the real interest rate. CHAPTER 15 • Investment, Time, and Capital Markets 573 EXAM PLE 15.3 THE VALUE OF A NEW YORK CITY TAXI MEDALLION We saw in Example 9.5 that in 2011, the number of taxi medallions in New York was roughly the same as in 1937, so that the price of a medallion was $880,000. (Recall that a medallion is a permit allowing a taxicab to be used to transport passengers.) The medallions are owned by taxi companies, which have successfully pressured the city government to limit the number in circulation, thereby maintaining the high price — at the cost of making it difficult for citizens to find a taxi. A taxi medallion allows its owner to lease a cab to a driver and thereby earn a profit from the operation of the cab
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. Is that profit high enough to justify an $880,000 value for each medallion? To find out, let’s calculate the flow of income a taxi company can expect from leasing a medallion to one or more taxi drivers. The taxi company charges the driver a flat fee for use of the medallion, but that fee is capped by the city. In 2011, the fee was $110 per 12-hour shift, or $220 per day. Assuming the cab is driven 7 days per week and 50 weeks per year, the taxi company would earn (7)(50)($220) = $77,000 per year from the medallion. Little risk is involved (there is a shortage of taxis, so it is easy to find drivers willing to lease the medallion), and the capped fee has increased with inflation. Therefore a 5-percent discount rate would probably be appropriate for discounting future income flows. Assuming a time horizon of 20 years, the present value of this flow of income is therefore: PV = 70,000 1.05 + 70,000 1.052 + 70,000 1.053 + c + 70,000 1.0520 = $872,355 Thus a medallion price in the range of $880,000 is consistent with the flow of income that the medallion will bring to the taxi company. 15.5 Adjustments for Risk We have seen that a risk-free interest rate is an appropriate discount rate for future cash flows that are certain. For most projects, however, future cash flows are far from certain. At our electric motor factory, for example, we would expect uncertainty over future copper prices, over the future demand and the price of motors, and even over future wage rates. Thus the firm cannot know what its profits from the factory will be over the next 20 years. Its best estimate of profits might be $960,000 per year, but actual profits may turn out to be higher or lower. How should the firm take this uncertainty into account when calculating the net present value of the project? A common practice is to increase the discount rate by adding a risk premium to the risk-free rate. The idea is that the owners of the firm are risk averse, which makes future cash flows that are risky worth less than those that are certain. Increasing the discount rate takes this into account by reducing the present value of those future cash flows. But how large should the risk premium be? As we will see, the answer depends on the nature of the
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risk. • risk premium Amount of money that a risk-averse individual will pay to avoid taking a risk. 574 PART 3 • Market Structure and Competitive Strategy • diversifiable risk Risk that can be eliminated either by investing in many projects or by holding the stocks of many companies. • nondiversifiable risk Risk that cannot be eliminated by investing in many projects or by holding the stocks of many companies. Diversifiable versus Nondiversifiable Risk Adding a risk premium to the discount rate must be done with care. If the firm’s managers are operating in the stockholders’ interests, they must distinguish between two kinds of risk—diversifiable and nondiversifiable.12 Diversifiable risk can be eliminated by investing in many projects or by holding the stocks of many companies. Nondiversifiable risk cannot be eliminated in this way. Only nondiversifiable risk affects the opportunity cost of capital and should enter into the risk premium. DIVERSIFIABLE RISK To understand this, recall from Chapter 5 that diversifying can eliminate many risks. For example, I cannot know whether the result of a coin flip will be heads or tails. But I can be reasonably sure that out of a thousand coin flips, roughly half will be heads. Similarly, an insurance company that sells me life insurance cannot know how long I will live. But by selling life insurance to thousands of people, it can be reasonably sure about the percentage of those who will die each year. Much the same is true about capital investment decisions. Although the profit flow from a single investment may be very risky, overall risk will be much less if the firm invests in dozens of projects (as most large firms do). Furthermore, even if the company invests in only one project, stockholders can easily diversify by holding the stocks of a dozen or more different companies, or by holding a mutual fund that invests in many stocks. Thus, stockholders—the owners of the firm—can eliminate diversifiable risk. Because investors can eliminate diversifiable risk, they cannot expect to earn a return higher than the risk-free rate by bearing it: No one will pay you for bearing a risk that there is no need to bear. And indeed, assets that have only diversifiable risk tend on average to earn a return close to the risk-free rate. Now, remember that the discount rate for a project is the opportunity cost of investing in that project rather than in some other project or asset with similar risk characteristics. Therefore, if the project’s only risk is
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diversifiable, the opportunity cost is the risk-free rate. No risk premium should be added to the discount rate. NONDIVERSIFIABLE RISK What about nondiversifiable risk? First, let’s be clear about how such risk can arise. For a life insurance company, the possibility of a major war poses nondiversifiable risk. Because a war may increase mortality rates sharply, the company cannot expect that an “average” number of its customers will die each year, no matter how many customers it has. As a result, most insurance policies, whether for life, health, or property, do not cover losses resulting from acts of war. For capital investments, nondiversifiable risk arises because a firm’s profits tend to depend on the overall economy. When economic growth is strong, corporate profits tend to be higher. (For our electric motor factory, the demand for motors is likely to be strong, so profits increase.) On the other hand, profits tend to fall in a recession. Because future economic growth is uncertain, diversification cannot eliminate all risk. Investors should (and indeed can) earn higher returns by bearing this risk. To the extent that a project has nondiversifiable risk, the opportunity cost of investing in that project is higher than the risk-free rate. Thus a risk premium 12Diversifiable risk is also called nonsystematic risk and nondiversifiable risk is called systematic risk. Adding a simple risk premium to the discount rate may not always be the correct way of dealing with risk. See, for example, Richard Brealey and Stewart Myers, Principles of Corporate Finance (New York: McGraw-Hill, 2011). CHAPTER 15 • Investment, Time, and Capital Markets 575 must be included in the discount rate. Let’s see how the size of that risk premium can be determined. The Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM) measures the risk premium for a capital investment by comparing the expected return on that investment with the expected return on the entire stock market. To understand the model, suppose, first, that you invest in the entire stock market (say, through a mutual fund). In that case, your investment would be completely diversified and you would bear no diversifiable risk. You would, however, bear nondiversifiable risk because the stock market tends to move with the overall economy. (The stock market reflects expected future profits, which depend in part on the economy.) As a result, the expected return on the stock
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market is higher than the risk-free rate. Denoting the expected return on the stock market by rm and the risk-free rate by rf, the risk - rf. This is the additional expected return you get premium on the market is rm for bearing the nondiversifiable risk associated with the stock market. Now consider the nondiversifiable risk associated with one asset, such as a company’s stock. We can measure that risk in terms of the extent to which the return on the asset tends to be correlated with (i.e., move in the same direction as) the return on the stock market as a whole. For example, one company’s stock might have almost no correlation with the market as a whole. On average, the price of that stock would move independently of changes in the market, so it would have little or no nondiversifiable risk. The return on that stock should therefore be about the same as the risk-free rate. Another stock, however, might be highly correlated with the market. Its price changes might even amplify changes in the market as a whole. That stock would have substantial nondiversifiable risk, perhaps more than the stock market as a whole. If so, its return on average will exceed the market return rm. The CAPM summarizes this relationship between expected returns and the risk premium by the following equation: ri - rj = b(rm - rf) (15.6) where ri is the expected return on an asset. The equation says that the risk premium on the asset (its expected return less the risk-free rate) is proportional to the risk premium on the market. The constant of proportionality, b, is called the asset beta. It measures the sensitivity of the asset’s return to market movements and, therefore, the asset’s nondiversifiable risk. If a 1-percent rise in the market tends to result in a 2-percent rise in the asset price, the beta is 2. If a 1-percent rise in the market tends to result in a 1-percent rise in the asset price, the beta is 1. And if a 1-percent rise in the market tends to result in no change in the price of the asset, the beta is zero. As equation (15.6) shows, the larger the beta, the greater the expected return on the asset. Why? Because the asset’s nondiversifiable risk is greater. THE RISK-ADJUSTED DISCOUNT R
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ATE Given beta, we can determine the correct discount rate to use in computing an asset’s net present value. That discount rate is the expected return on the asset or on another asset with the same risk. It is therefore the risk-free rate plus a risk premium to reflect nondiversifiable risk: Discount rate = rf + b(rm - rf) (15.7) • Capital Asset Pricing Model (CAPM) Model in which the risk premium for a capital investment depends on the correlation of the investment’s return with the return on the entire stock market. • asset beta A constant that measures the sensitivity of an asset’s return to market movements and, therefore, the asset’s nondiversifiable risk. 576 PART 3 • Market Structure and Competitive Strategy • company cost of capital Weighted average of the expected return on a company’s stock and the interest rate that it pays for debt. - rf), has been Over the past 60 years, the risk premium on the stock market, (rm about 8 percent on average. If the real risk-free rate were 4 percent and beta were 0.6, the correct discount rate would be 0.04 + 0.6(0.08) = 0.09, or 9 percent. If the asset is a stock, its beta can usually be estimated statistically.13 When the asset is a new factory, however, determining its beta is more difficult. Many firms therefore use the company cost of capital as a (nominal) discount rate. The company cost of capital is a weighted average of the expected return on the company’s stock (which depends on the beta of the stock) and the interest rate that it pays for debt. This approach is correct as long as the capital investment in question is typical for the company as a whole. It can be misleading, however, if the capital investment has much more or much less nondiversifiable risk than the company as a whole. In that case, it may be better to make a reasoned guess as to how much the revenues from the investment are likely to depend on the overall economy. EXAMPLE 15.4 CAPITAL INVESTMENT IN THE DISPOSABLE DIAPER INDUSTRY In Example 13.6 (page 515), we discussed the disposable diaper industry, which has been dominated by two companies, Procter & Gamble and Kimberly-Clark. We explained that their continuing R&D (research and development) expenditures have given these firms a cost
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advantage that deters entry. Now we’ll examine the capital investment decision of a potential entrant. Suppose you are considering entering this industry. To take advantage of scale economies in production, advertising, and distribution, you would need to build three plants at a cost of $60 million each, with the cost spread over three years. When operating at capacity, the plants would produce a total of 2.5 billion diapers per year. These would be sold at wholesale for about 16 cents per diaper, yielding revenues of about $400 million per year. You can expect your variable production costs to be about $290 million per year, for a net revenue of $110 million per year. You will, however, have other expenses. Using the experience of P&G and Kimberly-Clark as a guide, you can expect to spend about $60 million in R&D before start-up to design an efficient manufacturing process, and another $20 million in R&D during each year of production to maintain and improve that process. Finally, once you are operating at full capacity, you can expect to spend another $50 million per year for a sales force, advertising, and marketing. Your net operating profit will be $40 million per year. The plants will last for 15 years and will then be obsolete. 13You can estimate beta by running a linear regression of the return on the stock against the excess - rf. Or you can look it up on a financial Web site like Yahoo! Finance or return on the market, rm E*Trade, which give detailed information on individual stocks. In August 2011, Yahoo! Finance listed a beta of 1.07 for the Intel Corporation and 1.46 for Eastman Kodak. CHAPTER 15 • Investment, Time, and Capital Markets 577 Is the investment a good idea? To find out, let’s calculate its net present value. Table 15.5 shows the relevant numbers. We assume that production begins at 33 percent of capacity when the plant is completed in 2015, takes two years to reach full capacity, and continues through the year 2030. Given the net cash flows, the NPV is calculated as NPV = -120 - 93.4 (1 + R) - 56.6 (1 + R)2 + 40 (1 + R)3 + 40 (1 + R)4 + g + 40 (1 + R)15 Table 15.5 shows the NPV for discount rates of 5, 10, and 15 percent. Note that the NPV
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is positive for a discount rate of 5 percent, but it is negative for discount rates of 10 or 15 percent. What is the correct discount rate? First, we have ignored inflation, so the discount rate should be in real terms. Second, the cash flows are risky—we don’t know how efficient our plants will be, how effective our advertising and promotion will be, or even what the future demand for disposable diapers will be. Some of this risk is nondiversifiable. To calculate the risk premium, we will use a beta of 1, which is typical for a producer of consumer products of this sort. Using 4 percent for the real risk-free interest rate and 8 percent for the risk premium on the stock market, our discount rate should be R = 0.04 + 1(0.08) = 0.12 TABLE 15.5 DATA FOR NPV CALCULATION ($ MILLIONS) Sales LESS Variable cost Ongoing R&D Sales force, ads, and marketing Operating profit LESS Construction cost Initial R&D NET CASH FLOW PRE-2015 60.0 60.0 2015 133.3 96.7 20.0 50.0 −33.4 60.0 2016 266.7 193.3 20.0 50.0 3.4 60.0 2017 400.0 290.0 20.0 50.0 40.0 … … … … … … 2030 400.0 290.0 20.0 50.0 40.0 −120.0 −93.4 −56.6 40.0 … 40.0 Discount Rate: NPV: 0.05 0.10 0.15 80.5 −16.9 −75.1 578 PART 3 • Market Structure and Competitive Strategy At this discount rate, the NPV is clearly negative, so the investment does not make sense. You will not enter the industry, and P&G and Kimberly-Clark can breathe a sigh of relief. Don’t be surprised, however, that these firms can make money in this market while you cannot. Their experience, years of earlier R&D (they need not spend $60 million on R&D before building new plants), and brand name recognition give them a competitive advantage that a new entrant will find hard to overcome. 15.6 Investment Decisions by Consumers We have seen how firms value future cash flows and thereby decide whether to invest in long-lived capital. Consumers face similar decisions when they purchase durable goods, such as cars or
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major appliances. Unlike the decision to purchase food, entertainment, or clothing, the decision to buy a durable good involves comparing a flow of future benefits with the current purchase cost. Suppose that you are deciding whether to buy a new car. If you keep the car for six or seven years, most of the benefits (and costs of operation) will occur in the future. You must therefore compare the future flow of net benefits from owning the car (the benefit of having transportation less the cost of insurance, maintenance, and gasoline) with the purchase price. Likewise, when deciding whether to buy a new air conditioner, you must compare its price with the present value of the flow of net benefits (the benefit of a cool room less the cost of electricity to operate the unit). These problems are analogous to the problem of a firm that must compare a future flow of profits with the current cost of plant and equipment when making a capital investment decision. We can therefore analyze these problems just as we analyzed the firm’s investment problem. Let’s do this for a consumer’s decision to buy a car. The main benefit from owning a car is the flow of transportation services it provides. The value of those services differs from consumer to consumer. Let’s assume our consumer values the service at S dollars per year. Let’s also assume that the total operating expense (insurance, maintenance, and gasoline) is E dollars per year, that the car costs $20,000, and that after six years, its resale value will be $4000. The decision to buy the car can then be framed in terms of net present value: NPV = -20,000 + (S - E) + (S - E) (1 + R) + (S - E) (1 + R)2 (15.8) + g + (S - E) (1 + R)6 + 4000 (1 + R)6 What discount rate R should the consumer use? The consumer should apply the same principle that a firm does: The discount rate is the opportunity cost of money. If the consumer already has $20,000 and does not need a loan, the correct discount rate is the return that could be earned by investing the money in another asset—say, a savings account or a government bond. On the other hand, if the consumer is in debt, the discount rate would be the borrowing rate that he or she is already paying. Because this rate is likely to be much higher
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CHAPTER 15 • Investment, Time, and Capital Markets 579 than the interest rate on a bond or savings account, the NPV of the investment will be smaller. Consumers must often make trade-offs between up-front versus future payments. An example is the decision of whether to buy or lease a new car. Suppose you can buy a new Toyota Corolla for $15,000 and, after six years, sell it for $6000. Alternatively, you could lease the car for $300 per month for three years, and at the end of the three years, return the car. Which is better—buying or leasing? The answer depends on the interest rate. If the interest rate is very low, buying the car is preferable because the present value of the future lease payments is high. If the interest rate is high, leasing is preferable because the present value of the future lease payments is low. EXAM PLE 15.5 CHOOSING AN AIR CONDITIONER AND A NEW CAR Buying a new air conditioner involves making a trade-off. Some air conditioners cost less but are less efficient—they consume a lot of electricity relative to their cooling power. Others cost more but are more efficient. Should you buy an inefficient air conditioner that costs less now but will cost more to operate in the future, or an efficient one that costs more now but will cost less to operate? Let’s assume that you are comparing air conditioners of equivalent cooling power, so that they yield the same flow of benefits. We can then compare the present discounted values of their costs. Assuming an eight-year lifetime and no resale, the PDV of the cost of buying and operating air conditioner i is PDV = Ci + OCi + OCi (1 + R) + OCi (1 + R)2 + g + OCi (1 + R)8 where Ci is the purchase price of air conditioner i and OCi is its average annual operating cost. The preferred air conditioner depends on your discount rate. If you have little free cash and must borrow, you should use a high discount rate. Because this would make the present value of the future operating costs smaller, you would probably choose a less expensive but relatively inefficient unit. If you have plenty of free cash, so that your opportunity cost of money (and thus your discount rate) is low, you would probably buy the more expensive unit. An econometric study of household purchases of air conditioners shows that consumers tend
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to trade off capital costs and expected future operating costs in just this way, although the discount rates that people use are high—about 20 percent for the population as a whole.14 (American consumers seem to behave myopically by overdiscounting future savings.) The study 14See Jerry A. Hausman, “Individual Discount Rates and the Purchase and Utilization of EnergyUsing Durables,” Bell Journal of Economics 10 (Spring 1979): 33–54. 580 PART 3 • Market Structure and Competitive Strategy also shows that consumers’ discount rates vary inversely with their incomes. For example, people with above-average incomes used discount rates of about 9 percent, while those in the bottom quarter of the income distribution used discount rates of 39 percent or more. We would expect this result because higher-income people are likely to have more free cash available and therefore have a lower opportunity cost of money. Buying a new car involves a similar trade-off. One car might cost less than another but offer lower fuel efficiency and require more maintenance and repairs, so that expected future operating costs are higher. As with air conditioners, a consumer can compare two or more cars by calculating and comparing the PDV of the purchase price and expected average annual operating cost for each. An econometric study of automobile purchases found that consumers indeed trade off the purchase price and expected operating costs in this way.15 It found the average discount rate for all consumers to be in the range of 11 to 17 percent. These discount rate estimates are somewhat lower than those for air conditioners, and probably reflect the widespread availability of auto loans. 15.7 Investments in Human Capital So far, we have discussed how firms and consumers can decide whether to invest in physical capital—buildings and equipment, in the case of firms, and durable goods such as cars and major appliances, in the case of consumers. We have seen how to apply the net present value rule to these decisions: Invest when the present value of the gains from the investment exceeds the present value of the costs. Some very important investment decisions involve human capital rather than physical capital. Given that you are now reading this book, you are probably making an investment in your own human capital at this very moment.16 By studying microeconomics, perhaps as part of an undergraduate or graduate degree program, you are obtaining valuable knowledge and skills that will make you more productive in the future. Human capital is the knowledge, skills, and experience that make an individual more productive and thereby able to earn a
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higher income over a lifetime. If you go to college or graduate school, take postgraduate courses, or enroll in a specialized job training program, you are investing in human capital. Most likely, the money, time, and effort that you invest to build up your human capital will pay off in the form of more rewarding or high-paying job opportunities. How should an individual decide whether to invest in human capital? To answer this question, we can use the same net present value rule that we have applied to investments in physical capital. Suppose, for example, that upon completing high school you are deciding whether to go to college for four years or skip college and go to work 15See Mark K. Dreyfus and W. Kip Viscusi, “Rates of Time Preference and Consumer Valuations of Automobile Safety and Fuel Efficiency,” Journal of Law and Economics 38 (April 1995): 79–105. 16On the other hand, finding this book more entertaining than a good novel, you might be reading it purely for pleasure. • human capital Knowledge, skills, and experience that make an individual more productive and thereby able to earn a higher income over a lifetime. CHAPTER 15 • Investment, Time, and Capital Markets 581 instead. To keep things as simple as possible, let’s analyze this decision on a purely financial basis and ignore any pleasure (in the form of parties and football games) or pain (in the form of exams and papers) that college might entail. We will calculate the NPV of the costs and benefits of getting a college degree. THE NPV OF A COLLEGE EDUCATION There are two major costs associated with college. First, because you will be studying rather than working, you will incur the opportunity cost of the lost wages that you could have earned had you taken a job. For a typical high school graduate in the United States, those lost wages might be about $20,000 per year. The second major cost is for tuition, room and board, and related expenses (such as the cost of this book). Tuition and room and board can vary widely, depending on whether one is attending a public or private college, whether one is living at home or on campus, and whether one is receiving a scholarship. Let’s use $20,000 per year as a rough average number. (Most public universities are less expensive, but many private colleges and universities cost more.) Thus we will take the total economic cost of attending college to be
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$40,000 per year for each of four years. An important benefit of college is the ability to earn a higher salary throughout your working life. In the United States, a college graduate will on average earn about $20,000 per year more than a high school graduate. In practice, the salary differential is largest during the first 5 to 10 years following college graduation, and then becomes smaller. For simplicity, however, we will assume that this $20,000 salary differential persists for 20 years. In that case, the NPV (in $1000’s) of investing in a college education is NPV = -40 - 40 (1 + R) - 40 (1 + R)2 - 40 (1 + R)3 + 20 (1 + R)4 + g + 20 (1 + R)23 What discount rate, R, should one use to calculate this NPV? Because we have kept the costs and benefits fixed over time, we are implicitly ignoring inflation. Thus we should use a real discount rate. In this case, a reasonable real discount rate would be about 5 percent. This rate would reflect the opportunity cost of money for many households—the return that could be made by investing in assets other than human capital. You can check that the NPV is then about $66,000. With a 5-percent discount rate, investing in a college education is a good idea, at least as a purely financial matter. Although the NPV of a college education is a positive number, it is not very large. Why isn’t the financial return from going to college higher? Because in the United States, entry into college has become attainable for the majority of graduating high school seniors.17 In other words, a college education is an investment with close to free entry. As we saw in Chapter 8, in markets with free entry, we should expect to see zero economic profits, which implies that investments will earn a competitive return. Of course, a low economic return doesn’t mean that you shouldn’t complete your college degree—there are many benefits to a college education that go beyond increases in future earnings. 17This is not to say that all high school graduates can go to the college of their choice. Some colleges are selective and require high grades and test scores for admission. But the large number of colleges and universities in the United States makes an undergraduate education an option for the majority of high school graduates. In §15.4, we discuss real versus nominal discount
