Split (1)

train · 11.7k rows

text stringlengths 204 3.13k
; x ¼ ¼ 2,000 88 ð 8,796: Þ y ¼ ¼ 1=2 0:1 1,950 ð ’ Þ (19:21) (19:22) Total output has increased by 23 feet of newsprint with no change in total labor input. The market-based allocation was inefﬁcient because ﬁrm x did not take into account the negative effect of its hiring decisions on ﬁrm y. Marginal productivity. This can be illustrated in another way by computing the true social marginal productivity of labor input to ﬁrm x. If that ﬁrm were to hire one more worker, its own output would increase to 2,000 x ¼ 1=2 401 Þ ð ¼ 40,050: (19:23) As proﬁt maximization requires, the (private) marginal value product of the 401st worker is equal to the wage. But increasing x’s output now also has an effect on ﬁrm y—its output decreases by about 21 units. Hence the social marginal revenue product of labor to ﬁrm x $21). That is why the manager of a merged ﬁrm would actually amounts to only $29 ($50 ﬁnd it proﬁtable to shift some workers from ﬁrm x to ﬁrm y. ’ QUERY: Suppose a How would such an externality affect the allocation of labor? ¼ þ 0.1. What would that imply about the relationship between the ﬁrms? Chapter 19: Externalities and Public Goods 691 Solutions to the Externality Problem Incentive-based solutions to the allocational harm of externalities start from the basic observation that output of the externality-producing activity is too high under a marketdetermined equilibrium. Perhaps the ﬁrst economist to provide a complete analysis of this distortion was A. C. Pigou, who in the 1920s suggested that the most direct solution would simply be to tax the externality-creating entity.4 All incentive-based solutions to the externality problem stem from this basic insight.5 A graphic analysis Figure 19.1 provides the traditional illustration of an externality together with Pigou’s taxation solution. The competitive supply curve for good x also represents that good’s private marginal costs of production (MC). When the
demand for x is given by DD, the market equilibrium will occur at x1. The external costs involved in x production create a divergence between private marginal costs (MC) and overall social marginal costs (MC 0)—the vertical distance between the two curves represents the costs that x FIGURE 19.1 Graphic Analysis of an Externality The demand curve for good x is given by DD. The supply curve for x represents the private marginal costs (MC) involved in x production. If x production imposes external costs on third parties, social marginal costs (MC 0) will exceed MC by the extent of these costs. Market equilibrium occurs at x1 and, at this output level, social marginal costs exceed what consumers pay for good x. A tax of amount t that reﬂects the costs of the externalities would achieve the efﬁcient output of x—given by output level x2. Price, costs D MC′ S = MC p2 p1 t D x2 x1 Output of x per period 4A. C. Pigou, The Economics of Welfare (London: MacMillan, 1920). Pigou also recognized the importance of subsidizing goods that yield positive externalities. 5We do not discuss purely regulatory solutions here, although the study of such solutions forms an important part of most courses in environmental economics. See W. J. Baumol and W. E. Oates, The Theory of Environmental Policy, 2nd ed. (Cambridge: Cambridge University Press, 2005) and the Extensions to this chapter. 692 Part 8: Market Failure production poses for third parties (in our examples, only on ﬁrm y). Notice that the per-unit costs of these externalities need not be constant, independent of x output. In the ﬁgure, for example, the size of these external costs increases as x output expands (i.e., MC 0 and MC become further apart). At the market-determined output level x1, the comprehensive social marginal cost exceeds the market price p1, thereby indicating that the production of x has been pushed ‘‘too far.’’ It is clear from the ﬁgure that the optimal output level is x2, at which the market price p2 paid for the good now reﬂects all costs. As is the case for any tax, imposition of a Pigovian tax would create a vertical wedge between the demand and supply curves for good x
. In Figure 19.1 this optimal tax is shown as t. Imposition of this tax serves to reduce output to x2, the social optimum. Tax collections equal the precise amount of external harm that x production causes. These collections might be used to compensate ﬁrm y for these costs, but this is not crucial to the analysis. Notice here that the tax must be set at the level of harm prevailing at the optimum (i.e., at x2), not at the level of harm at the original market equilibrium (x1). This point is also made in the next example and more completely in the next section by returning to our simple general equilibrium model. EXAMPLE 19.2 A Pigovian Tax on Newsprint The inefﬁciency in Example 19.1 arises because the upstream newsprint producer (ﬁrm x) takes no account of the effect that its production has on ﬁrm y. A suitably chosen tax on ﬁrm x can cause it to reduce its hiring to a level at which the externality vanishes. Because the river can absorb the pollutants generated with an output of x 38,000, we might consider imposing a tax (t) on the ﬁrm’s output that encourages it to reduce output to this level. Because output will be 38,000 if lx ¼ 361, we can calculate t from the labor demand condition: ¼ or 1 ð t 1 MPL ¼ ð Þ ’ ’ t 1,000 Þ 361 Þ ð ’ 0:5 50, ¼ 0:05: t ¼ (19:24) (19:25) Such a 5 percent tax would effectively reduce the price ﬁrm x receives for its newsprint to $0.95 and provide it with an incentive to reduce its hiring by 39 workers. Now, because the river can handle all the pollutants that x produces, there is no externality in the production function of ﬁrm y. It will hire 400 workers and produce 40,000 feet of newsprint per day. Observe that total newsprint output is now 78,000, a signiﬁcantly higher ﬁgure than would be produced in the untaxed situation. The taxation solution provides a considerable improvement in the efﬁciency of resource allocation. QUERY: The tax rate proposed here (0.05) seems rather
unit is given by px ’ r, where r is the payment the ﬁrm must make for each unit it produces. Firm y must decide how many rights to sell to ﬁrm x. Because it will be paid r for each right, it must ‘‘choose’’ x output to maximize its proﬁts: xi, x0Þ þ ð the ﬁrst-order condition for a maximum is py ¼ pyg rx0; @py @x0 ¼ py g2 þ r ¼ 0 or r py g2: ¼ ’ (19:28) (19:29) Equation 19.29 makes clear that the equilibrium solution to pricing in the pollution rights market will be identical to the Pigovian tax equilibrium. From the point of view of ﬁrm x, it makes no difference whether a tax of amount t is paid to the government or a royalty r of the same amount is paid to ﬁrm y. So long as t r (a condition ensured by Equation 19.29), the same efﬁcient equilibrium will result. ¼ The Coase theorem In a famous 1960 paper, Ronald Coase showed that the key feature of the pollution rights equilibrium is that these rights be well deﬁned and tradable with zero transaction costs.6 The initial assignment of rights is irrelevant because subsequent trading will always yield the same efﬁcient equilibrium. In our example we initially assigned the rights to ﬁrm y, allowing that ﬁrm to trade them away to ﬁrm x for a per-unit fee r. If the rights had been assigned to ﬁrm x instead, that ﬁrm still would have to impute some cost to using these rights themselves rather than selling them to ﬁrm y. This calculation, in combination with ﬁrm y’s decision about how many such rights to buy, will again yield an efﬁcient result. 6R. Coase, ‘‘The Problem of Social Cost,’’ Journal of Law and Economics 3 (October 1960): 1–44. 694 Part 8: Market Failure To illustrate the Coase result, assume that ﬁrm x is given xT rights to produce (and to pollute). It can choose to use some of these to support its own production
(x0), or it may sell some to ﬁrm y (an amount given by xT x0). Gross proﬁts for x are given by ’ x0 þ rxT px ’ r f Þ ð yiÞ þ ¼ ð rxT (19:30) px ¼ and for y by pxx0 þ xT r ð x0Þ ¼ ð px ’ r Þ ’ py ¼ py g xi, x0Þ ’ ð r xT ð : x0Þ ’ (19:31) Clearly, proﬁt maximization in this situation will lead to precisely the same solution as in the case where ﬁrm y was assigned the rights. Because the overall total number of rights (xT) is a constant, the ﬁrst-order conditions for a maximum will be exactly the same in the two cases. This independence of initial rights assignment is usually referred to as the Coase theorem. Although the results of the Coase theorem may seem counterintuitive (how can the level of pollution be independent of who initially owns the rights?), it is in reality nothing more than the assertion that, in the absence of impediments to making bargains, all mutually beneﬁcial transactions will be completed. When transaction costs are high or when information is asymmetric, initial rights assignments will matter because the sorts of trading implied by the Coase theorem may not occur. Therefore, it is the limitations of the Coase theorem that provide the most interesting opportunities for further analysis. This analysis has been especially far reaching in the ﬁeld of law and economics,7 where the theorem has been applied to such topics as tort liability laws, contract law, and product safety legislation (see Problem 19.4). Attributes of Public Goods We now turn our attention to a related set of problems about the relationship between competitive markets and the allocation of resources: those raised by the existence of public goods. We begin by providing a precise deﬁnition of this concept and then examine why such goods pose allocational problems. We then brieﬂy discuss theoretical ways in which such problems might be mitigated before turning to examine how actual decisions on public goods are made through voting. The most common deﬁnitions of public goods stress two attributes of such goods: nonexclusivity and nonrivalness.
We now describe these attributes in detail. Nonexclusivity The ﬁrst property that distinguishes public goods concerns whether individuals may be excluded from the beneﬁts of consuming the good. For most private goods such exclusion is indeed possible: I can easily be excluded from consuming a hamburger if I don’t pay for it. In some cases, however, such exclusion is either very costly or impossible. National defense is the standard example. Once a defense system is established, everyone in a country beneﬁts from it whether they pay for it or not. Similar comments apply, on a more local level, to goods such as mosquito control or a program to inoculate against disease. In these cases, once the programs are implemented, no one in the community can be excluded from those beneﬁts whether he or she pays for them or not. Hence we can divide goods into two categories according to the following deﬁnition. 7The classic text is R. A. Posner, Economic Analysis of Law, 4th ed. (Boston: Little, Brown, 1992). A more mathematical approach is T. J. Miceli, Economics of the Law (New York: Oxford University Press, 1997). Chapter 19: Externalities and Public Goods 695 Exclusive goods. A good is exclusive if it is relatively easy to exclude individuals from beneﬁting from the good once it is produced. A good is nonexclusive if it is impossible (or costly) to exclude individuals from beneﬁting from the good. Nonrivalry A second property that characterizes public goods is nonrivalry. A nonrival good is one for which additional units can be consumed at zero social marginal cost. For most goods, of course, consumption of additional amounts involves some marginal costs of production. Consumption of one more hot dog requires that various resources be devoted to its production. However, for certain goods this is not the case. Consider, for example, having one more automobile cross a highway bridge during an off-peak period. Because the bridge is already in place, having one more vehicle cross requires no additional resource use and does not reduce consumption elsewhere. Similarly, having one more viewer tune in to a television channel involves no additional cost, even though this action would result in additional consumption taking place. Therefore, we have developed the following deﬁnition Nonrival goods. A good is nonrival if consumption of additional units of the good involves zero social marginal costs of production
. Typology of public goods The concepts of nonexclusion and nonrivalry are in some ways related. Many nonexclusive goods are also nonrival. National defense and mosquito control are two examples of goods for which exclusion is not possible and additional consumption takes place at zero marginal cost. Many other instances might be suggested. The concepts, however, are not identical: some goods may possess one property but not the other. For example, it is impossible (or at least very costly) to exclude some ﬁshing boats from ocean ﬁsheries, yet the arrival of another boat clearly imposes social costs in the form of a reduced catch for all concerned. Similarly, use of a bridge during off-peak hours may be nonrival, but it is possible to exclude potential users by erecting toll booths. Table 19.1 presents a cross-classiﬁcation of goods by their possibilities for exclusion and their rivalry. Several examples of goods that ﬁt into each of the categories are provided. Many of the examples, other than those in the upper left corner of the table (exclusive and rival private goods), are often produced by governments. That is especially the case for nonexclusive goods because, as we shall see, it is difﬁcult to develop ways of paying for such goods other than through compulsory taxation. Nonrival goods often are privately produced (there are, after all, private bridges, swimming pools, and highways that consumers must pay to use) as long as nonpayers can be excluded from consuming them.8 Still, we will use the following stringent deﬁnition, which requires both conditions. 8Nonrival goods that permit imposition of an exclusion mechanism are sometimes referred to as club goods, because provision of such goods might be organized along the lines of private clubs. Such clubs might then charge a ‘‘membership’’ fee and permit unlimited use by members. The optimal size of a club is determined by the economies of scale present in the production process for the club good. For an analysis, see R. Cornes and T. Sandler, The Theory of Externalities, Public Goods, and Club Goods (Cambridge: Cambridge University Press, 1986). 696 Part 8: Market Failure TABLE 19.1 EXAMPLES SHOWING THE TYPOLOGY OF PUBLIC AND PRIVATE GOODS Rival Yes No Yes Hot dogs, automobiles, houses Exclusive No Fishing grounds, public grazing land, clean air Bridges, swimming pools, satellite
television transmission (scrambled) National defense, mosquito control, justice Public good. A good is a (pure) public good if, once produced, no one can be excluded from beneﬁting from its availability and if the good is nonrival—the marginal cost of an additional consumer is zero. Public Goods and Resource Allocation To illustrate the allocational problems created by public goods, we again employ a simple general equilibrium model. In this model there are only two individuals—a single-person economy would not experience problems from public goods because he or she would incorporate all of the goods’ beneﬁts into consumption decisions. We denote these two individuals by A and B. There are also only two goods in this economy. Good y is an ordinary private good, and each person begins with an allocation of this good given by y A $ and y B $, respectively. Each person may choose to consume some of his or her y directly or to devote some portion of it to the production of a single public good, x. The amounts contributed are given by y A s, and the public good is produced according to the production function s and y B Resulting utilities for these two people in this society are given by and U A x; yA $ ð ’ yA s Þ (19:32) (19:33) (19:34) U B x; yB ð $ yB s Þ ’ Notice here that the level of public good production, x, enters identically into each person’s utility function. This is the way in which the nonexclusivity and nonrivalry characteristics of such goods are captured mathematically. Nonexclusivity is reﬂected by the fact that each person’s consumption of x is the same and independent of what he or she contributes individually to its production. Nonrivalry is shown by the fact that the consumption of x by each person is identical to the total amount of x produced. Consumption of x beneﬁts by A does not diminish what B can consume. These two characteristics of good x constitute the barriers to efﬁcient production under most decentralized decision schemes, including competitive markets. The necessary conditions for efﬁcient resource allocation in this problem consist of s ) that maximize, say, A’s choosing the levels of public goods subscriptions (y A utility for any given level of B’s utility. The Lagrangian expression for this
problem is s and y B + U A x19:35) Chapter 19: Externalities and Public Goods 697 where K is a constant level of B’s utility. The ﬁrst-order conditions for a maximum are @+ @yA ’ kU B 1 f 0 0, ¼ @+ @yB s ¼ U A 1 f 0 kU B 2 þ ’ kU B 1 f 0 0: ¼ A comparison of these two equations yields the immediate result that kU B 2 ¼ U A 2 : (19:36) (19:37) (19:38) As might have been expected here, optimality requires that the marginal utility of y consumption for A and B be equal except for the constant of proportionality, l. This equation may now be combined with either Equation 19.36 or 19.37 to derive the optimality condition for producing the public good x. Using Equation 19.36, for example, gives or, more simply, U A 1 U A 2 þ kU B 1 kU B 2 ¼ 1 f 0 MRSA MRSB þ 1 f 0 : ¼ (19:39) (19:40) The intuition behind this condition, which was ﬁrst articulated by P. A. Samuelson,9 is that it is an adaptation of the efﬁciency conditions described in Chapter 13 to the case of public goods. For such goods, the MRS in consumption must reﬂect the amount of y that all consumers would be willing to give up to get one more x, because everyone will obtain the beneﬁts of the extra x output. Hence it is the sum of each individual’s MRS that should be equated to dy/dx in production (here given by 1/f 0). Failure of a competitive market Production of goods x and y in competitive markets will fail to achieve this allocational goal. With perfectly competitive prices px and py, each individual will equate his or her MRS to the price ratio px /py. A producer of good x would also set 1/f 0 to be equal to px /py, as would be required for proﬁt maximization. This behavior would not achieve the optimality condition expressed in Equation 19.40. The price ratio px /py would be ‘‘too low’’ in that it
would provide too little incentive to produce good x. In the private market, a consumer takes no account of how his or her spending on the public good beneﬁts others, so that consumer will devote too few resources to such production. The allocational failure in this situation can be ascribed to the way in which private markets sum individual demands. For any given quantity, the market demand curve reports the marginal valuation of a good. If one more unit were produced, it could then be consumed by someone who would value it at this market price. For public goods, the value of producing one more unit is in fact the sum of each consumer’s valuation of that extra output, because all consumers will beneﬁt from it. In this case, then, individual demand curves should be added vertically (as shown in Figure 19.2) rather than horizontally (as they are in competitive markets). The resulting price on such a public good 9P. A. Samuelson, ‘‘The Pure Theory of Public Expenditure,’’ Review of Economics and Statistics (November 1954): 387–89. 698 Part 8: Market Failure FIGURE 19.2 Derivation of the Demand for a Public Good For a public good, the price individuals are willing to pay for one more unit (their ‘‘marginal valuations’’) is equal to the sum of what each individual would pay. Hence, for public goods, the demand curve must be derived by a vertical summation rather than the horizontal summation used in the case of private goods. Price D1 + D2 + D3 = D 3 2 1 3 2 D D3 D2 D1 Quantity per period demand curve will then reﬂect, for any level of output, how much an extra unit of output would be valued by all consumers. But the usual market demand curve will not properly reﬂect this full marginal valuation. Inefﬁciency of a Nash equilibrium An alternative approach to the production of public goods in competitive markets might rely on individuals’ voluntary contributions. Unfortunately, this also will yield inefﬁcient results. Consider the situation of person A, who is thinking about contributing sA of his or her initial y endowment to public goods production. The utility maximization problem for A is then choose sA to maximize U A[ f sB), y A $ sA þ ð sA]. ’ The ﬁ
rst-order condition for a maximum is ’ or U A 1 U A 2 ¼ MRSA 1 f 0 : ¼ (19:41) (19:42) Because a similar logic will apply to person B, the efﬁciency condition of Equation 19.40 will once more fail to be satisﬁed. Again the problem is that each person considers only his or her beneﬁt from investing in the public good, taking no account of the beneﬁts provided to others. With many consumers, this direct beneﬁt may be very small indeed. (For example, how much do one person’s taxes contribute to national defense in the United States?) In this case, any one person may opt for sA ¼ 0 and become a pure ‘‘free rider,’’ hoping to beneﬁt from the expenditures of others. If every person adopts this strategy, then no resources will be subscribed to public goods. Example 19.3 illustrates the free-rider problem in a situation that may be all too familiar. Chapter 19: Externalities and Public Goods 699 EXAMPLE 19.3 Purchasing a Public Good: The Roommates’ Dilemma To illustrate the nature of the public good problem numerically, suppose two roommates with identical preferences derive utility from the number of music compact disks (CDs, denoted by x) in their shared music collection and on the number of granola bars ( y) eaten. The speciﬁc utility function for i 1, 2 is given by ¼ Uið x, yiÞ ¼ x1=2y1=2 i : (19:43) ¼ x1 þ Utility for each roommate depends on the total number of CDs (x x2) in their collection but only on the number of granola bars eaten by the individual. Hence in this problem a CD is a public good and a granola bar is a private good. (We could justify the classiﬁcation of CDs as a public good by assuming that the purchaser of the CD cannot exclude his or her roommate from borrowing and playing it on their shared sound system. Playing the CD once does not diminish its value when played again, so there is nonrivalry in CD consumption.) Assume each roommate has $300 to spend and that px ¼ Nash equilibrium. We ﬁr
st consider the outcome if the roommates make their consumption decisions independently without coming to a more or less formal agreement about how many CDs to buy. Roommate 1’s decision depends on how many CDs roommate 2 buys and vice versa. We are in a strategic situation for which we need the tools of game theory from Chapter 8 to analyze. We will look for the Nash equilibrium, in which both roommates are playing a best response. $10 and py ¼ $1. roommate 2. Roommate 1 maximizes utility To ﬁnd roommate 1’s best response, take as given the number x2 of CDs purchased by x1 þ x2Þ 10x1 þ ¼ subject to the budget constraint 1=2y1=2 i (19:44) 300 y1, ð leading to the Lagrangian The ﬁrst-order conditions with respect to roommate 1 choice variables are + x1 þ ¼ ð x2Þ 1=2y1=2 i þ k 300 ð ’ 10x1 ’ : y1Þ @+ @x1 ¼ @+ @y1 ¼ 1 2 ð 1 2 ð x1 þ x1 þ x2Þ 1=2 y1=2 ’ i ’ 10k 1=2 1=2 y’ i x2Þ k ’ ¼ 0 ¼ 0: (19:45) (19:46) Solving Equations 19.46 in the usual way gives y1 ¼ x1 þ ð which, when substituted into 1’s budget constraint and rearranged, gives the best-response function, x2Þ (19:47) 10 x1 ¼ 15 ’ x2 2 : (19:48) Because the problem is symmetric, roommate 2’s best-response function will have the same form: x2 ¼ 15 ’ x1 2 : (19:49) These best-response functions reﬂect a free-rider problem in that the more CDs one roommate is expected to purchase, the fewer CDs the other wants to buy. Solving Equations 19.48 and 19.49 simultaneously gives x$1 ¼ y$2 ¼ into Equation 19.47 gives y$1 ¼ 200. Nash equilibrium utilities are U $1 ¼ x$2 ¼ U $2 + 63:2.
that each roommate will pay half of CD purchases, then each would face an effective price of CDs of $5. Since the utility functions for the roommates imply that half of each person’s total income of $300 will be spent on CDs, it follows that each will be willing to spend $150 on such music and will, if each is honest, report that he or she would like to have 15 CDs. Hence the solution will be x$$ 30 and y$$1 ¼ 150. This is indeed the efﬁcient solution calculated in Example 19.3. This solution works if the government knows enough about the roommates’ preferences that it can set the payment shares in advance and stick to them. Knowing that the roommates have symmetric preferences in this example, it could set equal payment shares a1 ¼ a2 ¼ 1=2, and rest assured that both will honestly report the same demands for the public good, x$$ 30. If, however, the government does not know their preferences, it would have to tweak the payment shares based on their reports to make sure the reported demands end up being equal as required for the Lindahl solution to be ‘‘in equilibrium.’’ Anticipating the effect of their reports on their payment shares, the roommates would have an incentive to underreport demand. In fact, this underreporting would lead to the same outcome as in the Nash equilibrium from Example 19.3. ¼ ¼ QUERY: Although the 50–50 sharing in this example might arise from social custom, in fact the optimality of such a split is a special feature of this problem. What is it about this problem that leads to such a Lindahl outcome? Under what conditions would Lindahl prices result in other than a 50–50 sharing? Shortcomings of the Lindahl solution Unfortunately, Lindahl’s solution is only a conceptual one. We have already seen in our examination of the Nash equilibrium for public goods production and in our roommates’ example that the incentive to be a free rider in the public goods case is very strong. This fact makes it difﬁcult to envision how the information necessary to compute equilibrium 702 Part 8: Market Failure Lindahl shares might be obtained. Because individuals know their tax shares will be based on their reported demands for public goods, they have a clear incentive to understate their true preferences—in so doing they hope that the ‘‘other guy�
�’ will pay. Hence, simply asking people about their demands for public goods should not be expected to reveal their true demands. We will discuss more sophisticated mechanisms for eliciting honest demand reports at the end of the chapter. Local public goods Some economists believe that demand revelation for public goods may be more tractable at the local level.11 Because there are many communities in which individuals might reside, they can indicate their preferences for public goods (i.e., for their willingness to pay Lindahl tax shares) by choosing where to live. If a particular tax burden is not utility maximizing then people can, in principle, ‘‘vote with their feet’’ and move to a community that does provide optimality. Hence, with perfect information, zero costs of mobility, and enough communities, the Lindahl solution may be implemented at the local level. Similar arguments apply to other types of organizations (such as private clubs) that provide public goods to their members; given a sufﬁciently wide spectrum of club offerings, an efﬁcient equilibrium might result. Of course, the assumptions that underlie the purported efﬁciency of such choices by individuals are quite strict. Even minor relaxation of these assumptions may yield inefﬁcient results owing to the fragile nature of the way in which the demand for public goods is revealed. EXAMPLE 19.5 The Relationship between Environmental Externalities and Public Goods Production In recent years, economists have begun to study the relationship between the two issues we have been discussing in this chapter: externalities and public goods. The basic insight from this examination is that one must take a general equilibrium view of these problems in order to identify solutions that are efﬁcient overall. Here we illustrate this point by returning to the computable general equilibrium model ﬁrms described in Chapter 13 (see Example 13.4). To simplify matters we will now assume that this economy includes only a single representative person whose utility function is given by utility U ð ¼ x, y, l, g, c Þ ¼ x0:5y0:3l 0:2g0:1c0:2, (19:58) where we have added terms for the utility provided by public goods ( g), which are initially ﬁnanced by a tax on labor, and by clean air (c). Production of the public good requires capital k0.5 l 0.5; there is
an externality in the and labor input according to the production function g 0.2y. The production production of good y, so that the quantity of clean air is given by c functions for goods x and y remain as described in Example 13.4, as do the endowments of k and l. Hence our goal is to allocate resources in such a way that utility is maximized. 10 ¼ ’ ¼ Base case: Optimal public goods production with no Pigovian tax. If no attempt is level of public goods made to control the externality in this problem, then the optimal 2.93 and this is ﬁnanced by a tax rate of 0.25 on labor. Output of good production requires g y in this case is 29.7, and the quantity of clean air is given by c 4.06. Overall utility in this situation is U 19.34. This is the highest utility that can be obtained in this situation without regulating the externality. 5.94 10 ¼ ¼ ’ ¼ ¼ 11The classic reference is C. M. Tiebout, ‘‘A Pure Theory of Local Expenditures,’’ Journal of Political Economy (October 1956): 416–24. Chapter 19: Externalities and Public Goods 703 A Pigovian tax. As suggested by Figure 19.1, a unit tax on the production of good y may improve matters in this situation. With a tax rate of 0.1, for example, output of good y is 4.52), and the revenue generated is used to expand public reduced to y 27.4 (c 19.38. By carefully specifying how the goods production to g revenue generated by the Pigovian tax is used, a general equilibrium model permits a more complete statement of welfare effects. 10 3.77. Utility is increased to U ¼ ¼ 5.48 ’ ¼ ¼ ¼ The ‘‘double dividend’’ of environmental taxes. The solution just described is not optimal, however. Production of public goods is actually too high in this case, since the revenues from environmental taxes are also used to pay for public goods. In fact, simulations show that optimality can be achieved by reducing the labor tax to 0.20 and public goods production to g 19.43. This result is sometimes referred to as the ‘‘double dividend’’ of environmental taxation: not only do these taxes reduce
externalities relative to the untaxed situation (now c 4.40), but also the extra governmental revenue made available thereby may permit the reduction of other distorting taxes. 3.31. With these changes, utility expands even further to U 5.60 10 ¼ ¼ ¼ ¼ ’ QUERY: Why does the quantity of clean air decrease slightly when the labor tax is reduced relative to the situation where it is maintained at 0.25? More generally, describe whether environmental taxes would be expected always to generate a double dividend. Voting and Resource Allocation Voting is used as a social decision process in many institutions. In some instances, individuals vote directly on policy questions. That is the case in some New England town meetings, many statewide referenda (for example, California’s Proposition 13 in 1977), and for many of the national policies adopted in Switzerland. Direct voting also characterizes the social decision procedure used for many smaller groups and clubs such as farmers’ cooperatives, university faculties, or the local Rotary Club. In other cases, however, societies have found it more convenient to use a representative form of government, in which individuals vote directly only for political representatives, who are then charged with making decisions on policy questions. For our study of public choice theory, we will begin with an analysis of direct voting. This is an important subject not only because such a procedure applies to many cases but also because elected representatives often engage in direct voting (in Congress, for example), and the theory we will illustrate applies to those instances as well. Majority rule Because so many elections are conducted on a majority rule basis, we often tend to regard that procedure as a natural and, perhaps, optimal one for making social choices. But even a cursory examination indicates that there is nothing particularly sacred about a rule requiring that a policy obtain 50 percent of the vote to be adopted. In the U.S. Constitution, for example, two thirds of the states must adopt an amendment before it becomes law. And 60 percent of the U.S. Senate must vote to limit debate on controversial issues. Indeed, in some institutions (Quaker meetings, for example), unanimity may be required for social decisions. Our discussion of the Lindahl equilibrium concept suggests there may exist a distribution of tax shares that would obtain unanimous support in voting for public goods. But arriving at such unanimous agreements is usually thwarted by emergence of the free-rider problem. Examining in detail the forces that lead societies to move 704 Part 8: Market Failure
TABLE 19.2 PREFERENCES THAT PRODUCE THE PARADOX OF VOTING Choices: A—Low Spending B—Medium Spending C—High Spending Preferences Smith A B C Jones B C A Fudd C A B away from unanimity and to choose some other determining fraction would take us too far aﬁeld here. We instead will assume throughout our discussion of voting that decisions will be made by majority rule. Readers may wish to ponder for themselves what kinds of situations might call for a decisive proportion of other than 50 percent. The paradox of voting In the 1780s, the French social theorist M. de Condorcet observed an important peculiarity of majority rule voting systems—they may not arrive at an equilibrium but instead may cycle among alternative options. Condorcet’s paradox is illustrated for a simple case in Table 19.2. Suppose there are three voters (Smith, Jones, and Fudd) choosing among three policy options. For our subsequent analysis we will assume the policy options represent three levels of spending (A low, B medium, or C high) on a particular public good, but Condorcet’s paradox would arise even if the options being considered did not have this type of ordering associated with them. Preferences of Smith, Jones, and Fudd among the three policy options are indicated in Table 19.2. These preferences give rise to Condorcet’s paradox. Consider a vote between options A and B. Here option A would win, because it is favored by Smith and Fudd and opposed only by Jones. In a vote between options A and C, option C would win, again by 2 votes to 1. But in a vote of C versus B, B would win and we would be back where we started. Social choices would endlessly cycle among the three alternatives. In subsequent votes, any choice initially decided upon could be defeated by an alternative, and no equilibrium would ever be reached. In this situation, the option ﬁnally chosen will depend on such seemingly nongermane issues as when the balloting stops or how items are ordered on an agenda—rather than being derived in some rational way from the preferences of voters. Single-peaked preferences and the median voter theorem Condorcet’s voting paradox arises because there is a degree of irreconcilability in the preferences of voters. Therefore, one might ask whether restrictions on the types of preferences allowed could yield situations where equilibrium voting outcomes are more likely.