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rates, and explain that the real discount rate is the nominal rate minus the expected rate of inflation. In §8.7 we explain that zero economic profit means that a firm is earning a competitive return on its investment. 582 PART 3 • Market Structure and Competitive Strategy EXAMPLE 15.6 SHOULD YOU GO TO BUSINESS SCHOOL? Many readers of this book are contemplating attending business school and earning an MBA degree or are already enrolled in an MBA program. Those of you thinking about business school (or already attending) might be wondering whether an MBA is worth the investment. Let’s see if we can help you with your concern. For most people, getting an MBA means an increase—very often a big increase—in salary. Table 15.6 shows estimates of average pre-MBA and post-MBA salaries for 32 business schools, 24 in the United States and 8 in other countries.18 As you can see, the increases in salaries are dramatic. Bear in mind, however, that not all MBA programs are included in Table 15.6. Indeed, because the list includes many of the top MBA programs—and because the salaries are self-reported—they probably overstate average MBA salaries for all graduates. For the United States as a whole, a rough estimate of the average salary of students about to enter business school is around $45,000 per year and the average increase in salary upon obtaining the MBA degree is about $30,000 per year. For our simple analysis, we will assume that this $30,000 per year gain in salary persists for 20 years. The typical MBA program in the United States takes two years and involves tuition and expenses of $45,000 per year. (Very few MBA students obtain scholarships.) In addition to tuition and expenses, it is important to include the opportunity cost of the foregone pre-MBA salary, i.e., another $45,000 per year. Thus, the total economic cost of getting an MBA is $90,000 per year for each of two years. The NPV of this investment is therefore NPV = -90 - 90 (1 + R) + 90 (1 + R)2 + g + 30 (1 + R)21 You can check that using a real discount rate of 5 percent, the NPV comes out to about $180,000. Why is the payoff from an MBA at schools like those listed in Table 15.6 so much higher than the payoff from a four-year undergraduate degree? Because entry into
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many MBA programs (and especially the programs listed in Table 15.6) is selective and difficult. (The same is true for other professional degree programs, such as law and medicine.) Because many more people apply to MBA programs than there are spaces, the return on the degree remains high. Should you go to business school? As we have just seen, the financial part of this decision is easy: Though costly, the return on this investment is very high. 18The data show the average 2011 salary of students who received their MBAs in 2007 and are from the Financial Times business school rankings of 100 top schools (http://rankings.ft.com/ businessschoolrankings/global-mba-rankings-2011). CHAPTER 15 • Investment, Time, and Capital Markets 583 TABLE 15.6 SALARIES BEFORE AND AFTER BUSINESS SCHOOL UNIVERSITY Stanford University University of Pennsylvania: Wharton Harvard Business School Columbia Business School MIT Sloan School of Management Dartmouth College: Tuck University of Chicago Yale School of Management Northwestern University: Kellogg Cornell University: Johnson New York University: Stern UCLA: Anderson Duke University: Fuqua University of Michigan University of Virginia Carnegie Mellon Georgetown University University of Texas at Austin University of Southern California Vanderbilt University: Owen Indiana University: Kelley University of Rochester: Simon Pennsylvania State University Purdue University: Krannert INTERNATIONAL BUSINESS SCHOOLS Indian Institute of Management, Ahmedabad (India) Insead (France/Singapore) London Business School International Institute for Management Development (IMD) (Switzerland) University of Cambridge: Judge (UK) Hong Kong UST Business School (China) HEC Paris (France) Incae Business School (Costa Rica) PRE-MBA SALARY AVERAGE SALARY 3 YEARS AFTER MBA $84,998 $78,544 $79,082 $77,127 $71,653 $73,114 $72,904 $65,000 $71,889 $67,852 $63,195 $66,459 $65,820 $65,788 $64,397 $63,509 $60,817 $61,359 $62,701 $55,886 $60,497 $52,965 $58,556 $51,676 $69,222 $71,141 $63,074 $77,005 $67,400 $55,097 $59,848 $43,307 $182,746 $175,153 $170,817 $
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167,366 $158,353 $155,732 $152,370 $151,451 $143,777 $140,454 $138,398 $136,906 $136,248 $134,208 $130,082 $127,018 $126,500 $118,422 $116,624 $114,567 $112,524 $111,226 $110,085 $100,252 $174,440 $147,974 $146,332 $145,539 $135,475 $133,334 $123,287 $89,212 Data from The Financial Times, Ltd., Global MBA Rankings 2011 (http://rankings.ft.com/businessschoolrankings/global-mba-rankings-2011). 584 PART 3 • Market Structure and Competitive Strategy Recall from §7.6 that with a learning curve, the firm’s cost of production falls over time as managers and workers become more experienced and more effective at using available plant and equipment. Of course, there are other factors that might influence your decision. Some students, for example, find the courses they take in business school (especially economics) to be very interesting. Others find the experience to be about as much fun as having a root canal. And then there is the question of whether your undergraduate grades and test scores are sufficiently high to make this particular investment in human capital an option for you. Finally, and most importantly, you might find another career choice more rewarding, whether or not it turns out to be more profitable. We leave it to you to calculate the returns to educational investments in the arts, law, or education itself (teaching). *15.8 Intertemporal Production Decisions— Depletable Resources Production decisions often have intertemporal aspects—production today affects sales or costs in the future. The learning curve, which we discussed in Chapter 7, is an example of this. By producing today, the firm gains experience that lowers future costs. In this case, production today is partly an investment in future cost reduction, and the value of this investment must be taken into account when comparing costs and benefits. Another example is the production of a depletable resource. When the owner of an oil well pumps oil today, less oil is available for future production. This must be taken into account when deciding how much to produce. Production decisions in cases like these involve comparisons between costs and benefits today with costs and benefits in the future. We can make those comparisons using the
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concept of present discounted value. We’ll look in detail at the case of a depletable resource, although the same principles apply to other intertemporal production decisions. The Production Decision of an Individual Resource Producer Suppose your rich uncle gives you an oil well. The well contains 1000 barrels of oil that can be produced at a constant average and marginal cost of $10 per barrel. Should you produce all the oil today, or should you save it for the future?19 You might think that the answer depends on the profit you can earn if you remove the oil from the ground. After all, why not remove the oil if its price is greater than the cost of extraction? However, this ignores the opportunity cost of using up the oil today so that it is not available for the future. The correct answer, then, depends not on the current profit level but on how fast you expect the price of oil to rise. Oil in the ground is like money in the bank: You should keep it in the ground only if it earns a return at least as high as the market interest rate. If you expect the price of oil to remain constant or rise very slowly, you would be better off extracting and selling all of it now and investing the proceeds. But if you expect the price of oil to rise rapidly, you should leave it in the ground. 19For most real oil wells, marginal and average cost are not constant, and it would be extremely costly to extract all the oil in a short time. We will ignore this complication. CHAPTER 15 • Investment, Time, and Capital Markets 585 How fast must the price rise for you to keep the oil in the ground? The value of each barrel of oil in your well is equal to the price of oil less the $10 cost of extracting it. (This is the profit you can obtain by extracting and selling each barrel.) This value must rise at least as fast as the rate of interest for you to keep the oil. Your production decision rule is therefore: Keep all your oil if you expect its price less its extraction cost to rise faster than the rate of interest. Extract and sell all of it if you expect price less cost to rise at less than the rate of interest. What if you expect price less cost to rise at exactly the rate of interest? Then you would be indifferent between extracting the oil and leaving it in the ground. Letting Pt be the price of oil this year, Pt+1 the price next year, and c the cost of extraction, we can write
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this production rule as follows: If (Pt+1 If (Pt+1 If (Pt+1 - c) > (1 + R)(Pt - c) < (1 + R)(Pt - c) = (1 + R)(Pt - c), keep the oil in the ground. - c), sell all the oil now. - c), makes no difference. Given our expectation about the growth rate of oil prices, we can use this rule to determine production. But how fast should we expect the market price of oil to rise? The Behavior of Market Price Suppose there were no OPEC cartel and the oil market consisted of many competitive producers with oil wells like our own. We could then determine how quickly oil prices are likely to rise by considering the production decisions of other producers. If other producers want to earn the highest possible return, they will follow the production rule we stated above. This means that price less marginal cost must rise at exactly the rate of interest.20 To see why, suppose price less cost were to rise faster than the rate of interest. In that case, no one would sell any oil. Inevitably, this would drive up the current price. If, on the other hand, price less cost were to rise at a rate less than the rate of interest, everyone would try to sell all of their oil immediately, which would drive the current price down. Figure 15.4 illustrates how the market price must rise. The marginal cost of extraction is c, and the price and total quantity produced are initially P0 and Q0. Part (a) shows the net price, P - c, rising at the rate of interest. Part (b) shows that as price rises, the quantity demanded falls. This continues until time T, when all the oil has been used up and the price PT is such that demand is just zero. User Cost We saw in Chapter 8 that a competitive firm always produces up to the point at which price is equal to marginal cost. However, in a competitive market for an exhaustible resource, price exceeds marginal cost (and the difference between price and marginal cost rises over time). Does this conflict with what we learned in Chapter 8? No, once we recognize that the total marginal cost of producing an exhaustible resource is greater than the marginal cost of extracting it from the ground. There is an additional opportunity cost because producing and selling a unit today makes it unavailable for production and sale in the future. We call this opportunity cost the user cost of
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production. In Figure 15.4, user cost is the 20This result is called the Hotelling rule because it was first demonstrated by Harold Hotelling in “The Economics of Exhaustible Resources,” Journal of Political Economy 39 (April 1931): 137–75. • user cost of production Opportunity cost of producing and selling a unit today and so making it unavailable for production and sale in the future. 586 PART 3 • Market Structure and Competitive Strategy Price PT P0 c P – c (a) Price PT P0 c Demand Marginal Extraction Cost T Time Q0 Quantity (b) FIGURE 15.4 PRICE OF AN EXHAUSTIBLE RESOURCE In (a), the price is shown rising over time. Units of a resource in the ground must earn a return commensurate with that on other assets. Therefore, in a competitive market, price less marginal production cost will rise at the rate of interest. Part (b) shows the movement up the demand curve as price rises. In §10.1, we explain that a monopolist maximizes its profit by choosing an output at which marginal revenue is equal to marginal cost. difference between price and marginal production cost. It rises over time because as the resource remaining in the ground becomes scarcer, the opportunity cost of depleting another unit becomes higher. Resource Production by a Monopolist What if the resource is produced by a monopolist rather than by a competitive industry? Should price less marginal cost still rise at the rate of interest? Suppose a monopolist is deciding between keeping an incremental unit of a resource in the ground, or producing and selling it. The value of that unit is the marginal revenue less the marginal cost. The unit should be left in the ground if its value is expected to rise faster than the rate of interest; it should be produced and sold if its value is expected to rise at less than the rate of interest. Since the monopolist controls total output, it will produce so that marginal revenue less marginal cost—i.e., the value of an incremental unit of resource—rises at exactly the rate of interest: (MRt + 1 - c) = (1 + R)(MRt - c) Note that this rule also holds for a competitive firm. For a competitive firm, however, marginal revenue equals the market price p. For a monopolist facing a downward-sloping demand curve, price is greater than marginal revenue. Therefore, if marginal revenue less marginal cost rises at the rate of interest, price less marginal
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cost will rise at less than the rate of CHAPTER 15 • Investment, Time, and Capital Markets 587 interest. We thus have the interesting result that a monopolist is more conservationist than a competitive industry. In exercising monopoly power, the monopolist starts out charging a higher price and depletes the resource more slowly. EXAM PLE 15.7 HOW DEPLETABLE ARE DEPLETABLE RESOURCES? Resources such as oil, natural gas, coal, uranium, copper, iron, lead, zinc, nickel, and helium are all depletable: Because there is a finite amount of each in the earth’s crust, the production and consumption of each will ultimately cease. Nonetheless, some resources are more depletable than others. For oil, natural gas, and helium, known and potentially discoverable in-ground reserves are equal to only 50 to 100 years of current consumption. For these resources, the user cost of production can be a significant component of the market price. Other resources, such as coal and iron, have a proven and potential reserve base equal to several hundred or even thousands of years of current consumption. For these resources, the user cost is very small. The user cost for a resource can be estimated from geological information about existing and potentially discoverable reserves, and from knowledge of the demand curve and the rate at which that curve is likely to shift out over time in response to economic growth. If the market is competitive, user cost can be determined from the economic rent earned by the owners of resource-bearing lands. Table 15.7 shows estimates of user cost as a fraction of the competitive price for crude oil, natural gas, uranium, copper, bauxite, nickel, iron ore, and gold.21 Note that only for crude oil and natural gas is user cost a substantial component of price. For the other resources, it is small and in some cases almost negligible. Moreover, although most of these resources have experienced sharp price fluctuations, user cost had almost nothing to do with those fluctuations. For example, oil prices changed because of OPEC and political turmoil in the Persian Gulf, natural gas prices because of changes in energy demand, uranium and bauxite prices because of cartelization during the 1970s, and copper prices because of strikes and changes in demand. TABLE 15.7 USER COST AS A FRACTION OF COMPETITIVE PRICE RESOURCE USER COST/COMPETITIVE PRICE Crude oil Natural gas Uranium Copper Bauxite Nickel Iron ore
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Gold.4 to.5.4 to.5.1 to.2.2 to.3.05 to.2.1 to.3.1 to.2.05 to.1 Resource depletion, then, has not been very important as a determinant of resource prices over the past few decades. Much more important have been market structure and changes in market demand. But the role of depletion should not be ignored. Over the long term, it will be the ultimate determinant of resource prices. 21These numbers are based on Michael J. Mueller, “Scarcity and Ricardian Rents for Crude Oil,” Economic Inquiry 23 (1985): 703–24; Kenneth R. Stollery, “Mineral Depletion with Cost as the Extraction Limit: A Model Applied to the Behavior of Prices in the Nickel Industry,” Journal of Environmental Economics and Management 10 (1983): 151–65; Robert S. Pindyck, “On Monopoly Power in Extractive Resource Markets,” Journal of Environmental Economics and Management 14 (1987): 128–42; Martin L. Weitzman, “Pricing the Limits to Growth from Mineral Depletion,” Quarterly Journal of Economics 114 (May 1999): 691–706; and Gregory M. Ellis and Robert Halvorsen, “Estimation of Market Power in a Nonrenewable Resource Industry,” Journal of Political Economy 110 (2002): 883–99. 588 PART 3 • Market Structure and Competitive Strategy 15.9 How Are Interest Rates Determined? We have seen how market interest rates are used to help make capital investment and intertemporal production decisions. But what determines interest rate levels? Why do they fluctuate over time? To answer these questions, remember that an interest rate is the price that borrowers pay lenders to use their funds. Like any market price, interest rates are determined by supply and demand—in this case, the supply and demand for loanable funds. The supply of loanable funds comes from households that wish to save part of their incomes in order to consume more in the future (or make bequests to their heirs). For example, some households have high incomes now but expect to earn less after retirement. Saving lets them spread their consumption more evenly over time. In addition, because they receive interest on the money they lend, they can consume more in the future in return for consuming less now. As a result, the higher
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the interest rate, the greater the incentive to save. The supply of loanable funds is therefore an upward-sloping curve, labeled S in Figure 15.5. The demand for loanable funds has two components. First, some households want to consume more than their current incomes, either because their incomes are low now but are expected to grow, or because they want to make a large purchase (e.g., a house) that must be paid for out of future income. These households are willing to pay interest in return for not having to wait to consume. However, the higher the interest rate, the greater the cost of consuming rather than waiting, so the less willing these households will be to borrow. The household demand for loanable funds is therefore a declining function of the interest rate. In Figure 15.5, it is the curve labeled DH. The second source of demand for loanable funds is firms that want to make capital investments. Remember that firms will invest in projects with NPVs that are positive because a positive NPV means that the expected return on the project exceeds the opportunity cost of funds. That opportunity cost—the discount rate used to calculate the NPV—is the interest rate, perhaps adjusted for R Interest rate R* FIGURE 15.5 SUPPLY AND DEMAND FOR LOANABLE FUNDS Market interest rates are determined by the demand and supply of loanable funds. Households supply funds in order to consume more in the future; the higher the interest rate, the more they supply. Households and firms both demand funds, but the higher the interest rate, the less they demand. Shifts in demand or supply cause changes in interest rates. S DH Q* DF DT Quantity of loanable funds CHAPTER 15 • Investment, Time, and Capital Markets 589 risk. Often firms borrow to invest because the flow of profits from an investment comes in the future while the cost of an investment must usually be paid now. The desire of firms to invest is thus an important source of demand for loanable funds. As we saw earlier, however, the higher the interest rate, the lower the NPV of a project. If interest rates rise, some investment projects that had positive NPVs will now have negative NPVs and will therefore be cancelled. Overall, because firms’ willingness to invest falls when interest rates rise, their demand for loanable funds also falls. The demand for loanable funds by firms is thus a downward-sloping curve; in Figure 15.5, it is labeled DF
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. The total demand for loanable funds is the sum of household demand and firm demand; in Figure 15.5, it is the curve DT. This total demand curve, together with the supply curve, determines the equilibrium interest rate. In Figure 15.5, that rate is R*. Figure 15.5 can also help us understand why interest rates change. Suppose the economy goes into a recession. Firms will expect lower sales and lower future profits from new capital investments. The NPVs of projects will fall, and firms’ willingness to invest will decline, as will their demand for loanable funds. DF, and therefore DT, will shift to the left, and the equilibrium interest rate will fall. Or suppose the federal government spends much more money than it collects through taxes—i.e., that it runs a large deficit. It will have to borrow to finance the deficit, shifting the total demand for loanable funds DT to the right, so that R increases. The monetary policies of the Federal Reserve are another important determinant of interest rates. The Federal Reserve can create money, shifting the supply of loanable funds to the right and reducing R. A Variety of Interest Rates Figure 15.5 aggregates individual demands and supplies as though there were a single market interest rate. In fact, households, firms, and the government lend and borrow under a variety of terms and conditions. As a result, there is a wide range of “market” interest rates. Here we briefly describe some of the more important rates that are quoted in the newspapers and sometimes used for capital investment decisions. • Treasury Bill Rate A Treasury bill is a short-term (one year or less) bond issued by the U.S. government. It is a pure discount bond—i.e., it makes no coupon payments but instead is sold at a price less than its redemption value at maturity. For example, a three-month Treasury bill might be sold for $98. In three months, it can be redeemed for $100; it thus has an effective three-month yield of about 2 percent and an effective annual yield of about 8 percent.22 The Treasury bill rate can be viewed as a short-term, risk-free rate. • Treasury Bond Rate A Treasury bond is a longer-term bond issued by the U.S. government for more than one year and typically for 10 to 30 years. Rates vary, depending on the maturity of the bond. • Discount Rate Commercial banks sometimes borrow for short periods from the Federal Reserve. These
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loans are called discounts, and the rate that the Federal Reserve charges on them is the discount rate. 22To be exact, the three-month yield is (100/98) - 1 = 0.0204, and the annual yield is (100/98)4 - 1 = 0.0842, or 8.42 percent. 590 PART 3 • Market Structure and Competitive Strategy • Federal Funds Rate This is the interest rate that banks charge one another for overnight loans of federal funds. Federal funds consist of currency in circulation plus deposits held at Federal Reserve banks. Banks keep funds at Federal Reserve banks in order to meet reserve requirements. Banks with excess reserves may lend these funds to banks with reserve deficiencies at the federal funds rate. The federal funds rate is a key instrument of monetary policy used by the Federal Reserve. • Commercial Paper Rate Commercial paper refers to short-term (six months or less) discount bonds issued by high-quality corporate borrowers. Because commercial paper is only slightly riskier than Treasury bills, the commercial paper rate is usually less than 1 percent higher than the Treasury bill rate. • Prime Rate This is the rate (sometimes called the reference rate) that large banks post as a reference point for short-term loans to their biggest corporate borrowers. As we saw in Example 12.4 (page 475), this rate does not fluctuate from day to day as other rates do. • Corporate Bond Rate Newspapers and government publications report the average annual yields on long-term (typically 20-year) corporate bonds in different risk categories (e.g., high-grade, medium-grade, etc.). These average yields indicate how much corporations are paying for long-term debt. However, as we saw in Example 15.2, the yields on corporate bonds can vary considerably, depending on the financial strength of the corporation and the time to maturity for the bond. SUMMARY 1. A firm’s holding of capital is measured as a stock, but inputs of labor and raw materials are flows. Its stock of capital enables a firm to earn a flow of profits over time. 2. When a firm makes a capital investment, it spends money now in order to earn profits in the future. To decide whether the investment is worthwhile, the firm must determine the present value of future profits by discounting them. 3. The present discounted value (PDV) of $1 paid one year from now is $1/(1 + R), where R is the interest rate. The PDV of $1 paid n years