A fundamental result about this probability was discovered by Duncan Black in 1948.12 Black showed that equilibrium voting outcomes always occur in cases where the issue being voted upon is one-dimensional (such as how much to spend on a public good) and where voters’ preferences are ‘‘single peaked.’’ To understand what the notion of single peaked means, consider again Condorcet’s paradox. In Figure 19.3 we illustrate the 12D. Black, ‘‘On the Rationale of Group Decision Making,’’ Journal of Political Economy (February 1948): 23–34. Chapter 19: Externalities and Public Goods 705 FIGURE 19.3 Single-Peaked Preferences and the Median Voter Theorem This ﬁgure illustrates the preferences in Table 19.2. Smith’s and Jones’s preferences are single peaked, but Fudd’s have two local peaks and these yield the voting paradox. If Fudd’s preferences had instead been single peaked (the dashed line), then option B would have been chosen as the preferred choice of the median voter (Jones). Utility Fudd Fudd (alternate) Jones Smith A B C Quantity of public good preferences that gave rise to the paradox by assigning hypothetical utility levels to options A, B, and C that are consistent with the preferences recorded in Table 19.2. For Smith and Jones, preferences are single peaked: as levels of public goods expenditures increase, there is only one local utility-maximizing choice (A for Smith, B for Jones). Fudd’s preferences, on the other hand, have two local maxima (A and C). It is these preferences that produced the cyclical voting pattern. If instead Fudd had the preferences represented by the dashed line in Figure 19.3 (where now C is the only local utility maximum), then there would be no paradox. In this case, option B would be chosen because that option would defeat both A and C by votes of 2 to 1. Here B is the preferred choice of the ‘‘median’’ voter (Jones), whose preferences are ‘‘between’’ the preferences of Smith and the revised preferences of Fudd. Black’s result is quite general and applies to any number of voters. If choices are unidimensional13 and if preferences are single peaked, then majority rule will result in the selection of the project that is most favored by the
median voter. Hence, that voter’s preferences will determine what public choices are made. This result is a key starting point for many models of the political process. In such models, the median voter’s preferences dictate policy choices—either because that voter determines which policy gets a majority of votes in a direct election or because the median voter will dictate choices in competitive elections in which candidates must adopt policies that appeal to this voter. A Simple Political Model To illustrate how the median voter theorem is applied in political models, suppose a community is characterized by a large number (n) of voters each with an income given by yi. 13The result can be generalized a bit to deal with multidimensional policies if individuals can be characterized in their support for such policies along a single dimension. 706 Part 8: Market Failure The utility of each voter depends on his or her consumption of a private good (ci) and of a public good ( g) according to the additive utility function utility of person i U i ¼ ci þ f g, Þ ð ¼ (19:59) where fg > 0 and fgg < 0. Each voter must pay income taxes to ﬁnance g. Taxes are proportional to income and are imposed at a rate t. Therefore, each person’s budget constraint is given by ci ¼ ð yi: Þ ’ 1 t The government is also bound by a budget constraint: n where y A denotes average income for all voters. g ¼ tny A, tyi ¼ 1 X (19:60) (19:61) Given these constraints, the utility of person i can be written as a function of his or her choice of g only: g U ið 19:62) Utility maximization for person i shows that his or her preferred level of expenditures on the public good satisﬁes dU i dg ¼ ’ yi ny A þ g f gð Þ ¼ 0 or g 1 f ’ g ¼ yi ny A! : " (19:63) This shows that desired spending on g is inversely related to income. Because (in this model) the beneﬁts of g are independent of income but taxes increase with income, highincome voters can expect to have smaller net gains (or even losses) from public spending than can low-income voters. The median voter equilibrium If g is determined here through majority rule, its
level will be chosen to be that level favored by the ‘‘median voter.’’ In this case, voters’ preferences align exactly with incomes, so g will be set at that level preferred by the voter with median income (y m). Any other level for g would not get 50 percent of the vote. Hence, equilibrium g is given by g$ ¼ 1 f ’ g y m ny 19:64) In general, the distribution of income is skewed to the right in practically every political jurisdiction in the world. With such an income distribution, ym < y A, and the difference between the two measures becomes larger the more skewed is the income distribution. Hence Equation 19.64 suggests that, ceteris paribus, the more unequal is the income distribution in a democracy, the higher will be tax rates and the greater will be spending on public goods. Similarly, laws that extend the vote to increasingly poor segments of the population can also be expected to increase such spending. Optimality of the median voter result Although the median voter theorem permits a number of interesting positive predictions about the outcome of voting, the normative signiﬁcance of these results is more difﬁcult Chapter 19: Externalities and Public Goods 707 to pinpoint. In this example, it is clear that the result does not replicate the Lindahl voluntary equilibrium—high-income voters would not voluntarily agree to the taxes imposed.14 The result also does not necessarily correspond to any simple criterion for social welfare. For example, under a ‘‘utilitarian’’ social welfare criterion, g would be chosen so as to maximize the sum of utilities: n n SW ’ $ yi y A þ f g ð ¼ Þ & ny A g nf g : Þ ð þ ’ (19:65) The optimal choice for g is then found by differentiation: dSW dg ¼ ’ 1 nf g ¼ þ 0, or g19:66) which shows that a utilitarian choice would opt for the level of g favored by the voter with average income. That output of g would be smaller than that favored by the median voter because y m < y A. In Example 19.6 we take this analysis a bit further by showing how it might apply to governmental transfer policy. EXAMPLE 19.6 Voting for Redistributive Taxation Suppose voters were considering adoption of a lump-sum transfer to
• Private markets will tend to underallocate resources to public goods because no single buyer can appropriate all of the beneﬁts that such goods provide. • A Lindahl optimal tax-sharing scheme can result in an efﬁcient allocation of resources to the production of public goods. However, computing these tax shares requires substantial information that individuals have incentives to hide. • Majority rule voting does not necessarily lead to an efﬁcient allocation of resources to public goods. The median voter theorem provides a useful way of modeling the actual outcomes from majority rule in certain situations. • Several truth-revealing voting mechanisms have been developed. Whether these are robust to the special assumptions made or capable of practical application remain unresolved questions. 19.1 A ﬁrm in a perfectly competitive industry has patented a new process for making widgets. The new process lowers the ﬁrm’s average cost, meaning that this ﬁrm alone (although still a price taker) can earn real economic proﬁts in the long run. a. If the market price is $20 per widget and the ﬁrm’s marginal cost is given by MC production for the ﬁrm, how many widgets will the ﬁrm produce? 0.4q, where q is the daily widget ¼ b. Suppose a government study has found that the ﬁrm’s new process is polluting the air and estimates the social marginal cost of 0.5q. If the market price is still $20, what is the socially optimal level of production widget production by this ﬁrm to be SMC for the ﬁrm? What should be the rate of a government-imposed excise tax to bring about this optimal level of production? ¼ c. Graph your results. 19.2 On the island of Pago Pago there are 2 lakes and 20 anglers. Each angler can ﬁsh on either lake and keep the average catch on his particular lake. On Lake x, the total number of ﬁsh caught is given by where lx is the number of people ﬁshing on the lake. For Lake y, the relationship is Fy 5ly: ¼ Fx 10lx ’ ¼ 1 2 l2 x, a. Under this organization of society, what will be the total number of ﬁsh caught? b. The chief of Pago Pago, having
once read an economics book, believes it is possible to increase the total number of ﬁsh caught by restricting the number of people allowed to ﬁsh on Lake x. What number should be allowed to ﬁsh on Lake x in order to maximize the total catch of ﬁsh? What is the number of ﬁsh caught in this situation? c. Being opposed to coercion, the chief decides to require a ﬁshing license for Lake x. If the licensing procedure is to bring about the optimal allocation of labor, what should the cost of a license be (in terms of ﬁsh)? d. Explain how this example sheds light on the connection between property rights and externalities. Chapter 19: Externalities and Public Goods 711 19.3 Suppose the oil industry in Utopia is perfectly competitive and that all ﬁrms draw oil from a single (and practically inexhaustible) pool. Assume that each competitor believes that it can sell all the oil it can produce at a stable world price of $10 per barrel and that the cost of operating a well for one year is $1,000. Total output per year (Q) of the oil ﬁeld is a function of the number of wells (n) operating in the ﬁeld. In particular, and the amount of oil produced by each well (q) is given by 500n Q ¼ ’ n2, Q n ¼ q ¼ 500 n: ’ (19:75) a. Describe the equilibrium output and the equilibrium number of wells in this perfectly competitive case. Is there a diver- gence between private and social marginal cost in the industry? b. Suppose now that the government nationalizes the oil ﬁeld. How many oil wells should it operate? What will total output be? What will the output per well be? c. As an alternative to nationalization, the Utopian government is considering an annual license fee per well to discourage overdrilling. How large should this license fee be if it is to prompt the industry to drill the optimal number of wells? 19.4 There is considerable legal controversy about product safety. Two extreme positions might be termed caveat emptor (let the buyer beware) and caveat vendor (let the seller beware). Under the former scheme producers would have no responsibility for the safety of their products: Buyers would absorb all losses. Under the latter scheme this liability assignment would be reversed
: Firms would be completely responsible under law for losses incurred from unsafe products. Using simple supply and demand analysis, discuss how the assignment of such liability might affect the allocation of resources. Would safer products be produced if ﬁrms were strictly liable under law? How do possible information asymmetries affect your results? 19.5 Suppose a monopoly produces a harmful externality. Use the concept of consumer surplus in a partial equilibrium diagram to analyze whether an optimal tax on the polluter would necessarily be a welfare improvement. 19.6 Suppose there are only two individuals in society. Person A’s demand curve for mosquito control is given by for person B, the demand curve for mosquito control is given by qn ¼ 100 p; ’ qb ¼ 200 p: ’ a. Suppose mosquito control is a pure public good; that is, once it is produced, everyone beneﬁts from it. What would be the optimal level of this activity if it could be produced at a constant marginal cost of $120 per unit? b. If mosquito control were left to the private market, how much might be produced? Does your answer depend on what each person assumes the other will do? c. If the government were to produce the optimal amount of mosquito control, how much will this cost? How should the tax bill for this amount be allocated between the individuals if they are to share it in proportion to beneﬁts received from mosquito control? 19.7 Suppose the production possibility frontier for an economy that produces one public good (y) and one private good (x) is given by 100y2 x2 þ ¼ 5,000: 712 Part 8: Market Failure This economy is populated by 100 identical individuals, each with a utility function of the form utility = xiyp, where xi is the individual’s share of private good production ( everyone beneﬁts equally from its level of production. ¼ x/100). Notice that the public good is nonexclusive and that ﬃﬃﬃﬃﬃﬃ a. If the market for x and y were perfectly competitive, what levels of those goods would be produced? What would the typical individual’s utility be in this situation? b. What are the optimal production levels for x and y? What would the typical individual’s utility level be? How should consumption of good x be taxed to achieve this result? H
int: The numbers in this problem do not come out evenly, and some approximations should sufﬁce. Analytical Problems 19.8 More on Lindahl equilibrium The analysis of public goods in this chapter exclusively used a model with only two individuals. The results are readily generalized to n persons—a generalization pursued in this problem. a. With n persons in an economy, what is the condition for efﬁcient production of a public good? Explain how the character- istics of the public good are reﬂected in these conditions. b. What is the Nash equilibrium in the provision of this public good to n persons? Explain why this equilibrium is inefﬁcient. Also explain why the underprovision of this public good is more severe than in the two-person cases studied in the chapter. c. How is the Lindahl solution generalized to n persons? Is the existence of a Lindahl equilibrium guaranteed in this more complex model? 19.9 Taxing pollution Suppose that there are n ﬁrms each producing the same good but with differing production functions. Output for each of these ﬁrms depends only on labor input, so the functions take the form qi ¼ fi (li). In its production activities each ﬁrm also produces some pollution, the amount of which is determined by a ﬁrm-speciﬁc function of labor input of the form gi (li). a. Suppose that the government wishes to place a cap of amount K on total pollution. What is the efﬁcient allocation of labor among ﬁrms? b. Will a uniform Pigovian tax on the output of each ﬁrm achieve the efﬁcient allocation described in part (a)? c. Suppose that, instead of taxing output, the Pigovian tax is applied to each unit of pollution. How should this tax be set? Will the tax yield the efﬁcient allocation described in part (a)? d. What are the implications of the problem for adopting pollution control strategies? (For more on this topic see the Exten- sions to this chapter.) 19.10 Vote trading Suppose there are three individuals in society trying to rank three social states (A, B, and C ). For each of the methods of social choice indicated, develop an example to show how the resulting social ranking of A, B, and C will be intrans
itive (as in the paradox of voting) or indeterminate. a. Majority rule without vote trading. b. Majority rule with vote trading. c. Point voting where each voter can give 1, 2, or 3 points to each alternative and the alternative with the highest point total is selected. 19.11 Public choice of unemployment beneﬁts Suppose individuals face a probability of u that they will be unemployed next year. If they are unemployed they will receive unemployment beneﬁts of b, whereas if they are employed they receive w (1 t), where t is the tax used to ﬁnance unemployment beneﬁts. Unemployment beneﬁts are constrained by the government budget constraint ub tw (1 u). ’ ¼ ’ Chapter 19: Externalities and Public Goods 713 a. Suppose the individual’s utility function is given by yiÞ d is the degree of constant relative risk aversion. What would be the utility-maximizing choices for b and t? ¼ ð U d=d, b. How would the utility-maximizing choices for b and t respond to changes in the probability of unemployment, u? c. How would b and t change in response to changes in the risk aversion parameter d? where 1 ’ 19.12 Probabilistic voting Probabilistic voting is a way of modeling the voting process that introduces continuity into individuals’ voting decisions. In this way, calculus-type derivations become possible. To take an especially simple form of this approach, suppose there are n voters and two candidates (labeled A and B) for elective ofﬁce. Each candidate proposes a platform that promises a net gain or loss to i and uB each voter. These platforms are denoted by uA 1,..., n. The probability that a given voter will vote for uB candidate A is given by pA, where f 0 > 0 > f 00. The probability that the voter will vote for candidate B is i Þ( pA pB i. i ¼ a. How should each candidate chose his or her platform so as to maximize the probability of winning the election subject to i, where i uA i Þ ’ Uið Uið i ¼ ’ ¼ 1 ½ f the constraint i uA i ¼ i uB i ¼ 0? (Do these constraints seem to apply to actual political candidates?) b.
Will there exist a Nash equilibrium in platform strategies for the two candidates? c. Will the platform adopted by the candidates be socially optimal in the sense of maximizing a utilitarian social welfare? P P [Social welfare is given by SW i Uið uiÞ.] ¼ P SUGGESTIONS FOR FURTHER READING Alchian, A., and H. Demsetz. ‘‘Production, Information Costs, and Economic Organization.’’ American Economic Review 62 (December 1972): 777–95. Uses externality arguments to develop a theory of economic organizations. Barzel, Y. Economic Analysis of Property Rights. Cambridge: Cambridge University Press, 1989. Provides a graphical analysis of several economic questions that are illuminated through use of the property rights paradigm. Black, D. ‘‘On the Rationale of Group Decision Making.’’ Journal of Political Economy (February 1948): 23–34. Reprinted in K. J. Arrow and T. Scitovsky, Eds., Readings in Welfare Economics. Homewood, IL: Richard D. Irwin, 1969. Early development of the median voter theorem. Buchanan, J. M., and G. Tullock. The Calculus of Consent. Ann Arbor: University of Michigan Press, 1962. Classic analysis of the properties of various voting schemes. Cheung, S. N. S. ‘‘The Fable of the Bees: An Economic Investigation.’’ Journal of Law and Economics 16 (April 1973): 11–33. Empirical study of how the famous bee-orchard owner externality is handled by private markets in the state of Washington. Coase, R. H. ‘‘The Market for Goods and the Market for Ideas.’’ American Economic Review 64 (May 1974): 384– 91. Speculative article about notions of externalities and regulation in the ‘‘marketplace of ideas.’’ ———. ‘‘The Problem of Social Cost.’’ Journal of Law and Economics 3 (October 1960): 1–44. Classic article on externalities. Many fascinating historical legal cases. Cornes, R., and T. Sandler. The Theory of Externalities, Public Goods, and Club Goods. Cambridge: Cambridge University Press, 1986. Good theoretical analysis of many of the issues raised in this chapter. Good discussions of the connections between returns to scale, ex
cludability, and club goods. Demsetz, H. ‘‘Toward a Theory of Property Rights.’’ American Economic Review, Papers and Proceedings 57 (May 1967): 347–59. Brief development of a plausible theory of how societies come to deﬁne property rights. Mas-Colell, A., M. D. Whinston, and J. R. Green. Microeconomic Theory. New York: Oxford University Press, 1995. Chapter 11 covers much of the same ground as this chapter does, though at a somewhat more abstract level. Olson, M. The Logic of Collective Action. Cambridge, MA: Harvard University Press, 1965. Analyzes the effects of individual incentives on the willingness to undertake collective action. Many fascinating examples. Persson, T., and G. Tabellini. Political Economics: Explaining Economic Policy. Cambridge, MA: MIT Press, 2000. A complete summary of recent models of political choices. Covers voting models and issues of institutional frameworks. Posner, R. A. Economic Analysis of Law, 5th ed. Boston:Little, Brown, 1998. In many respects the ‘‘bible’’ of the law and economics movement. Posner’s arguments are not always economically correct but are unfailingly interesting and provocative. Samuelson, P. A. ‘‘The Pure Theory of Public Expenditures.’’ Review of Economics and Statistics 36 (November 1954): 387–89. Classic statement of the efﬁciency conditions for public goods production. EXTENSIONS POLLUTION ABATEMENT Although our discussion of externalities focused on how Pigovian taxes can make goods’ markets operate more efﬁciently, similar results also apply to the study of the technology of pollution abatement. In these Extensions we brieﬂy review this alternative approach. We assume there are only two ﬁrms, A and B, and that their output levels (qA and qB, respectively) are ﬁxed throughout our discussion. It is an inescapable scientiﬁc principle that production of physical goods (as opposed to services) must obey the conservation of matter. Hence production of qA and qB is certain to involve some emission by-products, eA and eB. The physical amounts of these emissions (or at least their harmful components) can be abated
using inputs zA and zB (which cost p per unit). The resulting levels of emissions are given by f A qA, zAÞ ¼ ð eA and f B qB, zBÞ ¼ ð eB, (i) where, for each ﬁrm’s abatement function, f1 > 0 and f2 < 0. E19.1 Optimal abatement If a regulatory agency has decided that e$ represents the maximum allowable level of emissions from these ﬁrms, then this level would be achieved at minimal cost by solving the Lagrangian expression + pzA þ First-order conditions for a minimum are pzB $ : Þ p þ Hence we have kf A 2 ¼ 0 and p + kf B 2 ¼ 0: (ii) (iii) (iv) k p=f A p=f B 2 : ¼ ’ 2 ¼ ’ This equation makes the rather obvious point that costminimizing abatement is achieved when the marginal cost of abatement (universally referred to as MAC in the environmental literature) is the same for each ﬁrm. A uniform standard that required equal emissions from each ﬁrm would not be likely to achieve that efﬁcient result—considerable cost savings might be attainable under equalization of MACs as compared to such uniform regulation. E19.2 Emission taxes The optimal solution described in Equation iv can be achieved by imposing an emission tax (t) equal to l on each ﬁrm (presumably this tax would be set at a level that reﬂects the marginal harm that a unit of emissions causes). With this tax, tf i(qi, zi), which does each ﬁrm seeks to minimize pzi þ indeed yield the efﬁcient solution (v) t p=f A p=f B 2 : ¼ ’ 2 ¼ ’ Notice that, as in the analysis of Chapter 19, one beneﬁt of the taxation solution is that the regulatory authority need not know the details of the ﬁrms’ abatement functions. Rather, the ﬁrms themselves make use of their own private information in determining abatement strategies. If these functions differ signiﬁcantly among ﬁrms, then it would
References Hanley, N., J. F. Shogren, and B. White. Environmental Ecoin Theory and Practice. New York: Oxford nomics University Press, 1997. Milliman, S. R., and R. Prince. ‘‘Firm Incentive to Promote Technological Change in Pollution Control.’’ Journal of Environmental Economics and Management (November 1989): 247–65. Schmalensee, R., P. L. Joskow, A. D. Ellerman, J. P. Montero, and E. M. Bailey. ‘‘An Interim Evaluation of the Sulfur Dioxide Trading Program.’’ Journal of Economic Perspectives (Summer 1998): 53–68. would be expected to yield the same sort of cost savings as do taxation schemes. SO2 trading The U.S. Clean Air Act of 1990 established the ﬁrst large-scale program of tradable emission permits. These focused on sulfur dioxide emissions with the goal of reducing acid rain arising from power-plant burning of coal. Schmalensee et al. (1998) review early experiences under this program. They conclude that it is indeed possible to establish large and well-functioning markets in emission permits. More than ﬁve million (one-ton) emission permits changed hands in the most recent year examined—at prices that averaged about $150 per permit. The authors also show that ﬁrms using the permit system employed a wide variety of compliance strategies. This suggests that the ﬂexibility inherent in the permit system led to considerable cost savings. One interesting aspect of this review of SO2 permit trading is the authors’ speculations about why the permit prices were only about half what had been expected. They attribute a large part of the explanation to an initial ‘‘overinvestment’’ in emission cleaning technology by power companies in the mistaken belief that permit prices, once the system was implemented, would be in the $300–$400 range. With such large ﬁxed-cost investments, the marginal cost of removing a ton of SO2 may have been as low as $65/ton, thereby exerting a significant downward force on permit prices. E19.4 Innovation Although taxes and tradable permits appear to be mathematically equivalent in the models we have been describing, this This page intentionally left blank Brief Answers to Queries The following brief answers to the
queries that accompany each example in the text may help students test their understanding of the concepts being presented. 2.4 For different constants, each production possibility frontier is a successively larger quarter ellipse centered at the origin. CHAPTER 1 1.1 If price depends on quantity, differentiation of p(q) q would be more complicated. This would lead to the concept of marginal revenue—a topic we encounter in many places in this book.! 1.2 The reduced form in Equation 1.16 shows that @p"/@a ¼ 1/225. So, if a increases by 450, p" should increase by 2— which is what a direct solution shows. 1.3 200p If all labor is devoted to x production, then x ¼ 180p 14.1 with full employment and x 13.4 with ﬃﬃﬃﬃﬃﬃﬃﬃ unemployment. Hence the efﬁciency cost of unemployment is 0.7 units of x. Similar calculations show that the efﬁciency cost in terms of good y is about 1.5 units of that good. With reductions in both goods, one would need to know the relative price of x in terms of y in order to aggregate the losses. ¼ ¼ ﬃﬃﬃﬃﬃﬃﬃﬃ ¼ CHAPTER 2 2.1 The ﬁrst-order condition for a maximum is @p/@l 50/ 25, p" 250. 0, l" lp 10 $ ¼ ¼ ¼ ¼ ﬃﬃ 2.2 No, only the exponential function (or a function that approximates it over a range) has constant elasticity. 2.3 Putting all the terms over a common denominator gives y 165 3p ¼ ¼ 55 p. Hence, @y @p ¼ $ 55 p2. 1, ¼ ¼ 2. For y 10, the ‘‘circle’’ is a single point. 0 because x1 would always be set at b for opti- 2.5 These would be concentric circles centered at x1 ¼ x2 ¼ 2.6 @y"/@b mality, and the term (x1 $ 2.7 With x1 þ x2 & x1
¼ 3.464. In this case, 57.7 percent ( 3.464/12) of the distribution is within one standard! ¼ deviation of the mean. This is less than the comparable ﬁgure for the Normal distribution because the uniform distribution is not bunched around the mean. However, unlike the Normal, the entire uniform distribution is within two standard deviations of the mean because that distribution does not have long tails. $ CHAPTER 3 3.1 The derivation here holds utility constant to create an implicit relationship between y and x. Changes in x also implicitly change y because of this relationship (Equation 3.11). 3.2 The MRS is not changed by such a doubling in Examples 1 and 3. In Example 2, the MRS would be changed (1 because (1 2x)/(1 x)/(1 2y). y) þ þ 6¼ þ þ 3.3 For homothetic functions, the MRS is the same for every point along a positively sloped ray through the origin. 3.4 The indifference curves here are ‘‘horizontally parallel.’’ That is, for any given level of y, the MRS is the same no matter what the value of x is. One implication of this (as we shall see in Chapter 4) is that the effect of additional income on purchases of good y is zero—after a point all extra income is channeled into the good with constant marginal utility (good x). CHAPTER 4 4.1 Constant shares imply @x/@py ¼ 0. Notice py does not enter into Equation 4.23; px does not enter into 4.24. 0 and @y/@px ¼ 4.2 Budget shares are not affected by income, but they may be affected by changes in relative prices. This is the case for all homothetic functions. 4.3 Since a doubling of all prices and nominal income does not change the budget constraint, it will not change utility-maximizing choices. Indirect utility is homogeneous of degree zero in all prices and nominal income.!! 1 2 ¼ 30.5 3, E(1,3,2) 4.4 In the Cobb-Douglas case, with py ¼ ¼ 2 6.93, so this person should have his or! her income reduced by a lump-sum 1.07 to compensate for the fall in prices. In the ﬁ
income and substitution effects, this derivative could be 0 if the effects offset each other. The conclusion that @x/@py ¼ 0 implies the goods must be used in ﬁxed proportions would hold only if the income effect of this price change were 0. 6.2 Asymmetry can occur with homothetic preferences since, although substitution effects are symmetric, income effects may differ in size. 6.3 Since the relationships between py, pz, and ph never change, the maximization problem will always be solved the same way. Brief Answers to Queries 719 ﬂip is over $1 million. The value of the game in this case is 19 1,000,000/219 $20.91. þ ¼ 7.2 With linear utility, the individual would care only about expected dollar values and would be indifferent about buying actuarially fair insurance. When utility U is a convex function of wealth (U > 0, U 00 > 0), the individual prefers to gamble and will buy insurance only if it costs less than is actuarially justiﬁed. 7.3 If A 10$ 4: ¼ CE CE ð ð 0:5 107;000 102;000; $ 0:5 102;000 101;800: $!! 4 10$ 104! ð 2 Þ 4 10$ 106 4!! #1 #2 Þ ¼ ¼ Þ ¼ ¼ So the riskier allocation is preferred. On the other hand, if A 4 then the less risky allocation is preferred. 10$ 3 ¼! 7.4 Willingness to pay is a declining function of wealth 0 the person will pay 50 to (Equation 7.43). With R ¼ 10,000 but only 5 if W0 ¼ avoid a 1,000 bet if W0 ¼ 2 he or she will pay 149 to avoid a 100,000. With R ¼ 100,000. 10,000 but only 15 if W0 ¼ 1,000 bet if W0 ¼ 7.5 Option value may be low for a risk-averse person if one of the choices is relatively safe. Reworking the example 1=2 shows that the option value is 0.125 with A1ð x for the risk-neutral person but only about 0.11 for the risk-averse one. Þ ¼ 7.6 The actuarially fair price for such a