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from now is $1/(1 + R)n. 4. A bond is a contract in which a lender agrees to pay the bondholder a stream of money. The value of the bond is the PDV of that stream. The effective yield on a bond is the interest rate that equates that value with the bond’s market price. Bond yields differ because of differences in riskiness and time to maturity. 5. Firms can decide whether to undertake a capital investment by applying the net present value (NPV) criterion: Invest if the present value of the expected future cash flows is larger than the cost of the investment. 6. The discount rate that a firm uses to calculate the NPV for an investment should be the opportunity cost of capital—i.e., the return the firm could earn on a similar investment. 7. When calculating NPVs, if cash flows are in nominal terms (i.e., include inflation), the discount rate should also be nominal; if cash flows are in real terms (i.e., are net of inflation), a real discount rate should be used. 8. An adjustment for risk can be made by adding a risk premium to the discount rate. However, the risk premium should reflect only nondiversifiable risk. Using the Capital Asset Pricing Model (CAPM), the risk premium is the “asset beta” for the project multiplied by the risk premium on the stock market as a whole. The “asset beta” measures the sensitivity of the project’s return to movements in the market. 9. Consumers are faced with investment decisions that require the same kind of analysis as those of firms. When deciding whether to buy a durable good like a car or a major appliance, the consumer must consider the present value of future operating costs. 10. Investments in human capital—the knowledge, skills, and experience that make an individual more productive and thereby able to earn a higher income in the future—can be evaluated in much the same way as other investments. Investing in further education, for example, makes economic sense if the present value of the expected future increases in income exceeds the present value of the costs. CHAPTER 15 • Investment, Time, and Capital Markets 591 11. An exhaustible resource in the ground is like money in the bank and must earn a comparable return. Therefore, if the market is competitive, price less marginal extraction cost will grow at the rate of interest. The difference between price and marginal cost is called user cost—the opportunity
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cost of depleting a unit of the resource. 12. Market interest rates are determined by the demand and supply of loanable funds. Households supply funds so that they can consume more in the future. Households, firms, and the government demand funds. Changes in demand or supply cause changes in interest rates. QUESTIONS FOR REVIEW 1. A firm uses cloth and labor to produce shirts in a factory that it bought for $10 million. Which of its factor inputs are measured as flows and which as stocks? How would your answer change if the firm had leased a factory instead of buying one? Is its output measured as a flow or a stock? What about its profit? 2. How do investors calculate the net present value of a bond? If the interest rate is 5 percent, what is the present value of a perpetuity that pays $1000 per year forever? 3. What is the effective yield on a bond? How does one calculate it? Why do some corporate bonds have higher effective yields than others? 4. What is the net present value (NPV) criterion for investment decisions? How does one calculate the NPV of an investment project? If all the cash flows for a project are certain, what discount rate should be used to calculate NPV? 5. You are retiring from your job and are given two options: You can accept a lump sum payment from the company, or you can accept a smaller annual payment that will continue for as long as you live. How would you decide which option is best? What information do you need? 6. You have noticed that bond prices have been rising over the past few months. All else equal, what does this suggest has been happening to interest rates? Explain. 7. What is the difference between a real discount rate and a nominal discount rate? When should a real discount rate be used in an NPV calculation and when should a nominal rate be used? 8. How is risk premium used to account for risk in NPV calculations? What is the difference between diversifiable and nondiversifiable risk? Why should only nondiversifiable risk enter into the risk premium? 9. What is meant by the “market return” in the Capital Asset Pricing Model (CAPM)? Why is the market return greater than the risk-free interest rate? What does an asset’s “beta” measure in the CAPM? Why should high-beta assets have a higher expected return than low-beta assets? 10. Suppose you are deciding whether to invest
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$100 million in a steel mill. You know the expected cash flows for the project, but they are risky—steel prices could rise or fall in the future. How would the CAPM help you select a discount rate for an NPV calculation? 11. How does a consumer trade off current and future costs when selecting an air conditioner or other major appliance? How could this selection be aided by an NPV calculation? 12. What is meant by the “user cost” of producing an exhaustible resource? Why does price minus extraction cost rise at the rate of interest in a competitive market for an exhaustible resource? 13. What determines the supply of loanable funds? The demand for loanable funds? What might cause the supply or demand for loanable funds to shift? How would such a shift affect interest rates? EXERCISES 1. Suppose the interest rate is 10 percent. If $100 is invested at this rate today, how much will it be worth after one year? After two years? After five years? What is the value today of $100 paid one year from now? Paid two years from now? Paid five years from now? 2. You are offered the choice of two payment streams: (a) $150 paid one year from now and $150 paid two years from now; (b) $130 paid one year from now and $160 paid two years from now. Which payment stream would you prefer if the interest rate is 5 percent? If it is 15 percent? 3. Suppose the interest rate is 10 percent. What is the value of a coupon bond that pays $80 per year for each of the next five years and then makes a principal repayment of $1000 in the sixth year? Repeat for an interest rate of 15 percent. 4. A bond has two years to mature. It makes a coupon payment of $100 after one year and both a coupon payment of $100 and a principal repayment of $1000 after two years. The bond is selling for $966. What is its effective yield? 592 PART 3 • Market Structure and Competitive Strategy 5. Equation (15.5) (page 572) shows the net present value of an investment in an electric motor factory. Half of the $10 million cost is paid initially and the other half after a year. The factory is expected to lose money during its first two years of operation. If the discount rate is 4 percent, what is the NPV? Is the investment worthwhile? 6. The market interest rate
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is 5 percent and is expected to stay at that level. Consumers can borrow and lend all they want at this rate. Explain your choice in each of the following situations: a. Would you prefer a $500 gift today or a $540 gift next year? b. Would you prefer a $100 gift now or a $500 loan without interest for four years? c. Would you prefer a $350 rebate on an $8000 car or one year of financing for the full price of the car at 0 percent interest? d. You have just won a million-dollar lottery and will receive $50,000 a year for the next 20 years. How much is this worth to you today? e. You win the “honest million” jackpot. You can have $1 million today or $60,000 per year for eternity (a right that can be passed on to your heirs). Which do you prefer? f. In the past, adult children had to pay taxes on gifts of over $10,000 from their parents, but parents could make interest-free loans to their children. Why did some people call this policy unfair? To whom were the rules unfair? 7. Ralph is trying to decide whether to go to graduate school. If he spends two years in graduate school, paying $15,000 tuition each year, he will get a job that will pay $60,000 per year for the rest of his working life. If he does not go to school, he will go into the workforce immediately. He will then make $30,000 per year for the next three years, $45,000 for the following three years, and $60,000 per year every year after that. If the interest rate is 10 percent, is graduate school a good financial investment? 8. Suppose your uncle gave you an oil well like the one described in Section 15.8. (Marginal production cost is constant at $50.) The price of oil is currently $80 but is controlled by a cartel that accounts for a large fraction of total production. Should you produce and sell all your oil now or wait to produce? Explain your answer. 9. You are planning to invest in fine wine. Each case costs $100, and you know from experience that the value of a case of wine held for t years is 100t1/2. One hundred cases of wine are available for sale, and the interest rate is 10 percent. a. How many cases should you buy, how long should you wait to sell them
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, and how much money will you receive at the time of their sale? b. Suppose that at the time of purchase, someone offers you $130 per case immediately. Should you take the offer? c. How would your answers change if the interest rate were only 5 percent? 10. Reexamine the capital investment decision in the disposable diaper industry (Example 15.4) from the point of view of an incumbent firm. If P&G or Kimberly-Clark were to expand capacity by building three new plants, they would not need to spend $60 million on R&D before start-up. How does this advantage affect the NPV calculations in Table 15.5 (page 577)? Is the investment profitable at a discount rate of 12 percent? 11. Suppose you can buy a new Toyota Corolla for $20,000 and sell it for $12,000 after six years. Alternatively, you can lease the car for $300 per month for three years and return it at the end of the three years. For simplification, assume that lease payments are made yearly instead of monthly—i.e., that they are $3600 per year for each of three years. a. If the interest rate, r, is 4 percent, is it better to lease or buy the car? b. Which is better if the interest rate is 12 percent? c. At what interest rate would you be indifferent between buying and leasing the car? 12. A consumer faces the following decision: She can buy a computer for $1000 and $10 per month for Internet access for three years, or she can receive a $400 rebate on the computer (so that its cost is $600) but agree to pay $25 per month for three years for Internet access. For simplification, assume that the consumer pays the access fees yearly (i.e., $10 per month = $120 per year). a. What should the consumer do if the interest rate is 3 percent? b. What if the interest rate is 17 percent? c. At what interest rate will the consumer be indiffer- ent between the two options? Part Four Information, Market Failure, and the Role of Government Part Four shows how markets can sometimes fail and explains how government intervention can be used to achieve economic efficiency. Much of the analysis in the first three parts of this book has focused on positive questions—how consumers and firms behave and how that behavior affects different market structures. Part IV takes a more normative approach. Here we will describe the goal of
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economic efficiency, show when markets generate efficient outcomes, and explain when they fail and thus require government intervention. Chapter 16 discusses general equilibrium analysis, in which the interactions among related markets are taken into account. This chapter also analyzes the conditions that are required for an economy to be efficient and shows when and why a perfectly competitive market is efficient. Chapter 17 examines an important source of market failure—incomplete information. We show that when some economic participants have better information than others, markets may fail to allocate goods efficiently or may not even exist. We also show how sellers can avoid problems of asymmetric information by giving potential buyers signals about product quality. Finally, Chapter 18 discusses two additional sources of market failure: externalities and public goods. We show that although these failures can sometimes be resolved through private bargaining, at other times they require government intervention. We also discuss a number of remedies for market failures, such as pollution taxes and tradeable emission permits. C H A P T E R S 16 General Equilibrium and Economic Efficiency 595 17 Markets with Asymmetric Information 631 18 Externalities and Public Goods 661 593 This page intentionally left blank C H A P T E R 16 General Equilibrium and Economic Efficiency For the most part, we have studied individual markets in isolation. But markets are often interdependent: Conditions in one can affect prices and outputs in others either because one good is an input to the production of another good or because two goods are substitutes or complements. In this chapter, we see how a general equilibrium analysis can be used to take these interrelationships into account. We also expand the concept of economic efficiency that we introduced in Chapter 9, and we discuss the benefits of a competitive market economy. To do this, we first analyze economic efficiency, beginning with the exchange of goods among people or countries. We then use this analysis of exchange to discuss whether the outcomes generated by an economy are equitable. To the extent that these outcomes are deemed inequitable, government can help redistribute income. We then go on to describe the conditions that an economy must satisfy if it is to produce and distribute goods efficiently. We explain why a perfectly competitive market system satisfies those conditions. We also show why free international trade can expand the production possibilities of a country and make its consumers better off. Most markets, however, are not perfectly competitive, and many deviate substantially from that ideal. In the final section of the chapter (as a preview to our detailed discussion of market failure in Chapters 17 and 18), we discuss some key reasons
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why markets may fail to work efficiently. 16.1 General Equilibrium Analysis So far, our discussions of market behavior have been largely based on partial equilibrium analysis. When determining the equilibrium prices and quantities in a market using partial equilibrium analysis, we presume that activity in one market has little or no effect on other markets. For example, in Chapters 2 and 9, we presumed that the wheat market was largely independent of the markets for related products, such as corn and soybeans 16.1 General Equilibrium Analysis 595 16.2 Efficiency in Exchange 602 16.3 Equity and Efficiency 610 16.4 Efficiency in Production 613 16.5 The Gains from Free Trade 618 16.6 An Overview—The Efficiency of Competitive Markets 623 16.7 Why Markets Fail 625 16.1 The Global Market for Ethanol 598 16.2 “Contagion” across Stock Markets around the World 600 16.3 Trading Tasks and iPod Production 621 16.4 The Costs and Benefits of Special Protection 622 16.5 Inefficiency in the Health Care System 626 595 596 PART 4 • Information, Market Failure, and the Role of Government • partial equilibrium analysis Determination of equilibrium prices and quantities in a market independent of effects from other markets. • general equilibrium analysis Simultaneous determination of the prices and quantities in all relevant markets, taking feedback effects into account. In §2.1, we explain that two goods are substitutes if an increase in the price of one leads to an increase in the quantity demanded of the other. Often a partial equilibrium analysis is sufficient to understand market behavior. However, market interrelationships can be important. In Chapter 2, for example, we saw how a change in the price of one good can affect the demand for another if they are complements or substitutes. In Chapter 8, we saw that an increase in a firm’s input demand can cause both the market price of the input and the product price to rise. Unlike partial equilibrium analysis, general equilibrium analysis determines the prices and quantities in all markets simultaneously, and it explicitly takes feedback effects into account. A feedback effect is a price or quantity adjustment in one market caused by price and quantity adjustments in related markets. Suppose, for example, that the U.S. government taxes oil imports. This policy would immediately shift the supply curve for oil to the left (by making foreign oil more expensive) and raise the price of oil. But the effect of the tax would not end there. The higher price of oil
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would increase the demand for and then the price of natural gas. The higher natural gas price would in turn cause oil demand to rise (shift to the right) and increase the oil price even more. The oil and natural gas markets will continue to interact until eventually an equilibrium is reached in which the quantity demanded and quantity supplied are equated in both markets. In practice, a complete general equilibrium analysis, which evaluates the effects of a change in one market on all other markets, is not feasible. Instead, we confine ourselves to two or three markets that are closely related. For example, when looking at a tax on oil, we might also look at markets for natural gas, coal, and electricity. Two Interdependent Markets—Moving to General Equilibrium To study the interdependence of markets, let’s examine the competitive markets for DVD rentals and movie theater tickets. The two markets are closely related because DVD players give most consumers the option of watching movies at home as well as at the theater. Changes in pricing policies that affect one market are likely to affect the other, which in turn causes feedback effects in the first market. Figure 16.1 shows the supply and demand curves for DVDs and movies. In part (a), the price of movie tickets is initially $6.00; the market is in equilibrium at the intersection of DM and SM. In part (b), the DVD market is also in equilibrium with a price of $3.00. Now suppose that the government places a tax of $1 on each movie ticket purchased. The effect of this tax is determined on a partial equilibrium basis by shift* in Figure 16.1 (a). ing the supply curve for movies upward by $1, from SM to SM Initially, this shift causes the prices of movies to increase to $6.35 and the quantity = of movie tickets sold to fall from QM to Q M. This is as far as a partial equilibrium analysis takes us. But we can go further with a general equilibrium analysis by doing two things: (1) looking at the effects of the movie tax on the market for DVDs, and (2) seeing whether there are any feedback effects from the DVD market to the movie market. The movie tax affects the market for DVDs because movies and DVDs are = substitutes. A higher movie price shifts the demand for DVDs from DV to D V in Figure 16.1 (b). In turn, this shift causes the rental price of DVDs to increase from $3.00 to $3.50. Note that
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a tax on one product can affect the prices and sales of other products—something that policymakers should remember when designing tax policies. CHAPTER 16 • General Equilibrium and Economic Efficiency 597 Price ($) 6.82 6.75 6.35 6.00 S*M Price ($) 3.58 3.50 3.00 SM D*M DM DM QM Q M Q*M QM (a) Number of movie tickets QV QV Q*V (b) SV D*V DV DV Number of DVDs FIGURE 16.1 TWO INTERDEPENDENT MARKETS: (A) MOVIE TICKETS AND (B) DVD RENTALS When markets are interdependent, the prices of all products must be simultaneously determined. *, as shown in (a). The Here a tax on movie tickets shifts the supply of movies upward from SM to SM higher price of movie tickets ($6.35 rather than $6.00) initially shifts the demand for DVDs upward = ), causing the price of DVDs to rise (from $3.00 to $3.50), as shown in (b). The higher (from DV to DV = and the video price feeds back into the movie ticket market, causing demand to shift from DM to D M price of movies to increase from $6.35 to $6.75. This continues until a general equilibrium is reached, * in (a), with a movie ticket of $6.82, and the intersection of as shown at the intersection of D M D V * and SM * and SV in (b), with a DVD price of $3.58. What about the market for movies? The original demand curve for movies presumed that the price of DVDs was unchanged at $3.00. But because that = price is now $3.50, the demand for movies will shift upward, from DM to D M in * Figure 16.1 (a). The new equilibrium price of movies (at the intersection of SM = and D M ) is $6.75, instead of $6.35, and the quantity of movie tickets purchased = has increased from Q M. Thus a partial equilibrium analysis would have underestimated the effect of the tax on the price of movies. The DVD market is so closely related to the market for movies that to determine the tax’s full effect, we need a general equilibrium analysis. == to Q M Reaching General Equilibrium Our analysis is not yet complete. The change in the market price of movies will generate a feedback
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effect on the price of DVDs that, in turn, will affect the price of movies, and so on. In the end, we must determine the equilibrium prices and quantities of both movies and DVDs simultaneously. The equilibrium movie price of $6.82 is given in Figure 16.1 (a) by the intersection of the equilibrium supply * ). The equilibrium DVD price and demand curves for movie tickets (SM of $3.58 is given in Figure 16.1 (b) by the intersection of the equilibrium sup* ). These are the correct general ply and demand curves for DVDs (SV and D V equilibrium prices because the DVD market supply and demand curves have * and D M 598 PART 4 • Information, Market Failure, and the Role of Government been drawn on the assumption that the price of movie tickets is $6.82. Likewise, the movie ticket curves have been drawn on the assumption that the price of DVDs is $3.58. In other words, both sets of curves are consistent with the prices in related markets, and we have no reason to expect that the supply and demand curves in either market will shift further. To find the general equilibrium prices (and quantities) in practice, we must simultaneously find two prices that equate quantity demanded and quantity supplied in all related markets. For our two markets, we need to find the solution to four equations (supply of movie tickets, demand for movie tickets, supply of DVDs, and demand for DVDs). Note that even if we were only interested in the market for movies, it would be important to account for the DVD market when determining the impact of a movie tax. In this example, partial equilibrium analysis would lead us to conclude that the tax will increase the price of movie tickets from $6.00 to $6.35. A general equilibrium analysis, however, shows us that the impact of the tax on the price of movie tickets is greater: It would in fact increase to $6.82. Movies and DVDs are substitute goods. By drawing diagrams analogous to those in Figure 16.1, you should be able to convince yourself that if the goods in question are complements, a partial equilibrium analysis will overstate the impact of a tax. Think about gasoline and automobiles, for example. A tax on gasoline will cause its price to go up, but this increase will reduce demand for automobiles, which in turn reduces the demand for gasoline, causing its price to fall somewhat. Recall from §2.1 that two goods are complements if an increase in the price of one
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leads to a decrease in the quantity demanded of the other. E XAM PLE 16.1 THE GLOBAL MARKET FOR ETHANOL High crude oil prices, harmful emissions, and growing dependency on volatile foreign oil supplies have led to a growing interest in alternative fuel sources such as ethanol. Ethanol is a clean-burning, high-octane fuel produced from renewable resources such as sugar cane and corn. It is highly touted as a means of reducing automobile emissions and of responding to concerns about global warming. There is a high degree of interdependence between the production and sale of Brazilian ethanol (from sugar cane) and ethanol produced in the United States (from corn). We will see that U.S. regulation of its ethanol market has had significant effects on the Brazilian market, which in turn has had a feedback effect on the market in the United States. Although this interdependence has in all likelihood benefited U.S. producers, it has also had adverse consequences for U.S. consumers, Brazilian producers, and, probably, Brazilian consumers. The world ethanol market is dominated by Brazil and the United States, which accounted for over 90 percent of world production in 2005.1 Ethanol is not new; the Brazilian government started promoting ethanol in the mid-1970s as a response to rising oil prices and declining sugar prices, and the program has flourished. In 2007, about 40 percent of all Brazilian automobile fuel was ethanol, a response to the skyrocketing growth in the demand for flex-fuel cars, which can run on any mixture of ethanol and gasoline. U.S. ethanol production was first encouraged by the Energy Tax Act of 1978, which provided for tax exemptions for ethanol-gasoline blends. More recently, the Energy Policy Act of 2005 required that U.S. fuel production 1This example is based on Amani Elobeid and Simla Tokgoz, “Removal of U.S. Ethanol Domestic and Trade Distortions: Impact on U.S. and Brazilian Ethanol Markets,” Working paper, 2006. CHAPTER 16 • General Equilibrium and Economic Efficiency 599 include a minimum amount of renewable fuel each year—a stipulation which essentially mandated a baseline level of ethanol production. The U.S. and Brazilian ethanol markets are closely tied to each other. As a consequence, the U.S. regulation of its own ethanol market can significantly affect Brazil’s market. This global interdependence was made evident by the Energy Security Act of 1979, by
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which the U.S. offered a tax credit of $0.51 per gallon of ethanol to spur alternatives to gasoline. Moreover, to prevent foreign ethanol producers from reaping the benefits of this tax credit, the U.S. government imposed a $0.54 per gallon tax on imported ethanol. The policy has been highly effective: The U.S. has devoted more and more of its corn harvest to ethanol production, while Brazilian imports (which are made from sugar cane) have declined. While this policy has benefited corn producers, it is not in the interests of U.S. ethanol consumers. It is estimated that whereas Brazil can export ethanol for less than $0.90 per gallon, it costs $1.10 to produce a gallon of ethanol from Iowa corn. Thus American consumers would benefit if the tax and subsidy were removed—a move that would increase the imports of the cheaper sugar cane-based ethanol from Brazil. Figure 16.2 shows the predicted changes in the ethanol market if U.S. tariffs were completely removed in 2006. The top green line in Figure 16.2 (a) estimates Brazil’s ethanol exports without U.S. tariffs in place, and the blue line represents Brazil’s 2500 2000 1500 1000 500 a) Brazil Exports without Tariff Brazil Exports with Tariff 0 05 06 07 08 09 11 12 13 14 15 10 Year (b) U.S. Ethanol Price with Tariff.1 2.0 1.9 1.8 1.7 1.6 1.5 U.S. Ethanol Price without Tariff 05 06 07 08 09 11 12 13 14 15 10 Year FIGURE 16.2 REMOVING THE ETHANOL TARIFF ON BRAZILIAN EXPORTS If U.S. tariffs on ethanol produced abroad were to be removed, Brazil would export much more ethanol to the United States, displacing much of the more expensive corn-based ethanol produced domestically. As a result, the price of ethanol in the U.S. would fall, benefiting U.S. consumers. 600 PART 4 • Information, Market Failure, and the Role of Government exports with U.S. tariffs in place. Figure 16.2 (b) shows the price of ethanol in the United States with and without the tariff. As you can see, Brazilian ethanol exports would increase dramatically if the tariffs were removed and U.S. consumers will benefit. This would also be advantageous to Brazilian producers and consumers. The adverse incentive created by U.
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S. tariffs does not tell the entire story about ethanol and interdependent markets. In 1984, Congress passed the Caribbean Basin Initiative (CBI)—tax legislation designed to foster economic development in Caribbean countries. Under the CBI, ethanol processed in those countries, up to 60 million gallons a year, receives duty-free status. In response, Brazil has invested in several ethanol dehydration plants in the Caribbean in order to export their sugar-based ethanol to the United States without paying the 54-cent per gallon tariff. The U.S. government has continued to impose tariffs on foreign ethanol, despite the resulting economic inefficiencies. In addition, Congress increased the subsidies to U.S. corn producers by raising the tax credit on ethanol. In 2011, these subsidies cost U.S. taxpayers around $20 billion. Why such generosity to U.S. corn producers? Because those corn producers, mostly in Iowa, have used campaign contributions and intensive lobbying to protect their self-interest. These policies have helped to make the United States the world’s largest ethanol supplier, despite the cost to U.S. taxpayers and consumers and the fact that Brazil produces ethanol at less than half the cost of U.S. production. E XAM PLE 16.2 “CONTAGION” ACROSS STOCK MARKETS AROUND THE WORLD Stock markets around the world tend to move together, a phenomenon sometimes referred to as “contagion.” For example, the 2008 financial crisis led to sharp stock market declines in the United States, which in turn were mirrored by stock market declines in Europe, Latin America, and Asia. This tendency of stock markets around the world to move together is illustrated by Figure 16.3, which shows the three major stock market indices in the United States (the S&P 500), the United Kingdom (the FTSE), and Germany (the DAX). The S&P includes 500 U.S. companies with the highest market value listed on the New York Stock Exchange and the NASDAQ. The FTSE (fondly described as the “footsie”) has 100 of the largest U.K. companies on the London Stock Exchange, and the DAX has the 30 largest German companies on the Frankfurt Stock Exchange. (Each stock market index was set to 100 in 1984.) You can see that the overall pattern of stock price movements was the same in all three countries. Why do stock markets tend to move together? There are two fundamental reasons, both of
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which are manifestations of general equilibrium. First, stock (and bond) markets around the world have become highly integrated. Someone in the United States, for example, can easily buy or sell stocks that are traded in London, Frankfurt, or elsewhere in the world. Likewise, people in Europe and Asia can buy and sell stocks most anywhere in the world. As a result, if U.S. stock prices fall sharply and become relatively cheap compared to European and Asian stocks, European and Asian investors will sell some of their stocks and buy U.S. stocks, pushing down European and Asian stock prices. Thus any external shocks that affect stock prices in one country will have the same directional effect on prices in other countries. The second reason is that economic conditions around the world tend to be correlated, and economic conditions are an important determinant of stock prices. (During a recession, corporate profits fall, which causes stock prices to fall.) Suppose that the United States goes into a deep recession (as it did in 2008). Then Americans will consume less and U.S. imports will fall. But U.S. imports are the exports of other countries, so those exports will fall, reducing economic output and employment in those countries. Thus a recession in the United States can lead to a recession in Europe, and vice versa. This is another effect of general equilibrium that leads to “contagion” across stock markets. CHAPTER 16 • General Equilibrium and Economic Efficiency 601 DAX S&P FTSE x e d n I 1400 1200 1000 800 600 400 200 0 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 FIGURE 16.3 STOCK PRICES IN THE UNITED STATES AND EUROPE Three stock market indices—the S&P 500 in the United States, the FTSE in the United Kingdom, and the DAX in Germany—are plotted together, scaled so that each starts at 100 in 1984. The indices tend to move together, increasing and decreasing at about the same time. Data from www.worldbank.org Economic Efficiency In Chapter 9 we saw that a competitive market is economically efficient because it maximizes aggregate consumer and producer surplus. This is what we normally mean when we use the term economic efficiency. But, how does this important concept of economic efficiency apply when we take into account the interrelationship of markets, whether open to free trade or restricted, whether market-oriented or planned, and whether highly regulated or not? Fortunately, there is a concept of economic efficiency that applies when
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there is no market at all, but instead people simply trade with each other. The rest of this chapter and, to some extent the remaining chapters in the book, address these questions about economic efficiency and evaluate their implications. The analysis that follows is somewhat more complex than what has gone before; we are now focusing on the interplay of multiple markets with multiple entities competing against each other or trading with each other. Moreover, there are important equity implications that flow from the workings of competitive markets in general equilibrium, and we need to consider those equity issues. To avoid losing many of our readers along the way, our strategy is to build the theoretical analysis slowly and step by step. 602 PART 4 • Information, Market Failure, and the Role of Government In § 6.1, we explained that production functions describe technical efficiency as being achieved when a firm uses each combination of inputs as effectively as possible. • exchange economy Market in which two or more consumers trade two goods among themselves. • Pareto efficient allocation Allocation of goods in which no one can be made better off unless someone else is made worse off. We will focus on two, rather than many countries (each represented by a different individual consumer or producer), and two, rather than many, goods and services. Furthermore, we’ll start in Section 16.2 with a model of exchange in which there is no production. (We’ll introduce production later.) We will also initially assume that the two individuals (representing two countries) have some endowment of goods (say, food and clothing), which they trade with each other. These trades are the result of bargaining, rather than competitive market outcomes, and they occur because trading makes both individuals better off. We will define a new efficiency concept that is particularly useful in analyzing this kind of exchange. Later (in Section 16.4) we’ll introduce production, and in so doing revisit another efficiency concept—technical efficiency. You may recall that we first discussed technical efficiency in Chapter 6 when we introduced the concept of a production function. Finally, we will move on to the analysis of the workings of competitive markets (Section 16.6). Along the way, we will pause to treat important issues relating to equity (Section 16.3) and international trade (Section 16.5). At times the models we present may seem too simplistic to inform our real-world experiences, but rest assured they can be generalized, and their implications are both broad and profound. 16.2 Efficiency in Exchange We begin with an
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exchange economy, analyzing the behavior of two consumers who can trade either of two goods between themselves. (The analysis also applies to trade between two countries.) Suppose the two goods are initially allocated so that both consumers can make themselves better off by trading with each other. In this case, the initial allocation of goods is economically inefficient. In a Pareto efficient allocation of goods, no one can be made better off without making someone else worse off. The term Pareto efficiency is named after the Italian economist Vilfredo Pareto, who developed the concept of efficiency in exchange. Notice, however, that Pareto efficiency is not the same as economic efficiency as we defined it in Chapter 9. With Pareto efficiency, we know that there is no way to improve the well-being of both individuals (if we improve one, it will be at the expense of the other), but we cannot be assured that this arrangement will maximize the joint welfare of both individuals. Note that there is an equity implication of Pareto efficiency. It may be possible to reallocate the goods in a way that increases the total well-being of the two individuals, but leaves one individual worse off. If we can reallocate goods so that one individual is just slightly worse off but the other individual is much, much better off, wouldn’t that be a good thing to do, even though it is not Pareto efficient? There is no simple answer to that question. Some readers might say yes, it would be a good thing to do, and other readers might say no, it wouldn’t be fair. Your own answer to this question will depend on what you think is or is not equitable. In §3.1, we explain that the marginal rate of substitution is the maximum amount of one good that the consumer is willing to give up to obtain one unit of another good. The Advantages of Trade As a rule, voluntary trade between two people or two countries is mutually beneficial.2 To see how trade makes people better off, let’s look in detail at a two-person exchange, assuming that exchange itself is costless. 2There are several situations in which trade may not be advantageous. First, limited information may lead people to believe that trade will make them better off when in fact it will not. Second, people may be coerced into making trades, either by physical threats or by the threat of future economic reprisals. Third, as we saw in Chapter 13, barriers to free
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trade can sometimes provide a strategic advantage to a country. CHAPTER 16 • General Equilibrium and Economic Efficiency 603 TABLE 16.1 THE ADVANTAGE OF TRADE INDIVIDUAL INITIAL ALLOCATION TRADE FINAL ALLOCATION James Karen 7F, 1C 3F, 5C - 1F, + 1C + 1F, - 1C 6F, 2C 4F, 4C Suppose James and Karen have 10 units of food and 6 units of clothing between them. Table 16.1 shows that initially James has 7 units of food and 1 unit of clothing, and Karen 3 units of food and 5 units of clothing. To decide whether a trade would be advantageous, we need to know their preferences for food and clothing. Suppose that because Karen has a lot of clothing and little food, her marginal rate of substitution (MRS) of food for clothing is 3: To get 1 unit of food, she will give up 3 units of clothing. However, James’s MRS of food for clothing is only 1/2: He will give up only 1/2 a unit of clothing to get 1 unit of food. There is thus room for mutually advantageous trade because James values clothing more highly than Karen does, whereas Karen values food more highly than James does. To get another unit of food, Karen would be willing to trade up to 3 units of clothing. But James will give up 1 unit of food for 1/2 unit of clothing. The actual terms of the trade depend on the bargaining process. Among the possible outcomes are a trade of 1 unit of food by James for anywhere between 1/2 and 3 units of clothing from Karen. Suppose Karen offers James 1 unit of clothing for 1 unit of food, and James agrees. Both will be better off. James will have more clothing, which he values more than food, and Karen will have more food, which she values more than clothing. Whenever two consumers’ MRSs are different, there is room for mutually beneficial trade because the allocation of resources is inefficient: Trading will make both consumers better off. Conversely, to achieve economic efficiency, the two consumers’ MRSs must be equal. This important result also holds when there are many goods and consumers: An allocation of goods is efficient only if the goods are distributed so that the marginal rate of substitution between any pair of goods is the same for all consumers. The Edgeworth Box Diagram If trade is beneficial, which trades can occur? Which of those trades will
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allocate goods efficiently among customers? How much better off will consumers then be? We can answer these questions for any two-person, two-good example by using a diagram called an Edgeworth box. Figure 16.4 shows an Edgeworth box in which the horizontal axis describes the number of units of food and the vertical axis the units of clothing. The length of the box is 10 units of food, the total quantity of food available; its height is 6 units of clothing, the total quantity of clothing available. In the Edgeworth box, each point describes the market baskets of both consumers. James’s holdings are read from the origin at OJ and Karen’s holdings in the reverse direction from the origin at OK. For example, point A represents the initial allocation of food and clothing. Reading on the horizontal axis from left to right at the bottom of the box, we see that James has 7 units of food; reading upward along the vertical axis on the left of the diagram, we see that he has 1 unit of clothing. For James, therefore, A represents 7F and 1C. This leaves 3F and • Edgeworth box Diagram showing all possible allocations of either two goods between two people or of two inputs between two production processes. 604 PART 4 • Information, Market Failure, and the Role of Government 10F 6C James’s Clothing 2C 1C OJ Karen’s Food 3F 4F OK B +1C –1F A Karen’s Clothing 4C 5C 6C James’s Food 6F 7F 10F FIGURE 16.4 EXCHANGE IN AN EDGEWORTH BOX Each point in the Edgeworth box simultaneously represents James’s and Karen’s market baskets of food and clothing. At A, for example, James has 7 units of food and 1 unit of clothing, and Karen 3 units of food and 5 units of clothing. 5C for Karen. Karen’s allocation of food (3F) is read from right to left at the top of the box diagram beginning at OK; we read her allocation of clothing (5C) from top to bottom at the right of the box diagram. We can also see the effect of trade between Karen and James. James gives up 1F in exchange for 1C, moving from A to B. Karen gives up 1C and obtains 1F, also moving from A to B. Point B thus represents the market baskets
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of both James and Karen after the mutually beneficial trade. Efficient Allocations A trade from A to B thus made both Karen and James better off. But is B an efficient allocation? The answer depends on whether James’s and Karen’s MRSs are the same at B, which depends in turn on the shape of their indifference curves. Figure 16.5 shows several indifference curves for both James and Karen. Because his allocations are measured from the origin OJ, James’s indifference curves are drawn in the usual way. But for Karen, we have rotated the indifference curves 180 degrees, so that the origin is at the upper right-hand corner of the box. Karen’s indifference curves are convex, just like James’s; we simply see them from a different perspective. Now that we are familiar with the two sets of indifference curves, let’s exam1 that pass through the initial allocation at A. ine the curves labeled U J Both James’s and Karen’s MRSs give the slope of their indifference curves at A. James’s MRS of clothing for food is equal to 1/2, while Karen’s is 3. The shaded area between these two indifference curves represents all possible allocations of 1 and U K CHAPTER 16 • General Equilibrium and Economic Efficiency 605 Karen’s Food OK D C B 3 UK 2 UK UK Karen’s Clothing 6C 10F 10F 6C James’s Clothing OJ James’s Food FIGURE 16.5 EFFICIENCY IN EXCHANGE The Edgeworth box illustrates the possibilities for both consumers to increase their satisfaction by trading goods. If A gives the initial allocation of resources, the shaded area describes all mutually beneficial trades. food and clothing that would make both James and Karen better off than at A. In other words, it describes all possible mutually beneficial trades. 2 and UK Starting at A, any trade that moved the allocation of goods outside the shaded area would make one of the two consumers worse off and should not occur. The move from A to B was mutually beneficial. But in Figure 16.5, B is not an effi2 intersect. In this case, James’s cient point because indifference curves U J and Karen’s MRSs are not the same and the allocation is not efficient. Starting at B, James would prefer to give up some food to obtain additional clothing. He
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would be willing to make any trade that left him no worse off and hopefully gave him some additional utility, and there are many trades that would do so. Karen, on the other hand, would be willing to give up some clothing to obtain more food, and there are many such trades that would make her better off. This situation illustrates an important point: Even if a trade from an inefficient allocation makes both people better off, the new allocation is not necessarily efficient. Suppose that from B the additional trade is made, with James giving up another unit of food to obtain another unit of clothing and Karen giving up a unit of clothing for a unit of food. Point C in Figure 16.5 gives the new allocation. At C, the MRSs of both people are identical, because at point C the indifference curves are tangent. Trading food for clothing and thereby moving from point B to point C has allowed James and Karen to achieve a Pareto efficient outcome, and they will both be better off. When the indifference curves are tangent, one person cannot be made better off without making the other person worse off. Therefore, C represents an efficient allocation. Of course, C is not the only possible efficient outcome of a bargain between James and Karen. For example, if James is an effective bargainer, a trade might 3 is change the allocation of goods from A to D, where indifference curve U J 606 PART 4 • Information, Market Failure, and the Role of Government • contract curve Curve showing all efficient allocations of goods between two consumers, or of two inputs between two production functions. 1. This allocation would leave Karen no worse tangent to indifference curve U K off than she was at A and James much better off. And because no further trade is possible, D is an efficient allocation. Thus C and D are both efficient allocations, although James prefers D to C and Karen C to D. In general, it is difficult to predict the allocation that will be reached in a bargain because the end result depends on the bargaining abilities of the people involved. The Contract Curve We have seen that from an initial allocation many possible efficient allocations can be reached through mutually beneficial trade. To find all possible efficient allocations of food and clothing between Karen and James, we look for all points of tangency between each of their indifference curves. Figure 16.6 shows the contract curve: the curve drawn through all such efficient allocations. The contract curve shows all allocations from which no mutually beneficial trade can be made. These allocations are efficient because there is no way
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to reallocate goods to make someone better off without making someone else worse off. In Figure 16.5 three allocations labeled E, F, and G are Pareto efficient, although each involves a different distribution of food and clothing, because one person could not be made better off without making someone else worse off. Several properties of the contract curve may help us understand the concept of efficiency in exchange. Once a point on a contract curve, such as E, has been chosen, there is no way to move to another point on the contract curve, say F, without making one person worse off (in this case, Karen). Karen is worse off because she has less food and less clothing at F than she had at E. Without making further comparison between James’s and Karen’s preferences, we cannot Karen’s Food OK James’s Clothing Contract Curve E G F Karen’s Clothing O J James’s Food FIGURE 16.6 THE CONTRACT CURVE The contract curve contains all allocations for which consumers’ indifference curves are tangent. Every point on the curve is efficient because one person cannot be made better off without making the other person worse off. CHAPTER 16 • General Equilibrium and Economic Efficiency 607 compare allocations E and F. We simply know that both are efficient. In this sense, Pareto efficiency is a modest goal: It says that we should make all mutually beneficial exchanges, but it does not say which exchanges are best. Pareto efficiency can be a powerful concept, however. If a change will improve efficiency, it is in everyone’s self-interest to support it. We can frequently improve efficiency even when one aspect of a proposed change makes someone worse off. We need only include a second change, such that the combined set of changes leaves someone better off and no one worse off. Suppose, for example, that we eliminate the quota on steel imports into the United States. Although U.S. consumers would then enjoy lower prices and a greater selection of cars, some U.S. workers would lose their jobs. But what if eliminating the quota were combined with federal tax breaks and job relocation subsidies for steelworkers? In that case, U.S. consumers would be better off (after accounting for the cost of the job subsidies) and the workers no worse off. This would increase efficiency. Consumer Equilibrium in a Competitive Market In a two-person exchange, the outcome can depend on the bargaining power of the two parties. Competitive
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markets, however, have many actual or potential buyers and sellers. As a result, each buyer and seller takes the price of the goods as fixed and decides how much to buy and sell at those prices. We can show how competitive markets lead to efficient exchange by using the Edgeworth box to mimic a competitive market. Suppose, for example, that there are many Jameses and many Karens. This allows us to think of each individual James and Karen as a price taker, even though we are working with only a two-person box diagram. Figure 16.7 shows the opportunities for trade when we start at the allocation given by point A and when the prices of both food and clothing are equal to 1. (The actual prices do not matter; what matters is the price of food relative to the price of clothing.) When the prices of food and clothing are equal, each unit of food can be exchanged for 1 unit of clothing. As a result, the price line PP’ in the diagram, which has a slope of -1, describes all possible allocations that exchange can achieve. Suppose each James decides to buy 2 units of clothing and sell 2 units of food in exchange. This would move each James from A to C and increase satisfaction 2. Meanwhile, each Karen buys 2 units of food from indifference curve UJ and sells 2 units of clothing. This would move each Karen from A to C as well, increasing satisfaction from indifference curve UK 2. 1 to UK 1 to UJ We choose prices for the two goods so that the quantity of food demanded by each Karen is equal to the quantity of food that each James wishes to sell; likewise, the quantity of clothing demanded by each James is equal to the quantity of clothing that each Karen wishes to sell. As a result, the markets for food and clothing are in equilibrium. An equilibrium is a set of prices at which the quantity demanded equals the quantity supplied in every market. This is also a competitive equilibrium because all suppliers and demanders are price takers. Not all prices are consistent with equilibrium. For example, if the price of food is 3 and the price of clothing is 1, any exchange of clothing for food must be done on a 3-to-1 basis, i.e., 3 units of clothing must be given up to obtain 1 unit of food. But then each James will be unwilling to trade any clothing to get additional food because his MRS of clothing for food is only 1/2, i.e., he would only be willing to give up
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2 units of clothing for 1 unit of food. Each Karen, on the other hand, would be happy to sell clothing to get more food but has no one In §8.7, we explain that in a competitive equilibrium, price-taking firms maximize profit, and the price of the product is such that the quantity demanded is equal to the quantity supplied. 608 PART 4 • Information, Market Failure, and the Role of Government 10F 6C Karen’s Food OK Price Line P James’s Clothing C Karen’s Clothing 2 U J A 1 UK 1 U J P' 2 UK 6C 10F O J James’s Food FIGURE 16.7 COMPETITIVE EQUILIBRIUM In a competitive market the prices of the two goods determine the terms of exchange among consumers. If A is the initial allocation of goods and the price line PP’ represents the ratio of prices, the competitive market will lead to an equilibrium at C, the point of tangency of both indifference curves. As a result, the competitive equilibrium is efficient. • excess demand When the quantity demanded of a good exceeds the quantity supplied. • excess supply When the quantity supplied of a good exceeds the quantity demanded. to trade with. The market is therefore in disequilibrium because the quantities of food and clothing demanded are not equal to the quantities supplied. This disequilibrium should be only temporary. In a competitive market, prices will adjust if there is excess demand in some markets (the quantity demanded of one good is greater than the quantity supplied) and excess supply in others (the quantity supplied is greater than the quantity demanded). In our example, each Karen’s quantity demanded for food is greater than each James’s willingness to sell it, whereas each Karen’s willingness to trade clothing is greater than each James’s quantity demanded. As a result of this excess quantity demanded for food and excess quantity supplied of clothing, we can expect the price of food to increase relative to the price of clothing. As the price changes, so will the quantities demanded by all those in the market. Eventually, the prices will adjust until an equilibrium is reached. In our example, the price of both food and clothing might be 2; we know from the previous analysis that when the price of clothing is equal to the price of food, the market will be in competitive equilibrium. (Recall that only relative prices matter; prices of 2 for clothing and food are equivalent to prices of 1 for each.) Note