.50. 187.50, C 125, and p ¼ ¼ ¼ 11.2 Factors other than p can be incorporated into the constant term a. These would shift D and MR but would not affect the elasticity calculations. ¼ 11.3 When w rises to 15, supply shifts inward to q 8P/5. When k increases to 100, supply shifts outward to q 25P/6. A change in v would not affect short-run marginal cost or the shutdown decision. ¼ ¼ 11.4 A change in v has no effect on SMC but it does affect ﬁxed costs. A change in w would affect SMC and shortrun supply. 11.5 A rise in wages for all ﬁrms would shift the market supply curve upward, raising the product price. Because Brief Answers to Queries 721 total output must fall given a negatively sloped demand curve, each ﬁrm must produce less. Again, both substitution and output effects would then be negative. CHAPTER 12 12.1 The ability to sum incomes in this linear case would require that each person have the same coefﬁcient for income. Because each person faces the same price, aggregation requires only adding the price coefﬁcients. 12.2 A value for b other than 0.5 would mean that the exponent of price would not be 1.0. The higher b is, the more price elastic is short-run supply. 12.3 Following steps similar to those used to derive Equation 12.30 yields eP;b eQ;b ¼ $ $ eS;P eQ;P 0.5, so eP, b ¼ $ eQ,w ¼ $ Here eQ, b ¼ ¼ 0.227. Multiplication by 0.20 (since wages rose 20 percent) predicts a price rise of 4.5 percent, very close to the number in the example. 0.5)/2.2 $ ( 12.4 The short-run supply curve is given by Qs ¼ þ 750, and the short-term equilibrium price is $643. Each ﬁrm earns approximately $2,960 in proﬁts in the short run. 0.5P 12.5 Total and average costs for Equation 12.55 exceed those for Equation 12.42 for q > 15.9. Marginal costs for Equation 12.55 always
exceed those for Equation 12.42. Optimal output is lower with Equation 12.55 than with Equation 12.42 because marginal costs increase more than average costs. 12.6 Losses from a given restriction in quantity will be greater when supply and/or demand is less elastic. The actor with the least elastic response will bear the greater share of the loss. 12.7 An increase in t unambiguously increases deadweight loss. Because increases in t reduce quantity, however, total tax revenues are subject to countervailing effects. Indeed, if t/(P 1/eQ,P then dtQ/dt < 0. t) þ & $ 722 Brief Answers to Queries CHAPTER 13 13.1 An increase in labor input will shift the ﬁrst frontier out uniformly. In the second case, such an increase will shift the y-intercept out farther than the x-intercept because good y uses labor intensively. 13.2 In all three scenarios the total value of output is 200w, composed half of wages and half of proﬁts. With the shift in supply, consumers still devote 100w to each good. Purchases of x are twice those of y because y costs twice as much. With the shift in demand, the consumer spends 20w on good x and 180w on good y. But good y now costs three times what x costs, so consumers buy only three times as much y as they do x. 13.3 All efﬁcient allocations require the ratio of x to y to be relatively high for A and low for B. Hence, when good x is allocated evenly, A must get less than half the amount of y available and B must get more than half. Because efﬁciency requires 2yA=xA ¼ 0:5yB=xB and the symmetry xA=yA for of the utility functions requires yB=xB ¼ 0:5yB. 2yA, xB ¼ equal utility, we can conclude xA ¼ 333.3, yB ¼ 333.3, xB ¼ 666.7, yA ¼ Utility for both parties is about 496. So xA ¼ 666.7. 13.4 The consumers here also spend some of their total income on leisure. For person 1, say, total income with the equilibrium prices is 40 11.4. The CobbDouglas
) $ $ ¼ $ ¼! ¼ CHAPTER 15 15.1 Members of a perfect cartel produce less than their best responses, so cartels may be unstable. 15.2 A point on ﬁrm 1’s best response must involve a tangency between 1’s isoproﬁt and a horizontal line of height q2. This isoproﬁt reaches a peak at this point. Firm 2’s isoproﬁts look something like right parentheses that peak on 2’s best-response curve. An increase in demand intercept would shift out both best responses, resulting in higher quantities in equilibrium. 15.3 The ﬁrst-order condition is the mathematical representation of the optimal choice. Imposing symmetry before taking a ﬁrst-order condition is like allowing ﬁrm i to choose the others’ outputs as well as its own. Making this mistake would lead to the monopoly rather than the Cournot outcome in this example. 15.4 An increase in the demand intercepts would shift out both best responses, leading to an increase in equilibrium prices. Brief Answers to Queries 723 15.5 Locating in the same spot leads to marginal cost pricing as in the Bertrand model with homogeneous products. Locating at opposite ends of the beach results in the softest price competition and the highest prices. 16.2 The conclusion does not depend on linearity. So long as the demand and supply curves are conventionally shaped, the curves will be shifted vertically by the parameters t and k. 15.6 It is reasonable to suppose that competing gas stations monitor each other’s prices and could respond to a price change within the day, so one day would be a reasonable period length. A year would be a reasonable period for producers of small cartons of milk for school lunches, because the contracts might be renegotiated each new school year. 15.7 Reverting to the stage-game Nash equilibrium is a less harsh punishment in a Cournot model (ﬁrms earn positive proﬁt) than a Bertrand model (ﬁrms earn zero proﬁt). 15.8 Firms might race to be the ﬁrst to market, investing in research and development and capacity before sufﬁcient demand has materialized. In this way, they may compete away all the proﬁts from being �
would allow the consumer to buy whatever number of ounces desired at the 10 cents per ounce price. Here the consumer is restricted to two cup sizes: 4 or 16 ounces. 18.5 The insurance company decides to offer just one policy targeted to red cars and ignores gray cars. 18.6 Gray-car owners obtain utility of 11.48033 in the competitive equilibrium under asymmetric information. They would obtain the same utility under full insurance with a premium of $3,207. The difference between this and the equilibrium premium ($453) is $2,754. Any premium between $3,000 and $3,207 would allow an insurance company to break even from its sales just for gray cars. The problem is that red-car owners would deviate to the policy, causing the company to make negative proﬁt. 18.7 If the reports are fairly credible, then gray cars may still be able to get as full insurance with reporting as without, but not as full as with 100 percent credibility. Auditors have short-run incentives to take bribes to issue ‘‘gray’’ reports. In the long run, dishonesty will reduce the fees the auditor can charge. He or she would like to maintain high fees by establishing a reputation for honest reporting (which would be ruined if ever discovered to be dishonest). 18.8 If there are fewer sellers than buyers, then all the cars b. will sell. A car of quality q will sell at a price of q If there are fewer buyers than sellers, then all buyers will purchase a car but some cars will be left unsold (a random selection of them). The equilibrium price will equal the car’s quality: q. þ 18.9 Yes, reservation prices can often help. The trade-offs involved in increasing the reservation price are, on the one hand, that buyers are encouraged to increase their bids, but, on the other hand, that the probability the object goes unsold increases. In a second-price auction, buyers bid their valuations without a reservation price, and a reservation price would not induce them to bid above their valuations. CHAPTER 19 19.1 Production of x would have a beneﬁcial impact on y so labor would be underallocated to x by competitive markets. 19.2 The tax is relatively small because of the nature of the externality that vanishes with only a relatively minor reduction in x output. A merged ﬁrm would also ﬁnd x
/@g d. @f/@g 0.5(40/g)2 0.5g(40/g)2 40(40/g) þ ¼ # 800/g2. 0.5(t$)2. ¼ # 0.8, so each 0.1 increase ¼ # ¼ # in g reduces maximum height by 0.08. gt # þ 5. With k 2.7 a. First-order conditions require f1 ¼ x2 ¼ ¼ 4, x1 ¼ # b. With k 4. c. x1 ¼ 5. Because marginal 15, x2 ¼ 20, x1 ¼ d. With k value of x1 is constant, every addition to k beyond 5 adds only to that variable. ¼ 0, x2 ¼ ¼ 10, x1 ¼ 1. 1. Hence, f2 ¼ 5. 2.9 Since fii < 0, the condition for concavity implies that the matrix of second-order partials is negative deﬁnite. Hence the quadratic form involving [ f1, f2] will be negative as required for quasi-concavity. The converse is not true, as shown by the Cobb-Douglas function with a b > 1. þ f 00 d(d 2.11 1)xd a. b. Since f11, f22 < 0 and f12, f21 ¼ c. This preserves quasi-concavity but not concavity. obviously holds. 2 < 0. ¼ # 0, Equation 2.98 # 2.13 a. From Equation 2.85, a function in one variable is concave if f 00(x) < 0. Using the quadratic Taylor to approximate f (x) near a point a Þð # :5f 00 a ð Þ þ Þð because f 00 and # Þð Þð ( # Þ þ Þ b. From Equation 2.98, a function in 2 variables is f 2 12 > 0 and we also know that 1 þ 0. This is the third term of a, concave if f11f22 # due to the concavity of the function, 0.5( f11dx2 f22dx2 2f12dx1dx2 þ 2) the quadratic Taylor expansion where dx dy
y þ ( ¼ f1(a,b)(x b). Which shows that any concave function must lie on or below its tangent plane. b. Thus, we have f (x, y) a) x ¼ # f (a,b) f2(a,b)(y # # þ # ( 2.15 a. Use Var(x) (E(x))2). b. Let y (x c. First part is trivial. Let E[(x # ¼ E(x))2] E(x2 2xE(x) # þ ¼ ¼ mx)2 and apply Markov’s inequality to y. xi=n E l nl=n # Var X d. Var(X) ð k ¼ Var(X) e. If r2 k ¼ Þ ¼ ¼ 2k Þ ¼ ¼ # 0.5. In this case Var(X) nr2=n2 (2k2 ¼ r2=n. P 1)s2 which is minimized for 0.5s2. If, say, k 0.7, 0.58s2 so it is not changed all that much. ¼ rr2 2, the weighted average is minimized if r). 1 ¼ r/(l þ ¼ ¼ X ð ¼ þ 727 728 Solutions to Odd-Numbered Problems CHAPTER 3 3.1 a. No b. Yes c. Yes d. No e. Yes 3.3 The shape of the marginal utility function is not necessarily an indicator of convexity of indifference curves. min(h, 2b, m, 0.5r). 3.5 a. U(h, b, m, r) ¼ b. A fully condimented hot dog c. $1.60 d. $2.10—an increase of 31 percent. e. Price would increase only to $1.725—an increase of 7.8 percent. f. Raise prices so that a fully condimented hot dog rises in price to $2.60. This would be equivalent to a lump-sum reduction in purchasing power. 3.7 a. Indifference curve is linear—MRS b. a c. Just knowing the MRS at a known point can iden- 2, b 1/3. ¼ ¼ ¼ 1. tify
x U must be 0.74 per unit and costs 8.29. ¼ e. With ﬁxed proportions the lump sum and single good subsidy would cost the same. pxU/a. If px/py > a/b then ¼ a/b then E pxU/a ¼ ¼ pyU/b. 4.9 If px/py < a/b then E pyU/b. If px/py ¼ E ¼ 4.11 a. Set MRS b. Set d c. Use pxx/pyy ¼ 0. ¼ px/py. (px/py)d/(d # 1). ¼ 4.13 a. See detailed solutions. b. Multiplying prices and income by 2 does not change V. c. Obviously @V/@I > 0. d. @V/@px, @V/@py < 0. e. Just exchange I and V. f. Multiplying the prices by 2 doubles E. g. Just take partials. h. Show @E/@px > 0, @2E/@p2 x < 0. Solutions to Odd-Numbered Problems 729 CHAPTER 5 CHAPTER 6 5.1 a. U b. x x 3 8 y. x þ I/px if px ( 0 if px > 3 8 py. 3 8 py. ¼ ¼ ¼ d. Changes in py don’t affect demand until reverse the inequality. Just two points (or vertical lines). e. 5.3 a. It is obvious since px/py doesn’t change. b. No good is inferior. 5.5 a. x I px # 2px, y I px þ 2py. ¼ ¼ b. V ð pxÞ þ 4pxpy Hence, changes in py do not affect x, but changes in px do affect y. I 2 and so E 4pxpyV px. ¼ ¼ c. The compensated demand function for x depends on py, whereas the uncompensated function did not. ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ p # 5.7 a. Use the Slutsky equation in elastic