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the important difference between exchange with two people and an economy with many people. When only two people are involved, bargaining leaves the outcome indeterminate. However, when many people are involved, CHAPTER 16 • General Equilibrium and Economic Efficiency 609 the prices of the goods are determined by the combined choices of demanders and suppliers of goods. The Economic Efficiency of Competitive Markets We can now understand one of the fundamental results of microeconomic analysis. We can see from point C in Figure 16.7 that the allocation in a competitive equilibrium is Pareto efficient. The key reason why this is so is that C must occur at the tangency of two indifference curves. If it does not, one of the Jameses or one of the Karens will not be achieving maximum satisfaction; he or she will be willing to trade to achieve a higher level of utility. This result holds in an exchange framework and in a general equilibrium setting in which all markets are perfectly competitive. It is the most direct way of illustrating the workings of Adam Smith’s famous invisible hand, because it tells us that the economy will automatically allocate resources in a Pareto efficient manner without the need for regulatory control. It is the independent actions of consumers and producers, who take prices as given, that allows markets to function in an economically efficient manner. Not surprisingly, the invisible-hand result is often used as the norm against which the workings of all real-world markets are compared. For some, the invisible hand supports the normative argument for less government intervention; they argue that markets are highly competitive. For others, the invisible hand supports a more expansive role for government; they reply that intervention is needed to make markets more competitive. Whatever one’s view of government intervention, most economists consider the invisible-hand result important. In fact, the result that a competitive equilibrium is Pareto efficient is often described as the first theorem of welfare economics, which involves the normative evaluation of markets and economic policy. Formally, the first theorem states the following: If everyone trades in the competitive marketplace, all mutually beneficial trades will be completed and the resulting equilibrium allocation of resources will be Pareto efficient. Let’s summarize what we know about a competitive equilibrium from the consumer’s perspective: 1. Because the indifference curves are tangent, all marginal rates of substitu- tion between consumers are equal. 2. Because each indifference curve is tangent to the price line, each person’s MRS of clothing for food is equal to the ratio of
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the prices of the two goods. To be as clear as possible, we will use the notation MRSFC to denote the MRS of food for clothing. Then, if PC and PF are the two prices, MRS FC J = PF/PC = MRSFC K (16.1) To achieve a Pareto efficient allocation when there are many consumers (and many producers) is not easy. It can be done if all markets are perfectly • welfare economics Normative evaluation of markets and economic policy. 610 PART 4 • Information, Market Failure, and the Role of Government competitive. But efficient outcomes can also be achieved by other means—for example, through a centralized system in which the government allocates all goods and services. The competitive solution is often preferred because it allocates resources with a minimum of information. All consumers must know their own preferences and the prices they face, but they need not know what is being produced or the demands of other consumers. Other allocation methods need more information, and as a result, they become difficult and cumbersome to manage. 16.3 Equity and Efficiency We have shown that different efficient allocations of goods are possible, and we have seen how a perfectly competitive economy generates a Pareto efficient allocation. But there are many Pareto efficient allocations, and some are likely to be more fair than others. How do we decide what is the most equitable allocation? That is a difficult question—economists and others disagree both about how to define equity and how to quantify it. Any such view would involve subjective comparisons of utility, and reasonable people could disagree about how to make these comparisons. In this section, we discuss this general point and then illustrate it in a particular case by showing that there is no reason to believe that the allocation associated with a competitive equilibrium will be equitable. The Utility Possibilities Frontier Recall that every point on the contract curve in our two-person exchange economy shows the levels of utility that James and Karen can achieve. In Figure 16.8 we put the information from the Edgeworth box in a different form. James’s utility is measured on the horizontal axis and Karen’s on the vertical axis. Every point in the Edgeworth box corresponds to a point in Figure 16.7 because every allocation generates utility for both people. Every movement to the right in Figure 16.8 represents an increase in James’s utility, and every upward movement an increase in Karen’s. The utility possibilities frontier represents all allocations that are Pareto efficient. It
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shows the levels of satisfaction that are achieved when the two individuals have • utility possibilities frontier Curve showing all efficient allocations of resources measured in terms of the utility levels of two individuals. FIGURE 16.8 UTILITY POSSIBILITIES FRONTIER The utility possibilities frontier shows the levels of satisfaction that each of two people achieve when they have traded to an efficient outcome on the contract curve. Points E, F, and G correspond to points on the contract curve and are efficient. Point H is inefficient because any trade within the shaded area will make one or both people better off. Karen’s Utility OJ E F H L G OK James’s Utility CHAPTER 16 • General Equilibrium and Economic Efficiency 611 reached the contract curve. Point OJ is one extreme at which James has no goods and therefore zero utility, while point OK is the opposite extreme at which Karen has no goods. Because all other points on the frontier, such as E, F, and G, correspond to points on the contract curve, one person cannot be made better off without making the other worse off. Point H, however, represents an inefficient allocation because any trade within the shaded area makes one or both parties better off. At L, both people would be better off, but L is not attainable because there is not enough of both goods to generate the levels of utility that the point represents. It might seem reasonable to conclude that an allocation must be Pareto efficient to be equitable. Compare point H with F and E. Both F and E are efficient, and (relative to H) each makes one person better off without making the other worse off. We might agree, therefore, that it is inequitable to James or Karen or both for an economy to yield allocation H as opposed to F or E. But suppose H and G are the only possible allocations. Is G more equitable than H? Not necessarily. Compared with H, G yields more utility for James and less for Karen. Some people may feel that G is more equitable than H; others may feel the opposite. We can conclude, therefore, that one Pareto inefficient allocation of resources may be more equitable than another Pareto efficient allocation. The problem is how to define an equitable allocation. Even if we restrict ourselves to all points on the utility possibilities frontier, we can still ask which of these points is the most equitable. The answer depends on what one thinks equity entails and, therefore, on the interpersonal comparisons of utility that one is willing to make. SOC
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IAL WELFARE FUNCTIONS In economics, we often use a social welfare function to describe the well-being of society as a whole in terms of utilities of individual members. A social welfare function is useful when we want to evaluate policies that affect some members of society differently than others. One such function, the utilitarian, weights everyone’s utility equally and consequently maximizes the total utility of all members of society. Each social welfare function can be associated with a particular view about equity. But some views do not explicitly weight individual utilities and cannot therefore be represented by a social welfare function. For example, a market-oriented view argues that the outcome of the competitive market process is equitable because it rewards those who are most able and who work the hardest. If E is the competitive equilibrium allocation, for example, E would be deemed to be more equitable than F, even though goods are less equally allocated. When more than two people are involved, the meaning of the word equity becomes even more complex. The Rawlsian view3 considers a world in which people do not know in advance what their individual endowments will be. Rawls argues that, faced with a world in which you do not know your own “fate,” you would opt for a system ensuring that the least well-off person in society will be treated reasonably well. Specifically, according to Rawls, the most equitable allocation maximizes the utility of the least-well-off person in society. The Rawlsian perspective could be egalitarian—involving an equal allocation of goods among all members of society. But it need not be. Suppose that by rewarding more productive people more highly than less productive people, we can get the most productive people to work harder. This policy could produce more goods and services, some of which could then be reallocated to make the poorest members of society better off. 3See John Rawls, A Theory of Justice (New York: Oxford University Press, 1971). • social welfare function Measure describing the well-being of society as a whole in terms of the utilities of individual members. 612 PART 4 • Information, Market Failure, and the Role of Government TABLE 16.2 FOUR VIEWS OF EQUITY 1. Egalitarian—all members of society receive equal amounts of goods 2. Rawlsian—maximize the utility of the least-well-off person 3. Utilitarian—maximize the total utility of all members of society 4. Market-oriented—the market outcome is
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the most equitable The four views of equity in Table 16.2 move roughly from most to least egalitarian. While the egalitarian view explicitly requires equal allocations, the Rawlsian puts a heavy weight on equality (otherwise, some people would be much worse off than others). The utilitarian is likely to require some difference between the best- and worst-off members of society. Finally, the market-oriented view may lead to substantial inequality in the allocations of goods and services. Equity and Perfect Competition A competitive equilibrium leads to a Pareto efficient outcome that may or may not be equitable. In fact, a competitive equilibrium could occur at any point on the contract curve, depending on the initial allocation. Imagine, for example, that the initial allocation gave all food and clothing to Karen. This would be at OJ in Figure 16.8, and Karen would have no reason to trade. Point OJ would then be a competitive equilibrium, as would point OK and all intermediate points on the contract curve. Because efficient allocations are not necessarily equitable, society must rely to some extent on government to achieve equity goals by redistributing income or goods among households. These goals can be reached through the tax system. For example, a progressive income tax whose funds are used for programs that benefit households proportionally to income will redistribute income from the wealthy to the poor. The government can also provide public services, such as medical aid to the poor (Medicaid), or it can transfer funds through such programs as food stamps. The result that a competitive equilibrium can sustain every point on the contract curve is a fundamental result in microeconomics. It is important because it suggests an answer to a basic normative question: Is there a trade-off between equity and efficiency? In other words, must a society that wishes to achieve a more equitable allocation of resources necessarily operate in a manner that is Pareto efficient? The answer, which is given by the second theorem of welfare economics, tells us that redistribution need not conflict with economic efficiency. Formally, the second theorem states the following: If individual preferences are convex, then every Pareto efficient allocation (every point on the contract curve) is a competitive equilibrium for some initial allocation of goods. Literally, this theorem tells us that any equilibrium deemed to be equitable can be achieved by a suitable distribution of resources among individuals and that such a distribution need not in itself generate inefficiencies. Unfortunately, all programs that redistribute income in our society are economically costly. Taxes may encourage individuals to work less or cause firms to
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devote resources to avoiding taxes rather than to producing output. So, in effect, there is a trade-off Recall from §3.1 that an indifference curve is convex if the MRS diminishes as one moves down along the curve. CHAPTER 16 • General Equilibrium and Economic Efficiency 613 between the goals of equity and efficiency, and hard choices must be made. Welfare economics, which builds on the first and second theorems, provides a useful framework for debating the normative issues that surround the equity– efficiency issue in public policy. 16.4 Efficiency in Production Having described the conditions required to achieve an efficient allocation in the exchange of two goods, we now consider the efficient use of inputs in the production process. We assume that there are fixed total supplies of two inputs, labor and capital, which are needed to produce the same two products, food and clothing. Instead of only two people, however, we now assume that many consumers own the inputs to production (including labor) and earn income by selling them. This income, in turn, is allocated between the two goods. This framework links the various supply and demand elements of the economy. People supply inputs to production and then use the income they earn to demand and consume goods and services. When the price of one input increases, the individuals who supply a lot of that input earn more income and consume more of one of the two goods. In turn, this increases the demand for the inputs needed to produce the good and has a feedback effect on the price of those inputs. Only a general equilibrium analysis can find the prices that equate supply and demand in every market. Input Efficiency To see how inputs can be combined efficiently, we must find the various combinations of inputs that can be used to produce each of the two outputs. A particular allocation of inputs into the production process is technically efficient if the output of one good cannot be increased without decreasing the output of another good. Because technical efficiency requires the appropriate combination of inputs, we will also call it input efficiency. Efficiency in production is not a new concept; in Chapter 6 we saw that a production function represents the maximum output that can be achieved with a given set of inputs. Here we extend the concept to the production of two goods rather than one. If input markets are competitive, a point of efficient production will be achieved. Let’s see why. If the labor and capital markets are perfectly competitive, then the wage rate w will be the same in all industries. Likewise, the rental rate of capital r will be the same whether
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capital is used in the food or clothing industry. We know from Chapter 7 that if producers of food and clothing minimize production costs, they will use combinations of labor and capital so that the ratio of the marginal products of the two inputs is equal to the ratio of the input prices: MPL/MPK = w/r But we also showed that the ratio of the marginal products of the two inputs is equal to the marginal rate of technical substitution of labor for capital MRTSLK. As a result, MRTSLK = w/r (16.2) • technical efficiency Condition under which firms combine inputs to produce a given output as inexpensively as possible. In §7.3, we explain that the rental rate is the cost per year for renting a unit of capital. In §6.3, we explain that the marginal rate of technical substitution of labor for capital is the amount by which the input of capital can be reduced when one extra unit of labor is used, so that output remains constant. 614 PART 4 • Information, Market Failure, and the Role of Government Because the MRTS is the slope of the firm’s isoquant, a competitive equilibrium can occur in the input market only if each producer uses labor and capital so that the slopes of the isoquants are equal to one another and to the ratio of the prices of the two inputs. As a result, the competitive equilibrium is efficient in production. The Production Possibilities Frontier The production possibilities frontier shows the various combinations of food and clothing that can be produced with fixed inputs of labor and capital, holding technology constant. The frontier in Figure 16.9 is derived from the production contract curve. Each point on both the contract curve and the production possibilities frontier describes an efficiently produced level of both food and clothing. Point OF represents one extreme, in which only clothing is produced, and OC represents the other extreme, in which only food is produced. Points B, C, and D correspond to points at which both food and clothing are efficiently produced. Point A, representing an inefficient allocation, lies inside the production possibilities frontier. All points within the triangle ABC involve the complete utilization of labor and capital in the production process. However, a distortion in the labor market, perhaps due to a rent-maximizing union, has caused the economy as a whole to be productively inefficient. Where we end up on the production possibilities frontier depends on consumer demand for the two goods. For example, suppose consumers tend to prefer food rather than clothing. A possible competitive
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equilibrium occurs at D in Figure 16.8. On the other hand, if consumers prefer clothing to food, the competitive equilibrium will occur on a point on the production possibilities frontier closer to OF. Why is the production possibilities frontier downward sloping? In order to produce more food efficiently, one must switch inputs from the production of clothing, which in turn lowers the clothing production level. Because all points lying within the frontier are inefficient, they are off the production contract curve. MARGINAL RATE OF TRANSFORMATION The production possibilities frontier is concave (bowed out)—i.e., its slope increases in magnitude as more food is produced. To describe this, we define the marginal rate of transformation of food for clothing (MRT) as the magnitude of the slope of the frontier at • production possibilities frontier Curve showing the combinations of two goods that can be produced with fixed quantities of inputs. Recall from §14.4 that a rent- maximizing union attempts to maximize the wages that members earn in excess of their opportunity cost. • marginal rate of transformation Amount of one good that must be given up to produce one additional unit of a second good. FIGURE 16.9 PRODUCTION POSSIBILITIES FRONTIER The production possibilities frontier shows all efficient combinations of outputs. The production possibilities frontier is concave because its slope (the marginal rate of transformation) increases as the level of production of food increases. Clothing (units) OF 60 0 B C A 1C B 1F D OC 100 Enlarged Areas D 2C 1F Food (units) CHAPTER 16 • General Equilibrium and Economic Efficiency 615 each point. The MRT measures how much clothing must be given up to produce one additional unit of food. For example, the enlarged areas of Figure 16.9 show that at B on the frontier, the MRT is 1 because 1 unit of clothing must be given up to obtain 1 additional unit of food. At D, however, the MRT is 2 because 2 units of clothing must be given up to obtain 1 more unit of food. Note that as we increase the production of food by moving along the production possibilities frontier, the MRT increases.4 This increase occurs because the productivity of labor and capital differs depending on whether the inputs are used to produce more food or clothing. Suppose we begin at OF, where only clothing is produced. Now we remove some labor and capital from clothing production, where their marginal products are relatively low, and put them into food production, where their marginal products are high. Under
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these circumstances, to obtain the first unit of food, very little clothing production is lost. (The MRT is much less than 1.) But as we move along the frontier and produce less clothing, the productivities of labor and capital in clothing production rise and the productivities of labor and capital in food production fall. At B, the productivities are equal and the MRT is 1. Continuing along the frontier, we note that because the input productivities in clothing rise more and the productivities in food decrease, the MRT becomes greater than 1. We can also describe the shape of the production possibilities frontier in terms of the costs of production. At OF, where very little clothing output is lost to produce additional food, the marginal cost of producing food is very low: A lot of output is produced with very little input. Conversely, the marginal cost of producing clothing is very high: It takes a lot of both inputs to produce another unit of clothing. Thus, when the MRT is low, so is the ratio of the marginal cost of producing food MCF to the marginal cost of producing clothing MCC. In fact, the slope of the production possibilities frontier measures the marginal cost of producing one good relative to the marginal cost of producing the other. The curvature of the production possibilities frontier follows directly from the fact that the marginal cost of producing food relative to the marginal cost of producing clothing is increasing. At every point along the frontier, the following condition holds: MRT = MCF/MCC (16.3) At B, for example, the MRT is equal to 1. Here, when inputs are switched from clothing to food production, 1 unit of output is lost and 1 is gained. If the input cost of producing 1 unit of either good is $100, the ratio of the marginal costs would be $100/$100, or 1. Equation (16.3) also holds at D (and at every other point on the frontier). Suppose the inputs needed to produce 1 unit of food cost $160. The marginal cost of food would be $160, but the marginal cost of clothing would be only $80 ($160/2 units of clothing). As a result, the ratio of the marginal costs, 2, is equal to the MRT. Output Efficiency For an economy to be efficient, goods must not only be produced at minimum cost; goods must also be produced in combinations that match people’s willingness to pay for them. To understand this principle, recall from Chapter 3 that the marginal
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4The production possibilities frontier need not have a continually increasing MRT. Suppose, for example, that there are strong diseconomies of scale in the production of food. In that case, as inputs are moved from clothing to food production, the amount of clothing that must be given up to obtain one more unit of food will decline. 616 PART 4 • Information, Market Failure, and the Role of Government rate of substitution of clothing for food (MRS) measures the consumer’s willingness to pay for an additional unit of food by consuming less clothing. The marginal rate of transformation measures the cost of an additional unit of food in terms of producing less clothing. An economy produces output efficiently only if, for each consumer, MRS = MRT (16.4) To see why this condition is necessary for efficiency, suppose the MRT equals 1, while the MRS equals 2. In that case, consumers are willing to give up 2 units of clothing to get 1 unit of food, but the cost of getting the additional food is only 1 unit of lost clothing. Clearly, too little food is being produced. To achieve efficiency, food production must be increased until the MRS falls and the MRT increases and the two are equal. The outcome is output efficient only when MRS = MRT for all pairs of goods. Figure 16.10 shows this important output efficiency condition graphically. Here, we have superimposed one consumer’s indifference curve on the production possibilities frontier from Figure 16.9. Note that C is the only point on the production possibilities frontier that maximizes the consumer’s satisfaction. Although all points on the production frontier are technically efficient, not all involve the most efficient production of goods from the consumer’s perspective. At the point of tangency of the indifference curve and the production frontier, the MRS (the slope of the indifference curve) and the MRT (the slope of the production frontier) are equal. If you were a planner in charge of managing an economy, you would face a difficult problem. To achieve output efficiency, you must equate the marginal rate of transformation with the consumer’s marginal rate of substitution. But if different consumers have different preferences for food and clothing, how can you decide what levels of food and clothing to produce and what amount of each to give to every consumer, so that all consumers have the same MRS? The informational and logistical costs are enormous. That is one reason why centrally planned economies, like that of the former Soviet Union, performed
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so poorly. Fortunately, a well-functioning competitive market system can achieve the same efficient outcome as an ideal managed economy. FIGURE 16.10 OUTPUT EFFICIENCY The efficient combination of outputs is produced when the marginal rate of transformation between the two goods (which measures the cost of producing one good relative to the other) is equal to the consumer’s marginal rate of substitution (which measures the marginal benefit of consuming one good relative to the other). Clothing (units) 60 MRS = MRT Production Possibilities Frontier C Indifference Curve 0 100 Food (units) CHAPTER 16 • General Equilibrium and Economic Efficiency 617 Efficiency in Output Markets When output markets are perfectly competitive, all consumers allocate their budgets so that their marginal rates of substitution between two goods are equal to the price ratio. For our two goods, food and clothing, MRS = PF/PC At the same time, each profit-maximizing firm will produce its output up to the point at which price is equal to marginal cost. Again, for our two goods, PF = MCF and PC = MCC Because the marginal rate of transformation is equal to the ratio of the marginal costs of production, it follows that MRT = MCF/MCC = PF/PC = MRS (16.5) When output and input markets are competitive, production will be output efficient in that the MRT is equal to the MRS. This condition is just another version of the marginal benefit–marginal cost rule discussed in Chapter 4. There we saw that consumers buy additional units of a good up to the point at which the marginal benefit of consumption is equal to the marginal cost. Here we see that the production of food and clothing is chosen so that the marginal benefit of consuming another unit of food is equal to the marginal cost of producing another unit of food; the same is true for the consumption and production of clothing. Figure 16.11 shows that efficient competitive output markets are achieved when production and consumption choices are separated. Suppose the market 1. If producers are using inputs efficiently, they generates a price ratio of PF will produce food and clothing at A, where the price ratio is equal to the MRT, the slope of the production possibilities frontier. When faced with this budget constraint, however, consumers would like to consume at B, where they maximize their satisfaction at the higher indifference curve U2. However, at the price 1/PC In §3.3, we explain that utility maximization is generally achieved when the marginal rate of substitution
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of one good for another is equal to the ratio of their two prices. In §3.3, we explain that utility maximization is achieved when the marginal benefit of consuming an additional unit of each product is equal to its marginal cost. Clothing (units) 1 1/PC PF * */PC PF C1 C2 C* 0 A B C U2 U1 F1 F * F2 Food (units) FIGURE 16.11 COMPETITION AND OUTPUT EFFICIENCY In a competitive output market, people consume to the point where their marginal rate of substitution is equal to the price ratio. Producers choose outputs so that the marginal rate of transformation is equal to the price ratio. Because the MRS equals the MRT, the competitive output market is efficient. Any other price ratio will lead to an excess demand for one good and an excess supply of the other. 618 PART 4 • Information, Market Failure, and the Role of Government 1/PC 1, producers will not produce the combination of food and clothing ratio PF at B. Because the producer wants to produce F1 units of food, while consumers want to buy F2, there will be an excess demand for food. Correspondingly, because consumers wish to buy C2 units of clothing while producers wish to sell C1, there will be an excess supply of clothing. Prices in the market will then adjust: The price of food will rise and that of clothing will fall. As price ratio PF/PC increases, the price line will move along the production frontier. An equilibrium results when the price ratio is PF * at C. In equilibrium, there is no way to make a consumer better off without making another consumer worse off. Hence, this equilibrium is Pareto efficient. Moreover, producers want to sell F* units of food and C* units of clothing; consumers want to buy the same amounts. At this equilibrium, the MRT and the MRS are equal again; therefore, the competitive equilibrium is output efficient. */PC 16.5 The Gains from Free Trade Clearly there are gains from international trade in an exchange economy. We have seen that two persons or two countries can benefit by trading to reach a point on the contract curve. However, there are additional gains from trade when the economies of two countries differ so that one country has a comparative advantage in producing one good while the other has a comparative advantage in producing another. Comparative Advantage Country 1 has a comparative advantage over Country 2 in producing a good if the cost of producing
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that good, relative to the cost of producing other goods in 1, is lower than the cost of producing the good in 2, relative to the cost of producing other goods in 2.5 Note that comparative advantage is not the same as absolute advantage. A country has an absolute advantage in producing a good if its cost is lower than the cost in another country. A comparative advantage, on the other hand, implies that a country’s cost, relative to the costs of other goods it produces, is lower than the other country’s. When each of two countries has a comparative advantage, they are better off producing what they are best at and purchasing the rest. To see this, suppose that the first country, Holland, has an absolute advantage in producing both cheese and wine. A worker there can produce a pound of cheese in 1 hour and a gallon of wine in 2 hours. In Italy, on the other hand, it takes a worker 6 hours TABLE 16.3 HOURS OF LABOR REQUIRED TO PRODUCE CHEESE AND WINE CHEESE (1 LB) WINE (1 GAL) Holland Italy 1 6 2 3 • comparative advantage Situation in which Country 1 has an advantage over Country 2 in producing a good because the cost of producing the good in 1, relative to the cost of producing other goods in 1, is lower than the cost of producing the good in 2, relative to the cost of producing other goods in 2. • absolute advantage Situation in which Country 1 has an advantage over Country 2 in producing a good because the cost of producing the good in 1 is lower than the cost of producing it in 2. 5Formally, if there are 2 goods, x and y, and 2 countries, i and j, we say that country i has a compara 6 i is the cost of producing good x in where ax tive advantage in the production of good x if country i. i ax i ay j ax j ay CHAPTER 16 • General Equilibrium and Economic Efficiency 619 to produce a pound of cheese and 3 hours to produce a gallon of wine. The production relationships are summarized in Table 16.3.6 Holland has a comparative advantage over Italy in producing cheese. Holland’s cost of cheese production (in terms of hours of labor used) is half its cost of producing wine, whereas Italy’s cost of producing cheese is twice its cost of producing wine. Likewise, Italy has a comparative advantage in producing wine, which it can produce at half
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the cost at which it can produce cheese. WHAT HAPPENS WHEN NATIONS TRADE The comparative advantage of each country determines what happens when they trade. The outcome will depend on the price of each good relative to the other when trade occurs. To see how this might work, suppose that with trade, one gallon of wine sells for the same price as one pound of cheese in both Holland and Italy. Suppose also that because there is full employment in both countries, the only way to increase production of wine is to take labor out of the production of cheese, and vice versa. Without trade, Holland could, with 24 hours of labor input, produce 24 pounds of cheese, 12 gallons of wine, or a combination of the two, such as 18 pounds of cheese and 3 gallons of wine. But Holland can do better. For every hour of labor, Holland can produce 1 pound of cheese, which it can trade for 1 gallon of wine; if the wine were produced at home, 2 hours of labor would be required. It is, therefore, in Holland’s interest to specialize in the production of cheese, which it will export to Italy in exchange for wine. If, for example, Holland produced 24 pounds of cheese and traded 6, it would be able to consume 18 pounds of cheese and 6 gallons of wine—a definite improvement over the 18 pounds of cheese and 3 gallons of wine available in the absence of trade. Italy is also better off with trade. Note that without trade, Italy can, with the same 24 hours of labor input, produce 4 pounds of cheese, 8 gallons of wine, or a combination of the two, such as 3 pounds of cheese and 2 gallons of wine. On the other hand, with every hour of labor, Italy can produce one-third of a gallon of wine, which it can trade for one-third of a pound of cheese. If it produced cheese at home, twice as much time would be involved. Specialization in wine production, therefore, is advantageous for Italy. Suppose that Italy produced 8 gallons of wine and traded 6; in that case, it would be able to consume 6 pounds of cheese and 2 gallons of wine—likewise an improvement over the 3 pounds of cheese and 2 gallons of wine available without trade. An Expanded Production Possibilities Frontier When there is comparative advantage, international trade has the effect of allowing a country to consume outside its production possibilities frontier. This can be seen graphically in Figure 16.12, which shows a production possibilities frontier for Holland. Suppose initially
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that Holland has been prevented from trading with Italy because of a protectionist trade barrier. What is the outcome of the competitive process in Holland? Production is at point A, on indifference curve U1, where the MRT and the pre-trade price of wine is twice the price of cheese. If Holland were able to trade, it would want to export 2 pounds of cheese in exchange for 1 gallon of wine. 6This example is based on “World Trade: Jousting for Advantage,” The Economist (September 22, 1990): 5–40. 620 PART 4 • Information, Market Failure, and the Role of Government Cheese (pounds) Exports CB CD World Prices Pre-trade Prices B A WB Imports D U1 WD U2 Wine (gallons) FIGURE 16.12 THE GAINS FROM TRADE Without trade, production and consumption are at point A, where the price of wine is twice the price of cheese. With trade at a relative price of 1 cheese to 1 wine, domestic production is now at B, while domestic consumption is at D. Free trade has allowed utility to increase from U1 to U2. Suppose now that the trade barrier is dropped and Holland and Italy are both open to trade. Suppose also that, as a result of differences in demand and costs in the two countries, trade occurs on a one-to-one basis. Holland will find it advantageous to produce at point B, the point of tangency of the 1/1 price line and Holland’s production possibilities frontier. That is not the end of the story, however. Point B represents the production decision in Holland. (Once the trade barrier has been removed, Holland will produce less wine and more cheese domestically.) With trade, however, consumption will occur at point D, at which the higher indifference curve U2 is tangent to the trade price line. Thus trade has the effect of expanding Holland’s consumption choices beyond its production possibilities frontier. Holland will import WD - WB units of wine and export CB - CD units of cheese. With trade, each country will undergo a number of important adjustments. As Holland imports wine, the production of domestic wine will fall, as will employment in the wine industry. Cheese production will increase, however, as will the number of jobs in that industry. Workers with job-specific skills may find it difficult to change employment. Not everyone will, therefore, gain as the result of free trade. Although consumers will clearly be better off, producers of wine and workers in
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the wine industry are likely to be worse off, at least temporarily. CHAPTER 16 • General Equilibrium and Economic Efficiency 621 EXAM PLE 16.3 TRADING TASKS AND IPOD PRODUCTION Most people think of foreign trade as importing or exporting manufactured products. However, trade often involves many steps that transform raw materials into finished products. At each of these steps, intermediate goods are combined with labor or machines to make part or all of finished products. For instance, workers might assemble a set of chips and other components for a computer. Thus, a typical product embodies a sequence of tasks, each of which can also be traded. Where and how those tasks are performed is an important part of efficient production and trade.7 Consider an Apple iPod. On the back, it says “Designed by Apple in California. Assembled in China.” But this is only the beginning and end of a long sequence of tasks needed to make an iPod, as can be seen in Table 16.4.8 Three things are of note. First, iPod manufacturing is a truly global undertaking. Product design occurs in one place, company management somewhere else, and actual assembly in yet a third location. This is true not only for the iPod as a whole, but also for its major components. This “unbundling” of production, which allows firms to use different countries’ comparative advantages in different steps of production, has been made possible by better communications technology and a decline in shipping costs. The United States, for instance, may have a comparative advantage in the task of product design. The designs are sent to China, which has a comparative advantage in the task of assembly. The assembled product is then shipped back to the United States, where U.S. companies perform distribution and retail tasks. Second, note that most of an iPod’s components are semi-finished products, such as storage or displays, rather than raw materials, such as plastic or silicon. To make production more efficient, specialized firms design and manufacture most parts. Certainly, Apple could have set up its own factories to make processors, storage, or displays, but it is more efficient to trade and make use of the production skills of other firms in other countries. For instance, Toshiba may have TABLE 16.4 DIFFERENT TASKS IN IPOD PRODUCTION MANUFACTURING LOCATION PRICE ($) % OF RETAIL PRICE COMPONENT COMPANY Product Design / Concept Apple (U
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.S.) Storage Display Video Processor Central Processor Unit Assembly Toshiba (Japan) Matsushita & Toshiba U.S. China Japan Broadcom (U.S.) Taiwan or Singapore PortalPlayer (U.S.) U.S. or Taiwan Inventec (Taiwan) China All other parts (about 450) Total Parts Distribution and Retail Retail Price - - - - - U.S. 79.85 73.39 20.39 8.36 4.94 3.70 33.62 144.40 74.75 299.00 26.7 24.6 6.8 2.8 1.7 1.2 11.2 48.3 25.0 100.0 7Gene M. Grossman and Esteban Rossi-Hansberg, “The Rise of Offshoring: It’s Not Wine for Cloth Anymore,” Working Paper, Princeton University, 2006. 8This example is based on Greg Linden, Kenneth L. Kraemer, and Jason Dedrick, “Who Captures Value in a Global Innovation System? The Case of Apple’s iPod,” PCIC UC-Irvine, June 2007. 622 PART 4 • Information, Market Failure, and the Role of Government a comparative advantage in making hard drives because of the sheer scale of its production capacity. Finally, observe that physical parts account for just under half of the iPod’s retail price. As with most products, a bundle of different services is needed to design, develop, and distribute the iPod. The firms that perform those services—Apple included—also end up with a sizable share of the final selling price. EXAMPLE 16.4 THE COSTS AND BENEFITS OF SPECIAL PROTECTION The demands for protectionist policies increased steadily during the 1980s and into the 1990s. They remain a subject of debate today, whether out of concern for trade with various Asian countries or in relation to the North American Free Trade Agreement (NAFTA). Protectionism can take many forms, including tariffs and quotas of the kind that we analyzed in Chapter 9, regulatory hurdles, subsidies to domestic producers, and controls on the use of foreign exchange. Table 16.5 highlights the findings of one study of U.S.-imposed trade restrictions.9 TABLE 16.5 QUANTIFYING THE COSTS OF PROTECTION INDUSTRY Book manufacturing Orange juice Textiles and apparel Carbon steel Color televisions Dairy products Meat Sugar PRODUCER GAINSa ($ MILL
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IONS) CONSUMER LOSSESb ($ MILLIONS) EFFICIENCY LOSSESc ($ MILLIONS) 622 796 44,883 7,753 388 10,201 3,264 1,431 1,020 1,071 55,084 13,873 857 11,221 3,672 2,882 59 265 9,895 673 14 2,795 296 614 aProducer gains in the tariff case are defined as the area of trapezoid A in Figure 9.15. bConsumer losses are the sum of areas A, B, C, and D in Figure 9.15. cThese are given by triangles B and C in Figure 9.15. 9This example is based on Cletus Coughlin, K. Alec Chrystal, and Geoffrey E. Wood, “Protectionist Trade Policies: A Survey of Theory, Evidence, and Rationale,” Federal Reserve Bank of St. Louis (January/February 1988): 12–30. The data in the table are taken from Gary Clyde Hufbauer, Diane T. Berliner, and Kimberly Ann Elliott, “Trade Protection in the United States: 31 Case Studies,” Institute for International Economics (1986). The dollar amounts have been scaled to 2011 using the CPI. The sugar data are from Figure 9.15. CHAPTER 16 • General Equilibrium and Economic Efficiency 623 Because one of the major purposes of protectionism is to protect jobs in particular industries, it is not surprising that these policies create gains to producers. The costs, however, involve losses to consumers and a substantial reduction in economic efficiency. These efficiency losses are the sum of the loss of producer surplus resulting from inefficient excess domestic production and the loss of consumer surplus resulting from higher domestic prices and lower consumption. As Table 16.5 shows, the textiles and apparel industry is the largest source of efficiency losses. Although there were substantial gains to producers, consumer losses are larger in each case. In addition, efficiency losses from excess (inefficient) domestic production of textiles and reduced domestic consumption of imported textile products were also large—an estimated $9.89 billion. The second largest source of inefficiency was the dairy industry, where losses amounted to $2.79 billion. Finally, note that the efficiency cost of helping domestic producers varies considerably across industries. In textiles the ratio of efficiency costs to producer gains is 22 percent and in dairy products 27 percent; only orange juice is higher (33
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.3 percent). However, much lower ratios apply to color televisions (3.7 percent), carbon steel (8.7 percent), and book manufacturing (9.5 percent). In §9.1, we explain that consumer surplus is the total benefit or value that consumers receive beyond what they pay for a good; producer surplus is the analogous measure for producers. 16.6 An Overview—The Efficiency of Competitive Markets Our analysis of general equilibrium and economic efficiency is now complete. In the process, we have obtained two remarkable results. First, we have shown that for any initial allocation of resources, a competitive process of exchange among individuals, whether through exchange, input markets, or output markets, will lead to a Pareto efficient outcome. The first theorem of welfare economics tells us that a competitive system, building on the self-interested goals of consumers and producers and on the ability of market prices to convey information to both parties, will achieve a Pareto efficient allocation of resources. Second, we have shown that with indifference curves that are convex, any efficient allocation of resources can be achieved by a competitive process with a suitable redistribution of those resources. Of course, there may be many Pareto efficient outcomes. But the second theorem of welfare economics tells us that under certain (admittedly ideal) conditions, issues of equity and efficiency can be treated distinctly from one another. If we are willing to put equity issues aside, then we know that there is a competitive equilibrium that maximizes consumer and producer surplus, i.e., is economically efficient. Both theorems of welfare economics depend crucially on the assumption that markets are competitive. Unfortunately, neither of these results necessarily holds when, for some reason, markets are no longer competitive. In the next two chapters, we will discuss ways in which markets fail and what government can do about it. Before proceeding, however, it is essential to review our understanding of the workings of the competitive process. We thus list the conditions required for economic efficiency in exchange, in input markets, and in output markets. 624 PART 4 • Information, Market Failure, and the Role of Government Recall from §3.3 that consumer satisfaction is maximized when the marginal rate of substitution of food for clothing is equal to the ratio of the price of food to that of clothing. These conditions are important; in each of these three cases, you should review the explanation of the conditions in this chapter and the underlying building blocks in prior chapters. 1. Efficiency in exchange: All allocations must lie on the exchange
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contract curve so that every consumer’s marginal rate of substitution of food for clothing is the same: MRS FC J = MRSFC K A competitive market achieves this efficient outcome because, for consumers, the tangency of the budget line and the highest attainable indifference curve ensure that: MRS FC J = PF/PC = MRSFC K 2. Efficiency in the use of inputs in production: Every producer’s marginal rate of technical substitution of labor for capital is equal in the production of both goods: MRTSLK F = MRTSLK C Recall from §7.3 that profit maximization requires that the marginal rate of technical substitution of labor for capital be equal to the ratio of the wage rate to the cost of capital. A competitive market achieves this technically efficient outcome because each producer maximizes profit by choosing labor and capital inputs so that the ratio of the input prices is equal to the marginal rate of technical substitution: MRTSLK F = w/r = MRTSLK C In §8.3, we explain that because a competitive firm faces a horizontal demand curve, choosing its output so that marginal cost is equal to price is profit-maximizing. 3. Efficiency in the output market: The mix of outputs must be chosen so that the marginal rate of transformation between outputs is equal to consumers’ marginal rates of substitution: MRTFC = MRSFC (for all consumers) A competitive market achieves this efficient outcome because profit- maximizing producers increase their output to the point at which marginal cost equals price: As a result, PF = MCF, PC = MCC MRTFC = MCF/MCC = PF/PC But consumers maximize their satisfaction in competitive markets only if PF/PC = MRSFC (for all consumers) Therefore, MRSFC = MRTFC CHAPTER 16 • General Equilibrium and Economic Efficiency 625 and the output efficiency conditions are satisfied. Thus efficiency requires that goods be produced in combinations and at costs that match people’s willingness to pay for them. 16.7 Why Markets Fail We can give two different interpretations of the conditions required for efficiency. The first stresses that competitive markets work. It also tells us that we ought to ensure that the prerequisites for competition hold, so that resources can be efficiently allocated. The second stresses that the prerequisites for competition are unlikely to hold. It tells us that we ought to concentrate on ways of dealing with market failures. Thus far we have focused on the first interpretation. For the