not veer, always veer), the second is (do not veer, do the opposite), and the third is (veer, never veer). f. (Do not veer, do the opposite) is a subgame-perfect equilibrium. 8.5 a. If all play blond, then one would prefer to deviate to brunette to obtain a positive payoff. If all play brunette, then one would prefer to deviate to blond for payoff a rather than b. b. Playing brunette provides a certain payoff of b and blond provides a payoff of a with probability 1 (the probability no other player approaches (1 # the blond). Equating the two payoffs yields p$ (b/a)1/(n # p)n # 1). ¼ # 1 c. The probability the blond is approached by at least one male equals 1 minus the probability no males 1). This (b/a)n/(n p$)n approach her: 1 # # expression is decreasing in n because n/(n 1) is decreasing in n and b/a is a fraction. (1 # # ¼ # 1 3.5 2.5 8.7 l2/4 for a. The best-response function is lLC ¼ þ l2/4 for the low-cost type of player 1, lHC ¼ þ!l1/4 for player 2, the high-cost type, and l2 ¼ þ where!l1 is the average for player 1. Solving these 3:5, and l$2 ¼ 4:5, l$HC ¼ equations yields l$LC ¼ c. The low-cost type of player 1 earns 20.25 in the Bayesian-Nash equilibrium and 20.55 in the fullinformation game, so it would prefer to signal its 4. 3 Solutions to Odd-Numbered Problems 731 þ c. ta bf (k, l); f (tk, tl) ¼ @f (tk, tl)/@t Æ t/f (k, l) 1 this is just a At t (a b. d., e. Apply the deﬁnitions using the derivatives from b)ta þ ¼ þ þ ¼ b. part (a). 9.7 a. b0 ¼ 0. 1 2 b1 l=k k=l b. MPk ¼. c. In general, s is
not constant. If b2 ¼ b3 ¼ ﬃﬃﬃﬃﬃﬃ p ﬃﬃﬃﬃﬃﬃ p 0, s s ¼1 b2 þ 1. If b1 ¼ ; MPL ¼. b3 þ 1 2 b1 ¼ 0, 9.9 a. If f (tk, tl ) l ) then eq,t ¼ tf (k, t/f (tk, tl ). If t ﬁ 1 then f (k, l )/f (k, l ) ¼ @f (tk, tl )/@t Æ 1. ¼ b. Apply Euler’s theorem and use part (a): f (k, l) fll. 2(1 fkk þ c. eq,t ¼ d. The production function has an upper bound of q). Hence q < 0.5 implies eq,t > 1 and # q > 0.5 implies eq,t < 1. ¼ 1. q ¼ 9.11 a. Apply Euler’s theorem to each fi. 2, k2fkk þ 1)f (k, l). 2klfkl þ b. With n ¼ 1, this implies fkl > 0. If k > 1, it is even If k clearer that fkl must be positive. For k < 1, the case is not so clear. l2fll ¼ k(k ¼ # c. Implies that fij > 0 is more common for k d. ( k(k 1). ai)2 1. ¼ # ai ¼ # 10.1 a. By deﬁnition. C(q1, 0) is the cost of producing just good 1 in one ﬁrm. b. By C 0, q2Þ q2 ð C q1, q2Þ q < assumption, ð. Multiplying respectively by q1 and q2 and q1, q2Þ q < C and C q1, 0 Þ ð q1 ð summing gives the economies-of-scope condition. 10.3 a. C q v=5 ð ¼ w=10 Þ þ 50, SC. AC 10v b. For q v=
� b. C ¼ c. wl/vk (v/w)s–1 (b/a)s. l/k d. Labor’s relative share is an increasing function of b/a. If s > 1, labor’s share moves in the same direction as v/w. If s < 1, labor’s relative share moves in the opposite direction to v/w. This accords with intuition on how substitutability should affect shares. ¼ ¼ 10.11 @ ln Ci=@ ln wj # a. sij ¼ @ ln Cj=@ ln wi # b. sij ¼ c. See detailed solutions. @ ln Cj =@ ln wj ¼ @ ln Ci=@ ln wi ¼ exc i, wj # exc j, wi# exc exc j, wj. i, wi. CHAPTER 11 11.1 a. q b. p c. q 50. 200. 5P # ¼ ¼ ¼ 50. wq2/4. 11.3 a. C ¼ b. p(P, w) c. q d. ¼ l(P, w) ¼ 2P/w. P 2/w. P 2/w2. ¼ 11.5 a. Diminishing returns is needed to ensure that a proﬁt-maximizing output choice exists. (w v)q2/100, P (P, v, w) 20, P v) þ 50P/(w ¼ 13,500. þ ¼ 25P2/(w 6,000. þ v). ¼ ¼ b. C(v, w, q) c. q d. q ¼ @P/@P 30, P ¼ ¼ ¼ 11.7 a., b. q a bP, P q/b aq)/b, ¼ ¼ a/b, and the mr curve has double the a/b, R # (q2 þ 2q/b ¼ mr slope of the demand curve, so d ¼ # # Pq ¼ mr # q/b. ¼ # 1/e) P(1 c. mr d. It follows since e ¼ þ 1/b). P(1 þ @q/@P Æ P/
q. ¼ ¼ 11.9 b. Diminishing returns is needed to ensure increasing marginal cost. c. s determines how ﬁrms adapt to disparate input prices. d. q @P=@P 1 # KPg= Þ v1 Þ. ð The size of s does not affect the supply elasticity, but greater substitutability implies that increases in one input price will shift the supply curve less. w1 þ Þ # # Þð r ð r 1 # g 1 # g= e. See detailed solutions. 11.11 a. Follow the indicated steps. By analogy to part c of Problem 11.10, @q$=@v @k=@P. b. As argued in the text, @l=@w ¼ # 0. By similar argu0, implying the last term of the ( ments, @k=@v displayed equation in part a is positive. ( c. First, differentiate the deﬁnitional relation with respect to w. Second, differentiate the relation with respect to v, and use this expression to substitute result for @k$=@w substitute @ls=@k$. @l$=@w. Finally, the d. The increase in long vs. short-run costs from a wage increase w 0 < w 00 can be compared by combining three facts: • C(v, w 0, q) • C(v, w 00, q) • SC(v, w 0, q, k 0) for k 0 SC(v, w 00, q, k 00) for k 00 ¼ ¼ SC(v, w 00, q, k 0). kc(v, w 0, q) kc(v, w 00, q) SC(v, w 00, q, k 00) ¼ ¼ ¼ ( 11.13 a. See detailed answers for proof. b. The formula for cross-price elasticity of input demand weighs both terms by the share of the other input. The effect of a change in the price of the other input will depend primarily on the importance of this other input. c. Using Shephard’s lemma and an implication of Euler’s Theorem (Cww ¼ # AKL: ALL ¼ # vKCwvC wLCwCv ¼ # Sk SL vCwv=w) shows 1
=16 and xs 11.15 If the assets are separate, the equilibrium investments a2=16, yielding joint surplus are xs G ¼ 3=16. If GM acquires both assets, equilibrium ð þ a2=4, yielding joint 0 and xb investments are xb surplus a2=4. The latter joint surplus is higher if 3p. a2 Þ ﬃﬃﬃ CHAPTER 12 12.1 a. q b. Q c. P Pp 10 1,000 ﬃﬃﬃ 25; Q ¼ ¼ ¼ 20. # Pp # 3,000. ﬃﬃﬃ ¼ 2,000. # ¼ 10,000P. 5.99. 12.3 6. a. P ¼ 60,100 b. q ¼ 6.01, P c. P ¼ 600. d. eq,p ¼ # a 0 P 6. ¼ b 0 Q 359,800 – 59,950P. ¼ 6.002; P c 0 P ¼ d 0 eq,p ¼ # 5.998. ¼ 0.6; eq,p ¼ # 3,597. 50, Q 72, Q 12.5 20, P a. n b. n 24, P c. The increase for the makers 10, and w 14, and w $5,368. The linear approximation for the supply curve yields approximately the same result. 1,000, q 1,728, q 200. 288 12.7 a. P ¼ b. P ¼ c. D PS ¼ d. D rents 11, Q 12, Q ¼ ¼ 750. 750. ¼ 500, and r ¼ 1,000, and r 1. ¼ 2. 12.9 a. Long-run equilibrium requires P a a MC k=q AC bq ¼ þ þ k=b P ¼ 2 q ¼ b. Want A p BP # Hence n ﬃﬃﬃﬃﬃﬃﬃ supply A A # # ¼ ¼ ¼ a þ kbp demand. ﬃﬃﬃﬃﬃ ¼ kbp B. 2 a þ ð Þ kbp B a þ ð k=bp ﬃ�
�ﬃﬃﬃ. Þ MC. AC ¼ 2bq Hence ¼ þ ¼ nq ¼ n k=b ¼ p ﬃﬃﬃﬃﬃﬃﬃ c. A has a positive effect on n. That makes sense since A reﬂects the ‘‘size’’ of the market. If a > 0, the effect of B on n is clearly negative. ﬃﬃﬃﬃﬃ ﬃﬃﬃﬃ d. Fixed costs (k) have a negative effect on n. Higher marginal costs raise price and therefore reduce the number of ﬁrms. 12.11 a. Use the deadweight loss formula from Problem 12.10: n n Solutions to Odd-Numbered Problems 733 n T @+=@T ¼ Thus ti ¼ # # 1 i ¼ P eS # tipixi ¼ eDÞ 0 =eSeD ¼ k ð b. The above formula suggests 1=eDÞ 1=eS # k ð that higher taxes should be applied to goods with more inelastic supply and demand. c. This result was obtained under a set of very restric- tive assumptions. CHAPTER 13 900; 9x2 900; x 10, ¼ ¼ 9 on the production possibility frontier, c. ¼ þ ¼ 20. 2x, x2 2(2x)2 13.1 b. If y y ¼ If x y ¼ If x Hence RPT is approximately 2 20:24. 819=2 11 on the frontier, y ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 0.25. p ¼ ¼ ¼ ¼ 779=2 ¼ Dy/Dx p # ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ # ¼ ( # 19:74. 0.50)/ ¼ ¼ C C ¼ ¼ þ þ Cloth. 100. 150. 13.3 Let F Food, C
162, pl ¼ 0.264, x 0.217, x ¼ ¼ 13.9 Computer simulations show that increasing returns to scale is still compatible with a concave production possibility frontier provided the input intensities of the two goods are suitably different. 13.11 a. Doubling prices leaves excess demands unchanged. b. Since, by Walras’ law, p1ED1 ¼ 0. The excess demand in market 1 can be calculated ex3p2 p1p2þ plicitly as: =p2 2p1p3Þ 1. This is also homogeneous of degree 0 in the prices. c. p2/p1 ¼ 0 and ED1 ¼ 6p2p3 þ 3, p3/p1 ¼ ED1 ¼ ð 3 þ 2 # 2p2 5. CHAPTER 14 14.1 24, P a. Q ¼ b. MC P c. Consumer surplus sumer surplus loss ¼ 5 and Q 288. ¼ ¼ ¼ ¼ 29, and p 576. ¼ 48. 1,152. Under monopoly, con576, deadweight ¼ ¼ 288, proﬁts ¼ 14.3 a. Q b. Q c. Q 14.5 a. P b. A ¼ ¼ ¼ ¼ ¼ 25, P 20, P 40, P ¼ ¼ ¼ 35, and p 50, and p 30, and p 625. 800. 800. ¼ ¼ ¼ 15, Q 3, P 5, C 15, Q ¼ ¼ ¼ ¼ 65, and p ¼ 6.05, and p 10. 12.25. ¼ 14.7 a. Under competition: P Under monopoly: P 10, Q ¼ 16, Q 500, CS ¼ 200, CS ¼ 400. 2,500. ¼ ¼ b. See graph in detailed solutions. c. Loss of 2,100, of which 800 is transferred to monopoly proﬁts, 400 is a loss from increased costs (not relevant in usual analysis), and 900 is a deadweight loss. ¼ 14.9 First-order conditions for a maximum imply X C(X)/C 0(X)—that is, X is chosen independently of Q. ¼ 14.11 a. @U/@Q b. P # Q(@P
/@Q) @C/@Q 0, @U/@X 0, ¼ @C/@Q 0. ¼ # @C/@X þ @P/@X Æ Q @C/@X 0. ¼ # ¼ c. Using the hint, parts (a) and (b) imply @SW/@Q # Q(@P/@Q) > 0. @U/@X d. @SW/@X # ¼ @P/@X Æ Q, where the derivatives are calculated at the monopolist’s proﬁt-maximizing choices. It is generally not possible to sign this expression. # ¼ CHAPTER 15 15.1 a. Pm b. Pc c. Pb 75, Pm Qm ¼ qc 50, pc i ¼ 0, Qb ¼ 2,500. i ¼ 150, pb 0. 5,625. ¼ i ¼ ¼ ¼ ¼ 15.3 a. Equilibrium quantities are qc (1 i ¼ c2)/3, P c ¼ pc 1 þ ¼ CSc. Further, Qc (2 c1 # ¼ # c2)2/9, Pc pc 2c1 þ (1 i ¼ Pc c2)2/18, and Wc c1 # b. The diagram looks like Figure 15.2. A reduction in ﬁrm 1’s cost would shift its best response out, increasing its equilibrium output and reducing 2’s. 2ci þ # c1 þ (1 þ 2, CSc pc ¼ cj)/3. c2)/3, (2 # ¼ þ # 1/(2 (1 b). # 2b)/(2 15.5 a. p$i ¼ b); p$i ¼ b. q$i ¼ c. The diagram would look like Figure 15.4. An increase in b would shift out both best responses and result in higher equilibrium prices for both. b)2. 1/(2 # # # 75=2. 15.7 a. q$1 ¼ 75, q$2 ¼ b. If ﬁrm 1 accommodates 2’s entry, it earns 2,812.5. 2’s deter To produce 1 needs K2p. Firm 1
q 1,200x ¼ ¼ 240x # @TR/@x ¼ 10x2. MRP 2x2, total revenue is 5q 1,200 20x. ¼ # lp. Total cost ¼ @C/@x ﬃﬃ MC 600. # Production of pelts x 10x2. Marginal cost tition, price of pelts 20x; x MC ¼ ¼ 30, px ¼ b. From Dan’s perspective, demand for pelts ¼ ¼ ¼ ¼ 1,200 20x, R px Æ x 1,200x ¼ ¼ 1,200 ¼ 20x. Yields x ¼ ¼ # ginal revenue: @R/@x marginal cost # # 20, px ¼ c. From UF’s perspective, supply of pelts ¼ 20x2 and MEx ¼ ¼ 1,200 MRPx ¼ 40x ¼ # 20, px ¼ 400. ¼ 40x. So MEx ¼ ¼ ¼ a solution of x px, total cost pxx 20x ¼ wl ¼ ¼ ¼ 20x. Under compepx ¼ 20x, MRP MRP ¼ 20x2. Mar40x set equal to 800. MC ¼ @C/@x 20x with 16.9 U E U E ½ ½ yjob1Þ+ ¼ ð yjob2Þ+ ¼ ð ¼ 40 100 ) E wh U ð ½ 800w # # Þ+ ¼ 0:5 ) ½ 0:5 1,600 ) E 100wh ½ 36w2 3; 200: wh + Þ 800w ¼ 0:5 # 64w2 2 ð + ¼ þ 50w2: # 16.11 a. @V/@w ¼ b. @xi/@w c. MEl ¼ l(1 ¼ (@V/@w)/(@V/@n). h) ¼ # ll(w, n), @V/@n l, l(w, n) ¼ @xi/@w\|U w ¼ @wl/@l ¼ constant þ ¼ l@w/@l ¼ þ l[@xi/@n]. w[1 þ 1
/(el,w)]. index increase. Total 1/4 into the answers for proﬁt, and the Herﬁndahl output, consumer surplus, and welfare decrease. c2 ¼ 1/4, Q$ 1/8, and W$ 1/2, P$ 1/4. Also, H 1/2, P$ 1/2. c. Substituting c1 ¼ 15.3, we have q$i ¼ 1/8, CS$ ¼ d. Substituting c1 ¼ for 15.3, we have q$1 ¼ 5/12, P$ P$ ¼ 107/288. Also, H ¼ ¼ 0 and c2 ¼ 5/12, q$2 ¼ 29/144, CS$ ¼ 29/49. ¼ ¼ 1/4 into the answers 7/12, 49/288, and W$ 2/12, Q$ ¼ ¼ ¼ ¼ e. Comparing part (a) with (b) suggests that increases in the Herﬁndahl index are associated with lower welfare. The opposite is evidenced in the comparison of part (c) to (d). ¼ 15.11 a. This is the indifference condition for a consumer located distance x from ﬁrm i. b. The proﬁt-maximizing price is p c. Setting p answer. ¼ t/n)/2. p$ and solving for p$ gives the speciﬁed (p$ þ þ ¼ c d. Substituting p p$ c t/n into the proﬁt func- ¼ tion gives the speciﬁed answer. K þ ¼ ¼ # 0 and solving for n yields n$. transportation costs equal e. Setting t/n2 t=K the number of f. Total p ﬃﬃﬃﬃﬃﬃﬃﬃ half-segments between ﬁrms, 2n, times the transportation costs of consumers on the half segment, 1=2n t=8n2. Total ﬁxed cost equal nF. The 0 number of ﬁrms minimizing the sum of the two is R n$$ tx dx t=K 1=2 ¼ ¼. ¼ ð �
� CHAPTER 16 p ﬃﬃﬃﬃﬃﬃﬃﬃ 16.1 a. Full income b. c. d. Supply is asymptotic to 2,000 hours as w rises. 1,400 hours. 1,700 hours. 2,000 hours. 40,000; l ¼ ¼ ¼ ¼ l l 16.3 a. Grant If I I I b. Grant ¼ ¼ ¼ ¼ ¼ 8,000. ¼ # 0.75(I). Grant Grant Grant 6,000 0 2,000 4,000 0 when 6,000 6,000. 4,500. 3,000. 0.75I ¼ ¼ ¼ # 0, I ¼ 6,000/0.75 CHAPTER 17 ¼ c. Assume there are 8,000 hours in the year. Full 4 Income d. Full Income ¼ - 8,000 32,000 c þ ¼ 4h. ¼ 32,000 32,000 38,000 ¼ ¼ ¼ þ þ # grant 6,000 24,000 0.75 Æ 4(8,000 4h c 3h h) # ¼ þ # þ 17.1 b. Income and substitution effects work in opposite directions. If @c1/@r < 0, then c2 is price elastic. c. Budget constraint passes through y1, y2, and rotates through this point as r changes. Income effect depends on whether y1 > c1 or y1 < c1 initially. 736 Solutions to Odd-Numbered Problems 17.3 25 years 17.5 a. Not at all. b. Tax would be on opportunity cost of capital. c. Taxes are paid later, so cost of capital is reduced. d. If tax rates decline, the beneﬁt of accelerated depre- ciation is reduced. 17.7 Using equation 17.66, we get e.75(p0 # p(15) ¼ e.75p0 # p(15) ¼ e.75p0 # 125 ¼ 63.6. p0 ¼ c0) þ e.75c0 þ 7(e.75 e# þ 0.3 c0e# 0.3 c0e# 0.3) 17.9 a. Maximizes expected utility. b.