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remainder of the book, we concentrate on the second. Competitive markets fail for four basic reasons: market power, incomplete infor- mation, externalities, and public goods. We will discuss each in turn. Market Power We have seen that inefficiency arises when a producer or supplier of a factor input has market power. Suppose, for example, that the producer of food in our Edgeworth box diagram has monopoly power. It therefore chooses the output quantity at which marginal revenue (rather than price) is equal to marginal cost and sells less output at a price higher than it would charge in a competitive market. The lower output will mean a lower marginal cost of food production. Meanwhile, the freed-up production inputs will be allocated to produce clothing, whose marginal cost will increase. As a result, the marginal rate of transformation will decrease because MRTFC = MCF/MCC. We might end up, for example, at A on the production possibilities frontier in Figure 16.9. Producing too little food and too much clothing is an output inefficiency because firms with market power use different prices in their output decisions than consumers use in their consumption decisions. A similar argument would apply to market power in an input market. Suppose that unions gave workers market power over the supply of their labor in the production of food. Too little labor would then be supplied to the food industry at too high a wage (wF) and too much labor to the clothing industry at too low a wage (wC). In the clothing industry, the input efficiency conditions C = wC/r. But in the food industry, the wage would be satisfied because MRTSLK paid would be greater than the wage paid in the clothing industry. Therefore, C. The result is input inefficiency because MRTSLK efficiency requires that the marginal rates of technical substitution be equal in the production of all goods. F = wF/r 7 wC/r = MRTSLK Incomplete Information If consumers do not have accurate information about market prices or product quality, the market system will not operate efficiently. This lack of information may give producers an incentive to supply too much of some products and too little of others. In other cases, while some consumers may not buy a product even though they would benefit from doing so, others buy products that leave them worse off. For example, consumers may buy pills that guarantee weight loss, only to find that they have no medical value. Finally, a lack of information In §10.2, we explain that
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a seller of a product has monopoly power if it can profitably charge a price greater than marginal cost; similarly, §10.5 explains that a buyer has monopsony power when its purchasing decision can affect the price of a good. 626 PART 4 • Information, Market Failure, and the Role of Government may prevent some markets from ever developing. It may, for example, be impossible to purchase certain kinds of insurance because suppliers of insurance lack adequate information about consumers likely to be at risk. Each of these informational problems can lead to competitive market inefficiency. We will describe informational inefficiencies in detail in Chapter 17 and see whether government intervention might help to reduce them. Externalities The price system works efficiently because market prices convey information to both producers and consumers. Sometimes, however, market prices do not reflect the activities of either producers or consumers. There is an externality when a consumption or production activity has an indirect effect on other consumption or production activities that is not reflected directly in market prices. As we explained in Section 9.2 (page 323), the word externality is used because the effects on others (whether benefits or costs) are external to the market. Suppose, for example, that a steel plant dumps effluent in a river, thus making a recreation site downstream unsuitable for swimming or fishing. There is an externality because the steel producer does not bear the true cost of wastewater and so uses too much wastewater to produce its steel. This externality causes an input inefficiency. If this externality prevails throughout the industry, the price of steel (which is equal to the marginal cost of production) will be lower than if the cost of production reflected the effluent cost. As a result, too much steel will be produced, and there will be an output inefficiency. We will discuss externalities and ways to deal with them in Chapter 18. Public Goods The last source of market failure arises when the market fails to supply goods that many consumers value. A public good can be made available cheaply to many consumers, but once it is provided to some consumers, it is very difficult to prevent others from consuming it. For example, suppose a firm is considering whether to undertake research on a new technology for which it cannot obtain a patent. Once the invention is made public, others can duplicate it. As long as it is difficult to exclude other firms from selling the product, the research will be unprofitable. Markets therefore undersupply public goods. We will see in Chapter 18 that government can
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sometimes resolve this problem either by supplying a good itself or by altering the incentives for private firms to produce it. • public good Nonexclusive, nonrival good that can be made available cheaply but which, once available, is difficult to prevent others from consuming. E XAM PLE 16.5 INEFFICIENCY IN THE HEALTH CARE SYSTEM The United States spends a larger fraction of its GDP on health care than do most other countries. Does this mean that the U.S. health care system is less “efficient” than other health care systems? This is an important public policy question that we can clarify by taking advantage of the analysis presented in this chapter. There are two distinct efficiency issues here. First, is the U.S. health care system technically efficient in production, in the sense of utilizing the best combination of such inputs as hospital beds, physicians, nurses, and drugs to obtain better health outcomes? Second, is the United States output efficient in the provision of health care; that is, are the health benefits from the marginal dollar spent on health care greater than the opportunity cost of other goods and services that might be provided instead? CHAPTER 16 • General Equilibrium and Economic Efficiency 627 We discussed the question of technical efficiency in Chapter 6. As we saw in Example 6.1, as more and more health care is produced, there are diminishing returns, so that even if we are on the production frontier, it will take more and more resources to eke out small gains in health outcomes (e.g., increases in life expectancy). But we saw that there is reason to believe that the health care industry is operating below the frontier, so that if inputs were used more efficiently, better health outcomes could be achieved with little or no increase in resources. For example, for every office-based physician in the United States there are 2.2 administrative workers. This is 25 percent higher than the equivalent number in the United Kingdom, 165 percent more than the Netherlands, and 215 percent more than Germany. It appears that substantially more time and expense is devoted to navigating the complex credentialing, claim reporting, verification, and billing requirements of various insurers in the U.S. relative to other developed countries. In addition, a number of low cost, highly effective treatments seem to be under-prescribed in the United States. Beta blockers, for example, cost just a few cents per dose and are believed to reduce heart attack mortality by 25%, yet in some parts of the country they are rarely prescribed. What about
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output efficiency? It has been suggested that the increasing fraction of income being devoted to health expenditures in the United States is evidence of inefficiency. But, as we saw in Example 3.4, this could simply reflect a strong preference for health care on the part of the U.S. population, whose incomes have generally been increasing. The study underlying that example calculated the marginal rate of substitution between health related and nonhealth related goods and found that as consumption increases, the marginal utility of consumption for non-health related goods falls quickly. As we explained, this should not be surprising; as individuals age and their incomes increase, an extra year of life expectancy becomes much more valuable than a new car or a second home. Thus an increasing share of income devoted to health is entirely consistent with output efficiency. SUMMARY 1. Partial equilibrium analyses of markets assume that related markets are unaffected. General equilibrium analyses examine all markets simultaneously, taking into account feedback effects of other markets on the market being studied. 2. An allocation is efficient when no consumer can be made better off by trade without making someone else worse off. When consumers make all mutually advantageous trades, the outcome is Pareto efficient and lies on the contract curve. 3. A competitive equilibrium describes a set of prices and quantities. When each consumer chooses her most preferred allocation, the quantity demanded is equal to the quantity supplied in every market. All competitive equilibrium allocations lie on the exchange contract curve and are Pareto efficient. 4. The utility possibilities frontier measures all efficient allocations in terms of the levels of utility that each of two people achieves. Although both individuals prefer some allocations to an inefficient allocation, not every efficient allocation must be so preferred. Thus an inefficient allocation can be more equitable than an efficient one. 5. Because a competitive equilibrium need not be equitable, the government may wish to help redistribute wealth from rich to poor. Because such redistribution is costly, there is some conflict between equity and efficiency. 6. An allocation of production inputs is technically efficient if the output of one good cannot be increased without decreasing the output of another. 7. A competitive equilibrium in input markets occurs when the marginal rate of technical substitution between pairs of inputs is equal to the ratio of the prices of the inputs. 8. The production possibilities frontier measures all efficient allocations in terms of the levels of output that can be produced with a given combination of inputs. The marginal rate of transformation of good 1 for good 2 increases as more of good 1 and less of good 2 are produced. The marginal rate of transformation
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is equal to the ratio of the marginal cost of producing good 1 to the marginal cost of producing good 2. 9. Efficiency in the allocation of goods to consumers is achieved only when the marginal rate of substitution 628 PART 4 • Information, Market Failure, and the Role of Government of one good for another in consumption (which is the same for all consumers) is equal to the marginal rate of transformation of one good for another in production. 10. When input and output markets are perfectly competitive, the marginal rate of substitution (which equals the ratio of the prices of the goods) will equal the marginal rate of transformation (which equals the ratio of the marginal costs of producing the goods). 11. Free international trade expands a country’s production possibilities frontier. As a result, consumers are better off. 12. Competitive markets may be inefficient for four reasons. First, firms or consumers may have market power in input or output markets. Second, consumers or producers may have incomplete information and may therefore err in their consumption and production decisions. Third, externalities may be present. Fourth, some socially desirable public goods may not be produced. QUESTIONS FOR REVIEW 1. Why can feedback effects make a general equilibrium analysis substantially different from a partial equilibrium analysis? 2. In the Edgeworth box diagram, explain how one point can simultaneously represent the market baskets owned by two consumers. 3. In the analysis of exchange using the Edgeworth box diagram, explain why both consumers’ marginal rates of substitution are equal at every point on the contract curve. 4. “Because all points on a contract curve are efficient, they are all equally desirable from a social point of view.” Do you agree with this statement? Explain. 5. How does the utility possibilities frontier relate to the contract curve? 6. In the Edgeworth production box diagram, what conditions must hold for an allocation to be on the production contract curve? Why is a competitive equilibrium on the contract curve? 7. How is the production possibilities frontier related to the production contract curve? 8. What is the marginal rate of transformation (MRT)? Explain why the MRT of one good for another is equal to the ratio of the marginal costs of producing the two goods. 9. Explain why goods will not be distributed efficiently among consumers if the MRT is not equal to the consumers’ marginal rate of substitution. EXERCISES 10. Why can free trade between two countries make con- sumers of both countries better off? 11. If Country A has an
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absolute advantage in the production of two goods compared to Country B, then it is not in Country A’s best interest to trade with Country B. True or false? Explain. 12. Do you agree or disagree with each of the following statements? Explain. a. If it is possible to exchange 3 pounds of cheese for 2 bottles of wine, then the price of cheese is 2/3 the price of wine. b. A country can only gain from trade if it can produce a good at a lower absolute cost than its trading partner. c. If there are constant marginal and average costs of production, then it is in a country’s best interest to specialize completely in the production of some goods but to import others. d. Assuming that labor is the only input, if the opportunity cost of producing a yard of cloth is 3 bushels of wheat per yard, then wheat must require 3 times as much labor per unit produced as cloth. 13. What are the four major sources of market failure? Explain briefly why each prevents the competitive market from operating efficiently. 1. Suppose gold (G) and silver (S) are substitutes for each other because both serve as hedges against inflation. Suppose also that the supplies of both are fixed = 300) and that the = 75 and QS in the short run (QG demands for gold and silver are given by the following equations: PG = 975 - QG + 0.5PS and PS = 600 - QS + 0.5PG. a. What are the equilibrium prices of gold and silver? b. What if a new discovery of gold doubles the quantity supplied to 150? How will this discovery affect the prices of both gold and silver? 2. Using general equilibrium analysis, and taking into account feedback effects, analyze the following: a. The likely effects of outbreaks of disease on chicken farms on the markets for chicken and pork. b. The effects of increased taxes on airline tickets on travel to major tourist destinations such as Florida CHAPTER 16 • General Equilibrium and Economic Efficiency 629 and California and on the hotel rooms in those destinations. change if the monopsonist in the labor market were also a monopolist in the output market? 3. Jane has 3 liters of soft drinks and 9 sandwiches. Bob, on the other hand, has 8 liters of soft drinks and 4 sandwiches. With these endowments, Jane’s marginal rate of substitution (MRS) of soft drinks for sandwiches is 4 and Bob’s M
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RS is equal to 2. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is, explain why. If it is not, what exchanges will make both parties better off? 4. Jennifer and Drew consume orange juice and coffee. Jennifer’s MRS of orange juice for coffee is 1 and Drew’s MRS of orange juice for coffee is 3. If the price of orange juice is $2 and the price of coffee is $3, which market is in excess demand? What do you expect to happen to the prices of the two goods? 5. Fill in the missing information in the following tables. For each table, use the information provided to identify a possible trade. Then identify the final allocation and a possible value for the MRS at the efficient solution. (Note: There is more than one correct answer.) Illustrate your results using Edgeworth box diagrams. a. Norman’s MRS of food for clothing is 1 and Gina’s MRS of food for clothing is 4: INDIVIDUAL INITIAL ALLOCATION TRADE FINAL ALLOCATION Norman Gina 6F, 2C 1F, 8C b. Michael’s MRS of food for clothing is 1/2 and Kelly’s MRS of food for clothing is 3. INDIVIDUAL INITIAL ALLOCATION TRADE FINAL ALLOCATION Michael Kelly 10F, 3C 5F, 15C 6. In the analysis of an exchange between two people, suppose both people have identical preferences. Will the contract curve be a straight line? Explain. Can you think of a counterexample? 7. Give an example of conditions when the production possibilities frontier might not be concave. 8. A monopsonist buys labor for less than the competitive wage. What type of inefficiency will this use of monopsony power cause? How would your answer 9. The Acme Corporation produces x and y units of goods Alpha and Beta, respectively. a. Use a production possibility frontier to explain how the willingness to produce more or less Alpha depends on the marginal rate of transformation of Alpha or Beta. b. Consider two cases of production extremes: (i) Acme produces zero units of Alpha initially, or (ii) Acme produces zero units of Beta initially. If Acme always tries to stay on its production possibility frontier, describe the initial positions of cases (i) and (ii). What happens as the Acme Corporation begins
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to produce both goods? 10. In the context of our analysis of the Edgeworth production box, suppose that a new invention changes a constant-returns-to-scale food production process into one that exhibits sharply increasing returns. How does this change affect the production contract curve? 11. Suppose that country A and country B both produce wine and cheese. Country A has 800 units of available labor, while country B has 600 units. Prior to trade, country A consumes 40 pounds of cheese and 8 bottles of wine, and country B consumes 30 pounds of cheese and 10 bottles of wine. COUNTRY A COUNTRY B Labor per pound cheese Labor per bottle wine 10 50 10 30 a. Which country has a comparative advantage in the production of each good? Explain. b. Determine the production possibilities curve for each country, both graphically and algebraically. (Label the pretrade production point PT and the post-trade point P.) c. Given that 36 pounds of cheese and 9 bottles of wine are traded, label the post-trade consumption point C. d. Prove that both countries have gained from trade. e. What is the slope of the price line at which trade occurs? 12. Suppose a bakery has 16 employees to be designated as bread bakers (B) and cake bakers (C), so that B + C = 16. Draw the production possibilities frontier for bread (y) and cakes (x) for the following production functions: a. y = 2B.5 and x = C.5 b. y = B and x = 2C.5 This page intentionally left blank C H A P T E R 17 Markets with Asymmetric Information For most of this book, we have assumed that consumers and producers have complete information about the economic variables that are relevant for the choices they face. Now we will see what happens when some parties know more than others—i.e., when there is asymmetric information. Asymmetric information is quite common. Frequently, a seller of a product knows more about its quality than the buyer does. Workers usually know their own skills and abilities better than employers. And business managers know more about their firms’ costs, competitive positions, and investment opportunities than do the firms’ owners. Asymmetric information also explains many institutional arrangements in our society. It is one reason why automobile companies offer warranties on parts and service for new cars; why firms and employees sign contracts that include incentives and rewards; and why the shareholders of corporations must monitor the behavior of
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managers. We begin by examining a situation in which the sellers of a product have better information about its quality than buyers have. We will see how this kind of asymmetric information can lead to market failure. In the second section, we see how sellers can avoid some of the problems associated with asymmetric information by giving potential buyers signals about the quality of their product. Product warranties provide a type of insurance that can be helpful when buyers have less information than sellers. But as the third section shows, the purchase of insurance entails difficulties of its own when buyers have better information than sellers. In the fourth section, we show that managers may pursue goals other than profit maximization when it is costly for owners of private corporations to monitor their behavior. In other words, managers have better information than owners. We also show how firms can give managers an incentive to maximize profits even when monitoring their behavior is costly. Finally, we show that labor markets may operate inefficiently when employees have better information about their productivity than employers have 17.1 Quality Uncertainty and the Market for Lemons 632 17.2 Market Signaling 638 17.3 Moral Hazard 643 17.4 The Principal–Agent Problem 645 *17.5 Managerial Incentives in an Integrated Firm 651 17.6 Asymmetric Information in Labor Markets: Efficiency Wage Theory 654 17.1 Medicare 636 17.2 Lemons in Major League Baseball 637 17.3 Working into the Night 642 17.4 Reducing Moral Hazard: Warranties of Animal Health 645 17.5 CEO Salaries 647 17.6 Managers of Nonprofit Hospitals as Agents 649 17.7 Efficiency Wages at Ford Motor Company 656 631 632 PART 4 • Information, Market Failure, and the Role of Government • asymmetric information Situation in which a buyer and a seller possess different information about a transaction. 17.1 Quality Uncertainty and the Market for Lemons Suppose you bought a new car for $20,000, drove it 100 miles, and then decided you really didn’t want it. There was nothing wrong with the car—it performed beautifully and met all your expectations. You simply felt that you could do just as well without it and would be better off saving the money for other things. So you decide to sell the car. How much should you expect to get for it? Probably not more than $16,000—even though the car is brand new, has been driven only 100 miles, and has a
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warranty that is transferable to a new owner. And if you were a prospective buyer, you probably wouldn’t pay much more than $16,000 yourself. Why does the mere fact that the car is second-hand reduce its value so much? To answer this question, think about your own concerns as a prospective buyer. Why, you would wonder, is this car for sale? Did the owner really change his or her mind about the car just like that, or is there something wrong with it? Is this car a “lemon”? Used cars sell for much less than new cars because there is asymmetric information about their quality: The seller of a used car knows much more about the car than the prospective buyer does. The buyer can hire a mechanic to check the car, but the seller has had experience with it and will know more about it. Furthermore, the very fact that the car is for sale indicates that it may be a “lemon”—why sell a reliable car? As a result, the prospective buyer of a used car will always be suspicious of its quality—and with good reason. The implications of asymmetric information about product quality were first analyzed by George Akerlof and go far beyond the market for used cars.1 The markets for insurance, financial credit, and even employment are also characterized by asymmetric information about product quality. To understand the implications of asymmetric information, we will start with the market for used cars and then see how the same principles apply to other markets. The Market for Used Cars Suppose two kinds of used cars are available—high-quality cars and low-quality cars. Also suppose that both sellers and buyers can tell which kind of car is which. There will then be two markets, as illustrated in Figure 17.1. In part (a), SH is the supply curve for high-quality cars, and DH is the demand curve. Similarly, SL and DL in part (b) are the supply and demand curves for low-quality cars. For any given price, SH lies to the left of SL because owners of high-quality cars are more reluctant to part with them and must receive a higher price to do so. Similarly, DH is higher than DL because buyers are willing to pay more to get a high-quality car. As the figure shows, the market price for high-quality cars is $10,000, for low-quality cars $5000, and 50,000 cars of each type are sold. In reality,
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the seller of a used car knows much more about its quality than a buyer does. (Buyers discover the quality only after they buy a car and drive it for a while.) Consider what happens, then, if sellers know the quality of cars, but buyers do not. Initially, buyers might think that the odds are 50-50 that a car will be high quality. Why? Because when both sellers and buyers know 1George A. Akerlof, “The Market for ’Lemons’: Quality Uncertainty and the Market Mechanism,” Quarterly Journal of Economics (August 1970): 488–500. CHAPTER 17 • Markets with Asymmetric Information 633 PH $10,000 $7500 $5000 PL $10,000 $7500 $5000 SH DH DM DLM DL SL DM DLM DL 25,000 50,000 (a) High-Quality Cars 50,000 75,000 (b) Low-Quality Cars FIGURE 17.1 THE MARKET FOR USED CARS When sellers of products have better information about product quality than buyers, a “lemons problem” may arise in which low-quality goods drive out high-quality goods. In (a) the demand curve for high-quality cars is DH. However, as buyers lower their expectations about the average quality of cars on the market, their perceived demand shifts to DM. Likewise, in (b) the perceived demand curve for low-quality cars shifts from DL to DM. As a result, the quantity of high-quality cars sold falls from 50,000 to 25,000, and the quantity of low-quality cars sold increases from 50,000 to 75,000. Eventually, only low-quality cars are sold. the quality, 50,000 cars of each type are sold. When making a purchase, buyers therefore view all cars as “medium quality,” in the sense that there is an equal chance of getting a high-quality or a low-quality car. (Of course, after buying the car and driving it for a while, they will learn its true quality.) The demand for cars perceived to be medium quality, denoted by DM in Figure 17.1, is below DH but above DL. As the figure shows, these medium-quality cars will sell for about $7500 each. However, fewer high-quality cars (25,000) and more low-quality cars (75,000) will now be sold. As consumers