=@px & px; py; U ð. That is, px=xc. Þ Compensating Wage Differentials Differences in real wages that arise when the characteristics of occupations cause workers in their supply decisions to prefer one job over another. Complements (Gross) Two goods such that if the price of one rises, the quantity consumed of the other will fall. Goods x and y are gross complements if @x=@py < 0. See also Substitutes (Gross). Complements (Net) Two goods such that if the price of one rises, the quantity consumed of the other will fall, holding real income (utility) constant. Goods x and y are net complements if @x=@pyjU ¼ U < 0: – Such compensated cross-price effects are symmetric, that is, @x=@pyjU – U ¼ See also Substitutes (Net). Also called Hicksian substitutes and complements. @y=@pxjU U : – ¼ ¼ 739 740 Glossary of Frequently Used Terms Composite Commodity A group of goods whose prices all move together—the relative prices of goods in the group do not change. Such goods can be treated as a single commodity in many applications. Concave Function A function that lies everywhere below its tangent plane. Constant Cost Industry An industry in which expansion of output and entry by new ﬁrms has no effect on the cost curves of individual ﬁrms. Constant Returns to Scale See Returns to Scale. Consumer Surplus The area below the Marshallian demand curve and above market price. Shows what an individual would pay for the right to make voluntary transactions at this price. Changes in consumer surplus can be used to measure the welfare effects of price changes. Contingent Input Demand See Input Demand Functions. Contour Line The set of points along which a function has a constant value. Useful for graphing threedimensional functions in two dimensions. Individuals’ indifference curve maps and ﬁrms’ production isoquant maps are examples. Contract Curve The set of all the efﬁcient allocations of goods among those individuals in an exchange economy. Each of these allocations has the property that no one individual can be made better off without making someone else worse off. Cost Function See Total Cost Function. Cournot Equilibrium Equilibrium in duopoly quantitysetting game. A similar concept applies to an n-person game.
x ¼ Entry Conditions Characteristics of an industry that determine the ease with which a new ﬁrm may begin production. Under perfect competition, entry is assumed to be costless, whereas in a monopolistic industry there are signiﬁcant barriers to entry. Envelope Theorem A mathematical result: the change in the maximum value of a function brought about by a change in a parameter of the function can be found by partially differentiating the function with respect to the parameter (when all other variables take on their optimal values). Glossary of Frequently Used Terms 741 Equilibrium A situation in which no actors have an incentive to change their behavior. At an equilibrium price, the quantity demanded by individuals is exactly equal to that which is supplied by all ﬁrms. Fixed Costs Costs that do not change as the level of output changes in the short run. Fixed costs are in many respects irrelevant to the theory of short-run price determination. See also Variable Costs. Equivalent Variation The added cost of attaining the new utility level when prices change. Euler’s Theorem A mathematical theorem: if f is homogeneous of degree k, then x1;... ; xnÞ ð f1x1 þ f2x2 þ & & & þ fnxn ¼ kf x1;... ; xnÞ ð : Exchange Economy An economy in which the supply of goods is ﬁxed (that is, no production takes place). The available goods, however, may be reallocated among individuals in the economy. Expansion Path The locus of those cost-minimizing input combinations that a ﬁrm will choose to produce various levels of output (when the prices of inputs are held constant). Expected Utility The average utility expected from a risky situation. If there are n outcomes, x1;... ; xn with probabilities p1;... ; pn pi ¼ utility is given by, then the expected 1 Þ ð P p2U E U ð Þ ¼ p1U x1Þ þ ð x2Þ þ & & & þ ð pnU : xnÞ ð Expenditure Function A function derived from the individual’s dual expenditure minimization problem. Shows the minimum expenditure necessary to achieve a given utility level: expenditures E(px, py, U). ¼ Externality An
effect of one economic agent on another that is not taken into account by normal market behavior. F Financial Option Contract A contract offering the right, but not the obligation, to buy or sell an asset during some future period at a certain price. First-Mover Advantage The advantage that may be gained by the player who moves ﬁrst in a game. First-Order Conditions Mathematical conditions that must necessarily hold if a function is to take on its maximum or minimum value. Usually show that any activity should be increased to the point at which marginal beneﬁts equal marginal costs. First Theorem of Welfare Economics Every Walrasian Equilibrium is Pareto Optimal. G General Equilibrium Model A model of an economy that portrays the operation of many markets simultaneously. Giffen’s Paradox A situation in which the increase in a good’s price leads individuals to consume more of the good. Arises because the good in question is inferior and because the income effect induced by the price change is stronger than the substitution effect. H Hidden Action An action taken by one party to a contract that cannot be directly observed by the other party. Hidden Type A characteristic of one party to a contract that cannot be observed by the other party prior to agreeing to the contract. Homogeneous Function A function, f (x1, x2,..., xn), is homogeneous of degree k if mkf f ð ð mx1; mx2;... ; mxnÞ ¼ : x1; x2;... ; xnÞ Homothetic Function A function that can be represented as a monotonic transformation of a homogeneous function. The slopes of the contour lines for such a function depend only on the ratios of the variables that enter the function, not on their absolute levels. I Income and Substitution Effects Two analytically different effects that come into play when an individual is faced with a changed price for some good. Income effects arise because a change in the price of a good will affect an individual’s purchasing power. Even if purchasing power is held constant, however, substitution effects will cause individuals to reallocate their expectations. Substitution effects are reﬂected in movements along an indifference curve, whereas income effects entail a movement to a different indifference curve. See also Slutsky Equation. I=x. For the demand function Income Elasticity of Demand @x=@I ; ex;
I ¼ x Þ px; py; I & ð Increasing Cost Industry An industry in which the expansion of output creates cost-increasing externalities, which cause the cost curves of those ﬁrms in the industry to shift upward. Increasing Returns to Scale See Returns to Scale. 742 Glossary of Frequently Used Terms Indifference Curve Map A contour map of an individual’s utility function showing those alternative bundles of goods from which the individual derives equal levels of welfare. Indirect Utility Function A representative of utility as a function of all prices and income. Individual Demand Curve The ceteris paribus relationship between the quantity of a good an individual chooses to consume and the good’s price. A two-dimensional representation of x x (px, py, I) for one person. ¼ Inferior Good A good that is bought in smaller quantities as an individual’s income rises. Inferior Input A factor of production that is used in smaller amounts as a ﬁrm’s output expands. Input Demand Functions These functions show how input demand for a proﬁt-maximizing ﬁrm is based on input prices and on the demand for output. The input demand function for labor, for example, can be written as l output. Contingent input demand functions [l c(v, w, q)] are derived from cost minimization and do not necessarily reﬂect proﬁt-maximizing output choices. l (P, v, w), where P is the market price of the ﬁrm’s ¼ Isoquant Map A contour map of the ﬁrm’s production function. The contours show the alternative combinations of productive inputs that can be used to produce a given level of output. K First-order conditions for an Kuhn-Tucker Conditions optimization problem in which inequality constraints are present. These are generalizations of the ﬁrst-order conditions for optimization with equality constraints. Marginal Input Expense The increase in total costs that results from hiring one more unit of an input. Marginal Physical Product (MP ) The additional output that can be produced by one more unit of a particular input while holding all other inputs constant. It is usually assumed that an input’s marginal productivity diminishes as additional units of the input are put into use while holding other inputs ﬁxed. If q @q=
@l. f(k, l), MPl ¼ ¼ Marginal Rate of Substitution (MRS ) The rate at which an individual is willing to trade one good for another while remaining equally well off. The MRS is the absolute value of the slope of an indifference curve. MRS dy=dx ¼ $ U. – jU ¼ Marginal Revenue (MR ) The additional revenue obtained by a ﬁrm when it is able to sell one more unit of output. MR q=@q @p p 1 ð þ 1=eq; pÞ. ¼ ¼ & Marginal Revenue Product (MRP ) The extra revenue that accrues to a ﬁrm when it sells the output that is produced by one more unit of some input. In the case of labor, for example, MRPl = MR Æ MPl. Marginal Utility (MU ) The extra utility that an individual receives by consuming one more unit of a particular good. Market Demand The sum of the quantities of a good demanded by all individuals in a market. Will depend on the price of the good, prices of other goods, each consumer’s preferences, and on each consumer’s income. Market Period A very short period over which quantity supplied is ﬁxed and not responsive to changes in market price. L Limit Pricing Choice of low-price strategies to deter entry. Mixed Strategy A strategy in which a player chooses which pure strategy to play probabilistically. Lindahl Equilibrium A hypothetical solution to the public goods problem: the tax share that each individual pays plays the same role as an equilibrium market price in a competitive allocation. Long Run See Short Run–Long Run Distinction. Lump Sum Principle The demonstration that general purchasing power taxes or transfers are more efﬁcient than taxes or subsidies on individual goods. M Marginal Cost (MC ) The additional cost incurred by producing one more unit of output: MC @C=@q. ¼ Monopoly An industry in which there is only a single seller of the good in question. Monopsony An industry in which there is only a single buyer of the good in question. Moral Hazard The effect of insurance coverage on individuals’ decisions to undertake activities that may change the likelihood or sizes of losses. N Nash Equilibrium A strategy proﬁle such that, for each player i, si is a best response to the other i. players’ equilibrium strategies s( $
; py; I ð Price Taker An economic agent that makes decisions on the assumption that these decisions will have no effect on prevailing market prices. Principal-Agent Relationship The hiring of one person (the agent) by another person (the principal) to make economic decisions. Prisoners’ Dilemma Originally studied in the theory of games but has widespread applicability. The crux of the dilemma is that each individual, faced with the uncertainty of how others will behave, may be led to adopt a course of action that proves to be detrimental for all those individuals making the same decision. A strong coalition might have led to a solution preferred by everyone in the group. Producer Surplus The extra return that producers make by making transactions at the market price over and above what they would earn if nothing were produced. It is illustrated by the size of the area below the market price and above the supply curve. Production Function A conceptual mathematical function that records the relationship between a ﬁrm’s inputs and its outputs. If output is a function of capital and labor only, this would be denoted by q f (k, l). ¼ Production Possibility Frontier The locus of all the alternative quantities of several outputs that can be produced with ﬁxed amounts of productive inputs. Proﬁt Function The relationship between a ﬁrm’s maximum proﬁts (P) and the output and input prices it faces: P ¼ P*(P, v, w). Proﬁts The difference between the total revenue a ﬁrm receives and its total economic costs of production. Economic proﬁts equal zero under perfect competition in the long run. Monopoly proﬁts may be positive, however. Property Rights the rights of owners. Legal speciﬁcation of ownership and Public Good A good that once produced is available to all on a nonexclusive basis. Many public goods are also nonrival—additional individuals may beneﬁt from the good at zero marginal costs. 744 Glossary of Frequently Used Terms Q Quasi-concave Function A function for which the set of all points for which f (X) > k is convex. R Rate of Product Transformation (RPT ) The rate at which one output can be traded for another in the productive process while holding the total quantities of inputs constant. The RPT is the absolute value of the slope of the production possibility frontier. Rate
ima, 84–85 curvature and, 48–55 for maximum, 84, 121–122 quasi-concavity, 85 several variables, 34–35 Second-order partial derivatives, 29–30 Second-party preferences, 113 Second theorem of welfare economics, 478–481 Selﬁshness, 117–118 Selten, Reinhard, 275 Separating equilibrium, 286–287, 561 Sequential Battle of the Sexes game, 268–269 Sequential games, 268–274 backward induction, 273–274 Battle of the Sexes, 268–269 extensive form, 269–270 Nash equilibria, 270–271 subgame-perfect equilibrium, 271–273 Shadow (implicit) prices, 197–200 Sharpe, W. F., 245 Shephard, R. W., 157 Shephard’s lemma, 157–158 contingent demand for inputs and, 353–355 deﬁned, 721 elasticity of substitution and, 355 net substitutes and complements, 192 Shogren, J. F., 714 Short run, long run distinction, 355–362 ﬁxed and variable costs, 356 graphs of per-unit cost curves, 361–362 nonoptimality of, 356–367 relationship between long-run cost curves and, 358–361 short-run marginal and average costs, 358 total costs, 356 Short-run analysis, 355–362 ﬁxed and variable costs, 356 graphs of per-unit cost curves, 361–362 nonoptimality of, 356–367 price determination, 415–419 producer surplus in, 388–395 relationship between long-run cost curves and, 358–361 short-run marginal and average costs, 358 total costs, 356 Short-run average total cost function (SAC), 358, 361–362 Short-run ﬁxed costs, 356 Short-run marginal cost function (SMC), 358, 361–362 Short-run market supply function, 416–417 Short-run supply curve, 381–384, 416 Short-run supply elasticity, 416 Short-run variable costs, 356 Shutdown decision, 381–384 Signaling, 559–562, 670–672 in competitive insurance markets, 670 entry-deterrence model, 559–560 market for lemons, 671–672 pooling equilibrium, 561 predatory pricing, 561–562 separating equilibrium, 561 Signaling games, 278, 282
you a well-rounded thinker. When you read articles about economic issues, you will understand and be able to evaluate the writer’s argument. When you hear classmates, co-workers, or political candidates talking about economics, you will be able to distinguish between common sense and nonsense. You will find new ways of thinking about current events and about personal and business decisions, as well as current events and politics. The study of economics does not dictate the answers, but it can illuminate the different choices. 1.2 \| Microeconomics and Macroeconomics By the end of this section, you will be able to: • Describe microeconomics • Describe macroeconomics • Contrast monetary policy and fiscal policy Economics is concerned with the well-being of all people, including those with jobs and those without jobs, as well as those with high incomes and those with low incomes. Economics acknowledges that production of useful goods and services can create problems of environmental pollution. It explores the question of how investing in education helps to develop workers’ skills. It probes questions like how to tell when big businesses or big labor unions are operating in a way that benefits society as a whole and when they are operating in a way that benefits their owners or members at the expense of others. It looks at how government spending, taxes, and regulations affect decisions about production and consumption. It should be clear by now that economics covers considerable ground. We can divide that ground into two parts: Microeconomics focuses on the actions of individual agents within the economy, like households, workers, and businesses. Macroeconomics looks at the economy as a whole. It focuses on broad issues such as growth of production, the number of unemployed people, the inflationary increase in prices, government deficits, and levels of exports and imports. Microeconomics and macroeconomics are not separate subjects, but rather complementary perspectives on the overall subject of the economy. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 1 \| Welcome to Economics! 15 To understand why both microeconomic and macroeconomic perspectives are useful, consider the problem of studying a biological ecosystem like a lake. One person who sets out to study the lake might focus on specific topics: certain kinds of algae or plant life; the characteristics of particular fish or snails; or the trees surrounding the lake. Another person might take an overall view and instead consider the lake's ecosystem from top to bottom; what eats what, how the system stays
in a rough balance, and what environmental stresses affect this balance. Both approaches are useful, and both examine the same lake, but the viewpoints are different. In a similar way, both microeconomics and macroeconomics study the same economy, but each has a different viewpoint. Whether you are scrutinizing lakes or economics, the micro and the macro insights should blend with each other. In studying a lake, the micro insights about particular plants and animals help to understand the overall food chain, while the macro insights about the overall food chain help to explain the environment in which individual plants and animals live. In economics, the micro decisions of individual businesses are influenced by whether the macroeconomy is healthy. For example, firms will be more likely to hire workers if the overall economy is growing. In turn, macroeconomy's performance ultimately depends on the microeconomic decisions that individual households and businesses make. Microeconomics What determines how households and individuals spend their budgets? What combination of goods and services will best fit their needs and wants, given the budget they have to spend? How do people decide whether to work, and if so, whether to work full time or part time? How do people decide how much to save for the future, or whether they should borrow to spend beyond their current means? What determines the products, and how many of each, a firm will produce and sell? What determines the prices a firm will charge? What determines how a firm will produce its products? What determines how many workers it will hire? How will a firm finance its business? When will a firm decide to expand, downsize, or even close? In the microeconomics part of this book, we will learn about the theory of consumer behavior, the theory of the firm, how markets for labor and other resources work, and how markets sometimes fail to work properly. Macroeconomics What determines the level of economic activity in a society? In other words, what determines how many goods and services a nation actually produces? What determines how many jobs are available in an economy? What determines a nation’s standard of living? What causes the economy to speed up or slow down? What causes firms to hire more workers or to lay them off? Finally, what causes the economy to grow over the long term? We can determine an economy's macroeconomic health by examining a number of goals: growth in the standard of living, low unemployment, and low inflation, to name the most important. How can we use government macroeconomic policy to pursue these goals?