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begin to realize that most cars sold (about three-fourths of the total) are low quality, their perceived demand shifts. As Figure 17.1 shows, the new perceived demand curve might be DLM, which means that, on average, cars are thought to be of low to medium quality. However, the mix of cars then shifts even more heavily to low quality. As a result, the perceived demand curve shifts further to the left, pushing the mix of cars even further toward low quality. This shifting continues until only low-quality cars are sold. At that point, the market price would be too low to bring forth any high-quality cars for sale, so consumers correctly assume that any car they buy will be low quality. As a result, the only relevant demand curve will be DL. The situation in Figure 17.1 is extreme. The market may come into equilibrium at a price that brings forth at least some high-quality cars. But the fraction of high-quality cars will be smaller than it would be if consumers could identify 634 PART 4 • Information, Market Failure, and the Role of Government quality before making the purchase. That is why you should expect to sell your brand new car, which you know is in perfect condition, for much less than you paid for it. Because of asymmetric information, low-quality goods drive high-quality goods out of the market. This phenomenon, which is sometimes referred to as the lemons problem, is an important source of market failure. It is worth emphasizing: The lemons problem: With asymmetric information, low-quality goods can drive high-quality goods out of the market. Implications of Asymmetric Information Our used cars example shows how asymmetric information can result in market failure. In an ideal world of fully functioning markets, consumers would be able to choose between low-quality and high-quality cars. While some will choose low-quality cars because they cost less, others will prefer to pay more for highquality cars. Unfortunately, consumers cannot in fact easily determine the quality of a used car until after they purchase it. As a result, the price of used cars falls, and high-quality cars are driven out of the market. Market failure arises, therefore, because there are owners of high-quality cars who value their cars less than potential buyers of high-quality cars. Both parties could enjoy gains from trade, but, unfortunately, buyers’ lack of information prevents this mutually beneficial trade from occurring. ADVERSE SELECTION Our used
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car scenario is a simplified illustration of an important problem that affects many markets—the problem of adverse selection. Adverse selection arises when products of different qualities are sold at a single price because buyers or sellers are not sufficiently informed to determine the true quality at the time of purchase. As a result, too much of the low-quality product and too little of the high-quality product are sold in the marketplace. Let’s look at some other examples of asymmetric information and adverse selection. In doing so, we will also see how the government or private firms might respond to the problem. THE MARKET FOR INSURANCE Why do people over age 65 have difficulty buying medical insurance at almost any price? Older people do have a much higher risk of serious illness, but why doesn’t the price of insurance rise to reflect that higher risk? Again, the reason is asymmetric information. People who buy insurance know much more about their general health than any insurance company can hope to know, even if it insists on a medical examination. As a result, adverse selection arises, much as it does in the market for used cars. Because unhealthy people are more likely to want insurance, the proportion of unhealthy people in the pool of insured people increases. This forces the price of insurance to rise, so that more healthy people, aware of their low risks, elect not to be insured. This further increases the proportion of unhealthy people among the insured, thus forcing the price of insurance up more. The process continues until most people who want to buy insurance are unhealthy. At that point, insurance becomes very expensive, or—in the extreme—insurance companies stop selling the insurance. Adverse selection can make the operation of insurance markets problematic in other ways. Suppose an insurance company wants to offer a policy for • adverse selection Form of market failure resulting when products of different qualities are sold at a single price because of asymmetric information, so that too much of the low-quality product and too little of the high-quality product are sold. CHAPTER 17 • Markets with Asymmetric Information 635 a particular event, such as an auto accident that results in property damage. It selects a target population—say, men under age 25—to whom it plans to market this policy, and it estimates that the probability of an accident for people in this group is.01. However, for some of these people, the probability of having an accident is much less than.01; for others, it is much higher than.01. If the insurance company
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cannot distinguish between high- and low-risk men, it will base the premium on the average accident probability of.01. What will happen? Those people with low probabilities of having an accident will choose not to insure, while those with high probabilities of an accident will purchase the insurance. This in turn raises the accident probability among those who choose to be insured above.01, forcing the insurance company to raise its premium. In the extreme, only those who are likely to be in an accident will choose to insure, making it impractical to sell insurance. One solution to the problem of adverse selection is to pool risks. For health insurance, the government might take on this role, as it does with the Medicare program. By providing insurance for all people over age 65, the government eliminates the problem of adverse selection. Likewise, insurance companies will try to avoid or at least reduce the adverse selection problem by offering group health insurance policies at places of employment. By covering all workers in a firm, whether healthy or sick, the insurance company spreads risks and thereby reduces the likelihood that large numbers of high-risk individuals will purchase insurance.2 THE MARKET FOR CREDIT By using a credit card, many of us borrow money without providing any collateral. Most credit cards allow the holder to run a debt of several thousand dollars, and many people hold several credit cards. Credit card companies earn money by charging interest on the debit balance. But how can a credit card company or bank distinguish high-quality borrowers (who pay their debts) from low-quality borrowers (who don’t)? Clearly, borrowers have better information—i.e., they know more about whether they will pay than the lender does. Again, the lemons problem arises. Low-quality borrowers are more likely than high-quality borrowers to want credit, which forces the interest rate up, which increases the number of low-quality borrowers, which forces the interest rate up further, and so on. In fact, credit card companies and banks can, to some extent, use computerized credit histories, which they often share with one another, to distinguish low-quality from high-quality borrowers. Many people, however, think that computerized credit histories invade their privacy. Should companies be allowed to keep these credit histories and share them with other lenders? We can’t answer this question for you, but we can point out that credit histories perform an important function: They eliminate, or at least greatly reduce, the problem of asymmetric information and adverse selection—a problem that might otherwise prevent
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credit markets from operating. Without these histories, even the creditworthy would find it extremely costly to borrow money. 2Some people argue that pooling risks is not the main justification for Medicare, because most people’s medical histories are well established by age 65, making it feasible for insurance companies to distinguish among high-risk and low-risk individuals. Another justification for Medicare is a distributional one. After age 65, even relatively healthy people are likely to need more medical care, making insurance expensive even without asymmetric information, and many older people would not have sufficient income to purchase the insurance. 636 PART 4 • Information, Market Failure, and the Role of Government The Importance of Reputation and Standardization Asymmetric information is also present in many other markets. Here are just a few examples: • Retail stores: Will the store repair or allow you to return a defective product? The store knows more about its policy than you do. • Dealers of rare stamps, coins, books, and paintings: Are the items real or counterfeit? The dealer knows much more about their authenticity than you do. • Roofers, plumbers, and electricians: When a roofer repairs or renovates the roof of your house, do you climb up to check the quality of the work? • Restaurants: How often do you go into the kitchen to check if the chef is using fresh ingredients and obeying health laws? In all these cases, the seller knows much more about the quality of the product than the buyer does. Unless sellers can provide information about quality to buyers, low-quality goods and services will drive out high-quality ones, and there will be market failure. Sellers of high-quality goods and services, therefore, have a big incentive to convince consumers that their quality is indeed high. In the examples cited above, this task is performed largely by reputation. You shop at a particular store because it has a reputation for servicing its products; you hire particular roofers or plumbers because they have reputations for doing good work; you go to a particular restaurant because it has a reputation for using fresh ingredients and nobody you know has become sick after eating there. Amazon and other online vendors use another model to maintain their reputation. They allow customers to rate and comment on products. The rating and commenting feature reduces the lemons problem by giving customers more information and motivating vendors to uphold their end of the bargain. Sometimes, however, it is impossible for a business to develop a reputation. For example, because most of the
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customers of highway diners or motels go there only once or infrequently, the businesses have no opportunity to develop reputations. How, then, can they deal with the lemons problem? One way is standardization. In your hometown, you may not prefer to eat regularly at McDonald’s. But a McDonald’s may look more attractive when you are driving along a highway and want to stop for lunch. Why? Because McDonald’s provides a standardized product: The same ingredients are used and the same food is served in every McDonald’s anywhere in the country. Who knows? Joe’s Diner might serve better food, but at least you know exactly what you will be buying at McDonald’s. E XAM PLE 17.1 MEDICARE Health care reform has been at the forefront of policy debates in the United States and worldwide for years. A core issue in the United States is whether everyone should have health insurance, and whether participation in some kind of public or private insurance program should be mandatory. To understand the argument for mandatory participation, just look at Medicare. Medicare was created in 1965 as a public program that provides health insurance to all individuals over age 65 and those under age 65 with certain disabilities. Medicare has been financed by CHAPTER 17 • Markets with Asymmetric Information 637 payroll taxes, paid in part by workers and in part by employers. (In 2011, 1.45% was withheld from workers’ paychecks and a matching 1.45% was paid by the employers; those rates are scheduled to increase in 2013.) The central feature of Medicare is that participation is mandatory—essentially all workers are part of the program. Indeed, mandatory participation is what makes Medicare work, and what distinguishes it from other public and private health care programs. To see why mandatory participation is essential, imagine an alternative in which private insurers offer insurance policies to the elderly at a cost of $5,000 per year. Remember that there is asymmetric information: people know much more about their health, their lifestyles, and their likely health care needs in the future than insurance companies can possibly know. Now think about who will choose to buy the insurance and who will choose to forgo the $5,000 annual expense. Those seniors who have chronic diseases or for other reasons expect their health care costs to exceed $5,000 are much more likely to buy the insurance than those who are in excellent health and thus expect lower costs. This creates an adverse selection problem: mostly sick
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people will buy the insurance, which means the insurance company will be lose money and will need to raise the price of coverage, say to $7,000. But this is not a stable outcome, since only those people with relatively poor health who expect healthcare costs above $7,000 will buy coverage, and once again the insurance company will be in the red. Each time the insurance company raises its price, some of the healthier remaining customers will drop out, until finally only very sick people will want to buy insurance. (This was essentially the situation prior to 1965.) And what happens when some of the uninsured people get sick? Some may be wealthy enough to pay for their medical costs out of pocket. But most people are not so wealthy, and they will end up in the emergency room of their local hospital, which is required by law to treat them. As a result, the cost of health care for most seniors will be borne by society as a whole, in part through the subsidization of emergency room visits. Medicare solves this adverse selection problem. All people over 65 participate in Medicare—those expecting low health care costs along with those who expect high costs. Of course, the low-cost participants are subsidizing those with high costs. But because adverse selection is not a problem with a mandatory program, the overall cost of Medicare is lower than the cost of most private insurance systems. Indeed, Medicare has earned a reputation as one of the most successful and efficient public programs in the United States. EXAM PLE 17.2 LEMONS IN MAJOR LEAGUE BASEBALL How can we test for the presence of a lemons market? One way is to compare the performance of products that are resold with similar products that are seldom put up for resale. In a lemons market, because purchasers of secondhand products will have limited information, resold products should be lower in quality than products that rarely appear on the market. One such “second-hand” market was created some time ago by a change in the rules governing contracts in major league baseball.3 Before 1976, major league baseball teams had the exclusive right to renew a player’s contract. After a 1976 ruling declared this system illegal, a new contracting arrangement was created. After six years of major league service, players can now sign new contracts with their original teams or become free agents and sign with new teams. The availability of many free agents creates a second-hand market in baseball players. 3This example is based on Kenneth Lehn�
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�s study of the free-agent market. See “Information Asymmetries in Baseball’s Free-Agent Market,” Economic Inquiry (1984): 37–44. 638 PART 4 • Information, Market Failure, and the Role of Government Asymmetric information is prominent in the free-agent market. One potential purchaser, the player’s original team, has better information about the player’s abilities than other teams have. If we were looking at used cars, we could test for the existence of asymmetric information by comparing their repair records. In baseball, we can compare player disability records. If players are working hard and following rigorous conditioning programs, we would expect a low probability of injury and a high probability that they will be able to perform if injured. In other words, more motivated players will spend less time on the bench owing to disabilities. If a lemons market exists, we would expect free agents to have higher disability rates than players who are renewed. Players may also have preexisting physical conditions which their original teams know about and which make them less desirable candidates for contract renewal. Because more such players would become free agents, free agents would experience higher disability rates for health reasons. Table 17.1, which lists the post-contract performance of all players who have signed multiyear contracts, makes two points. First, both free agents and renewed players have increased disability rates after signing new contracts. The disabled days per season increase from an average of 4.73 to an average of 12.55. Second, the postcontract disability rates of renewed and non-renewed players are significantly different. On average, renewed players are disabled for 9.68 days, free agents for 17.23 days. These two findings suggest that there is a lemons market in free agents that exists because baseball teams know their own players better than the teams with which they compete. TABLE 17.1 PLAYER DISABILITY DAYS SPENT ON DISABLED LIST PER SEASON PRECONTRACT POSTCONTRACT PERCENTAGE CHANGE All players Renewed players Free agents 4.73 4.76 4.67 12.55 9.68 17.23 165.4 103.4 268.9 17.2 Market Signaling We have seen that asymmetric information can sometimes lead to a lemons problem: Because sellers know more about the quality of a good than buyers do, buyers may assume that quality is low, causing price to fall and only low-quality goods to be sold.
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We also saw how government intervention (in the market for health insurance, for example) or the development of a reputation (in service industries, for example) can alleviate this problem. Now we will examine another important mechanism through which sellers and buyers deal with the problem of asymmetric information: market signaling. The concept of market signaling was first developed by Michael Spence, who showed that in some markets, sellers send buyers signals that convey information about a product’s quality.4 To see how market signaling works, let’s look at a labor market, which is a good example of a market with asymmetric information. Suppose a firm is thinking about hiring some new people. The new workers (the “sellers” of labor) know 4Michael Spence, Market Signaling (Cambridge, MA: Harvard University Press, 1974). • market signaling Process by which sellers send signals to buyers conveying information about product quality. CHAPTER 17 • Markets with Asymmetric Information 639 much more about the quality of the labor they can provide than does the firm (the buyer of labor). For example, they know how hard they tend to work, how responsible they are, what their skills are, and so forth. The firm will learn these things only after workers have been hired and have been working for some time. Why don’t firms simply hire workers, see how well they work, and then fire those with low productivity? Because this policy is often very costly. In many countries, and in many firms in the United States, it is difficult to fire someone who has been working more than a few months. (The firm may have to show just cause or provide severance pay.) Moreover, in many jobs, workers do not become fully productive for at least six months. Before that time, considerable on-the-job training may be required, for which the firm must invest substantial resources. Thus the firm might not learn how good workers are for six months to a year. Clearly, firms would be much better off if they knew how productive potential employees were before they hired them. What characteristics can a firm examine to obtain information about people’s productivity before it hires them? Can potential employees convey information about their productivity? Dressing well for the job interview might convey some information, but even unproductive people can dress well. Dressing well is thus a weak signal—it doesn’t do much to distinguish high-productivity from lowproductivity people. To be strong, a signal must be
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easier for high-productivity people to give than for low-productivity people to give, so that high-productivity people are more likely to give it. For example, education is a strong signal in labor markets. A person’s educational level can be measured by several things—the number of years of schooling, degrees obtained, the reputation of the university or college that granted the degrees, the person’s grade-point average, and so on. Of course, education can directly and indirectly improve a person’s productivity by providing information, skills, and general knowledge that are helpful in work. But even if education did not improve productivity, it would still be a useful signal of productivity because more productive people find it easier to attain high levels of education. Not surprisingly, productive people tend to be more intelligent, more motivated, more disciplined, and more energetic and hard-working—characteristics that are also helpful in school. More productive people are therefore more likely to attain high levels of education in order to signal their productivity to firms and thereby obtain better-paying jobs. Thus, firms are correct in considering education a signal of productivity. A Simple Model of Job Market Signaling To understand how signaling works, we will discuss a simple model.5 Let’s assume that there are only low-productivity workers (Group I), whose average and marginal product is 1, and high-productivity workers (Group II), whose average and marginal product is 2. Workers will be employed by competitive firms whose products sell for $10,000, and who expect an average of 10 years’ work from each employee. We also assume that half the workers in the population are in Group I and the other half in Group II, so that the average productivity of all workers is 1.5. Note that the revenue expected to be generated from Group I workers is $100,000 ($10,000/year * 10 years) and from Group II workers is $200,000 ($20,000/year * 10 years). If firms could identify people by their productivity, they would offer them a wage equal to their marginal revenue product. Group I people would be paid $10,000 per year, Group II people $20,000. On the other hand, if firms could not 5This is essentially the model developed in Spence, Market Signaling. 640 PART 4 • Information, Market Failure, and the Role of Government identify productivity before they hired people, they would pay all workers an annual wage equal
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to the average productivity—$15,000. Group I people would then earn more ($15,000 instead of $10,000), at the expense of Group II people (who would earn $15,000 instead of $20,000). Now let’s consider what can happen with signaling via education. Suppose all the attributes of an education (degrees earned, grade-point average, etc.) can be summarized by a single index y that represents years of higher education. All education involves a cost, and the higher the educational level y, the higher the cost. This cost includes tuition and books, the opportunity cost of foregone wages, and the psychic cost of having to work hard to obtain high grades. What is important is that the cost of education is greater for the low-productivity group than for the high-productivity group. We might expect this to be the case for two reasons. First, low-productivity workers may simply be less studious. Second, low-productivity workers may progress more slowly through degree programs. In particular, suppose that for Group I people, the cost of attaining educational level y is given by CI(y) = $40,000y and the cost for Group II people is CII(y) = $20,000y Now suppose (to keep things simple and to dramatize the importance of signaling) that education does nothing to increase one’s productivity; its only value is as a signal. Let’s see if we can find a market equilibrium in which different people obtain different levels of education, and in which firms look at education as a signal of productivity. EQUILIBRIUM Consider the following possible equilibrium. Suppose firms use this decision rule: Anyone with an education level of y* or more is a Group II person and is offered a wage of $20,000, while anyone with an education level below y* is a Group I person and is offered a wage of $10,000. The particular level y* that the firms choose is arbitrary, but for this decision rule to be part of an equilibrium, firms must have identified people correctly. Otherwise, the firms will want to change the rule. Will it work? To answer this question, we must determine how much education the people in each group will obtain, given that firms are using this decision rule. To do this, remember that education allows one to get a better-paying job. The benefit of education B(y) is the increase in the wage associated
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Subsets and Splits
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