A nation's central bank conducts monetary policy, which involves policies that affect bank lending, interest rates, and financial capital markets. For the United States, this is the Federal Reserve. A nation's legislative body determines fiscal policy, which involves government spending and taxes. For the United States, this is the Congress and the executive branch, which originates the federal budget. These are the government's main tools. Americans tend to expect that government can fix whatever economic problems we encounter, but to what extent is that expectation realistic? These are just some of the issues that we will explore in the macroeconomic chapters of this book. 1.3 \| How Economists Use Theories and Models to Understand Economic Issues By the end of this section, you will be able to: Interpret a circular flow diagram • • Explain the importance of economic theories and models • Describe goods and services markets and labor markets 16 Chapter 1 \| Welcome to Economics! Figure 1.5 John Maynard Keynes One of the most influential economists in modern times was John Maynard Keynes. (Credit: Wikimedia Commons) John Maynard Keynes (1883–1946), one of the greatest economists of the twentieth century, pointed out that economics is not just a subject area but also a way of thinking. Keynes (Figure 1.5) famously wrote in the introduction to a fellow economist’s book: “[Economics] is a method rather than a doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct conclusions.” In other words, economics teaches you how to think, not what to think. Watch this video (http://openstax.org/l/Keynes) about John Maynard Keynes and his influence on economics. Economists see the world through a different lens than anthropologists, biologists, classicists, or practitioners of any other discipline. They analyze issues and problems using economic theories that are based on particular assumptions about human behavior. These assumptions tend to be different than the assumptions an anthropologist or psychologist might use. A theory is a simplified representation of how two or more variables interact with each other. The purpose of a theory is to take a complex, real-world issue and simplify it down to its essentials. If done well, this enables the analyst to understand the issue and any problems around it. A good theory is simple enough to understand, while complex enough to capture the key features of the object or situation you are studying. Sometimes economists use the term model instead of theory. Strict
ly speaking, a theory is a more abstract representation, while a model is a more applied or empirical representation. We use models to test theories, but for this course we will use the terms interchangeably. For example, an architect who is planning a major office building will often build a physical model that sits on a tabletop to show how the entire city block will look after the new building is constructed. Companies often build models of their new products, which are more rough and unfinished than the final product, but can still demonstrate how the new product will work. A good model to start with in economics is the circular flow diagram (Figure 1.6). It pictures the economy as consisting of two groups—households and firms—that interact in two markets: the goods and services market in which firms sell and households buy and the labor market in which households sell labor to business firms or other employees. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 1 \| Welcome to Economics! 17 Figure 1.6 The Circular Flow Diagram The circular flow diagram shows how households and firms interact in the goods and services market, and in the labor market. The direction of the arrows shows that in the goods and services market, households receive goods and services and pay firms for them. In the labor market, households provide labor and receive payment from firms through wages, salaries, and benefits. Firms produce and sell goods and services to households in the market for goods and services (or product market). Arrow “A” indicates this. Households pay for goods and services, which becomes the revenues to firms. Arrow “B” indicates this. Arrows A and B represent the two sides of the product market. Where do households obtain the income to buy goods and services? They provide the labor and other resources (e.g. land, capital, raw materials) firms need to produce goods and services in the market for inputs (or factors of production). Arrow “C” indicates this. In return, firms pay for the inputs (or resources) they use in the form of wages and other factor payments. Arrow “D” indicates this. Arrows “C” and “D” represent the two sides of the factor market. Of course, in the real world, there are many different markets for goods and services and markets for many different types of labor. The circular flow diagram simplifies this to make the
picture easier to grasp. In the diagram, firms produce goods and services, which they sell to households in return for revenues. The outer circle shows this, and represents the two sides of the product market (for example, the market for goods and services) in which households demand and firms supply. Households sell their labor as workers to firms in return for wages, salaries, and benefits. The inner circle shows this and represents the two sides of the labor market in which households supply and firms demand. This version of the circular flow model is stripped down to the essentials, but it has enough features to explain how the product and labor markets work in the economy. We could easily add details to this basic model if we wanted to introduce more real-world elements, like financial markets, governments, and interactions with the rest of the globe (imports and exports). Economists carry a set of theories in their heads like a carpenter carries around a toolkit. When they see an economic issue or problem, they go through the theories they know to see if they can find one that fits. Then they use the theory to derive insights about the issue or problem. Economists express theories as diagrams, graphs, or even as mathematical equations. (Do not worry. In this course, we will mostly use graphs.) Economists do not figure out the answer to the problem first and then draw the graph to illustrate. Rather, they use the graph of the theory to help them figure out the answer. Although at the introductory level, you can sometimes figure out the right answer without applying a model, if you keep studying economics, before too long you will run into issues and problems that you will need to graph to solve. We explain both micro and macroeconomics in terms of theories and models. The most well-known theories are probably those of supply and demand, but you will learn a number of others. 18 Chapter 1 \| Welcome to Economics! 1.4 \| How To Organize Economies: An Overview of Economic Systems By the end of this section, you will be able to: • Contrast traditional economies, command economies, and market economies • Explain gross domestic product (GDP) • Assess the importance and effects of globalization Think about what a complex system a modern economy is. It includes all production of goods and services, all buying and selling, all employment. The economic life of every individual is interrelated, at least to a small extent, with the economic lives of thousands or even millions of other individuals. Who organizes and coordinates this
system? Who insures that, for example, the number of televisions a society provides is the same as the amount it needs and wants? Who insures that the right number of employees work in the electronics industry? Who insures that televisions are produced in the best way possible? How does it all get done? There are at least three ways that societies organize an economy. The first is the traditional economy, which is the oldest economic system and is used in parts of Asia, Africa, and South America. Traditional economies organize their economic affairs the way they have always done (i.e., tradition). Occupations stay in the family. Most families are farmers who grow the crops using traditional methods. What you produce is what you consume. Because tradition drives the way of life, there is little economic progress or development. Figure 1.7 A Command Economy Ancient Egypt was an example of a command economy. (Credit: Jay Bergesen/ Flickr Creative Commons) Command economies are very different. In a command economy, economic effort is devoted to goals passed down from a ruler or ruling class. Ancient Egypt was a good example: a large part of economic life was devoted to building pyramids, like those in Figure 1.7, for the pharaohs. Medieval manor life is another example: the lord provided the land for growing crops and protection in the event of war. In return, vassals provided labor and soldiers to do the lord’s bidding. In the last century, communism emphasized command economies. In a command economy, the government decides what goods and services will be produced and what prices it will charge for them. The government decides what methods of production to use and sets wages for workers. The government provides many necessities like healthcare and education for free. Currently, Cuba and North Korea have command economies. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 1 \| Welcome to Economics! 19 Figure 1.8 A Market Economy Nothing says “market” more than The New York Stock Exchange. (Credit: Erik Drost/ Flickr Creative Commons) Although command economies have a very centralized structure for economic decisions, market economies have a very decentralized structure. A market is an institution that brings together buyers and sellers of goods or services, who may be either individuals or businesses. The New York Stock Exchange (Figure 1.8) is a prime example of a market which brings buyers and sellers together. In a market economy, decision-
making is decentralized. Market economies are based on private enterprise: the private individuals or groups of private individuals own and operate the means of production (resources and businesses). Businesses supply goods and services based on demand. (In a command economy, by contrast, the government owns resources and businesses.) Supply of goods and services depends on what the demands. A person’s income is based on his or her ability to convert resources (especially labor) into something that society values. The more society values the person’s output, the higher the income (think Lady Gaga or LeBron James). In this scenario, market forces, not governments, determine economic decisions. Most economies in the real world are mixed. They combine elements of command and market (and even traditional) systems. The U.S. economy is positioned toward the market-oriented end of the spectrum. Many countries in Europe and Latin America, while primarily market-oriented, have a greater degree of government involvement in economic decisions than the U.S. economy. China and Russia, while over the past several decades have moved more in the direction of having a market-oriented system, remain closer to the command economy end of the spectrum. The Heritage Foundation provides information about how free and thus market-oriented different countries' are, as the following Clear It Up feature discusses. For a similar ranking, but one that defines freedom more broadly, see the Cato Foundation's Human Freedom Index (https://openstax.org/l/cato). What countries are considered economically free? Who is in control of economic decisions? Are people free to do what they want and to work where they want? Are businesses free to produce when they want and what they choose, and to hire and fire as they wish? Are banks free to choose who will receive loans, or does the government control these kinds of choices? Each year, researchers at the Heritage Foundation and the Wall Street Journal look at 50 different categories of economic freedom for countries around the world. They give each nation a score based on the extent of economic freedom in each category. The 2016 Heritage Foundation’s Index of Economic Freedom report ranked 178 countries around the world: Table 1.1 lists some examples of the most free and the least free countries. Several additional countries were not ranked because of extreme instability that made judgments about economic freedom impossible. These countries include Afghanistan, Iraq, Libya, Syria, Somalia, and Yemen. The assigned rankings are inevitably based on estimates, yet even these rough measures can be useful for discerning trends.
In 2015, 101 of the 178 included countries shifted toward greater economic freedom, although 77 of the countries shifted toward less economic freedom. In recent decades, the overall trend has been a higher level of economic freedom around the world. 20 Chapter 1 \| Welcome to Economics! Most Economic Freedom Least Economic Freedom 1. Hong Kong 2. Singapore 3. New Zealand 4. Switzerland 5. Australia 6. Canada 7. Chile 8. Ireland 9. Estonia 10. United Kingdom 11. United States 12. Denmark 167. Timor-Leste 168. Democratic Republic of Congo 169. Argentina 170. Equatorial Guinea 171. Iran 172. Republic of Congo 173. Eritrea 174. Turkmenistan 175. Zimbabwe 176. Venezuela 177. Cuba 178. North Korea Table 1.1 Economic Freedoms, 2016 (Source: The Heritage Foundation, 2016 Index of Economic Freedom, Country Rankings, http://www.heritage.org/index/ranking) Regulations: The Rules of the Game Markets and government regulations are always entangled. There is no such thing as an absolutely free market. Regulations always define the “rules of the game” in the economy. Economies that are primarily market-oriented have fewer regulations—ideally just enough to maintain an even playing field for participants. At a minimum, these laws govern matters like safeguarding private property against theft, protecting people from violence, enforcing legal contracts, preventing fraud, and collecting taxes. Conversely, even the most command-oriented economies operate using markets. How else would buying and selling occur? The government heavily regulates decisions of what to produce and prices to charge. Heavily regulated economies often have underground economies (or black markets), which are markets where the buyers and sellers make transactions without the government’s approval. The question of how to organize economic institutions is typically not a black-or-white choice between all market or all government, but instead involves a balancing act over the appropriate combination of market freedom and government rules. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 1 \| Welcome to Economics! 21 Figure 1.9 Globalization Cargo ships are one mode of transportation for shipping goods in the global economy. (Credit: Raul Valdez/Flickr Creative Commons) The Rise of Globalization Recent decades have seen a trend toward globalization, which is the expanding cultural, political, and economic connections between people around the world. One measure of this is the increased buying and selling of goods, services
, and assets across national borders—in other words, international trade and financial capital flows. Globalization has occurred for a number of reasons. Improvements in shipping, as illustrated by the container ship in Figure 1.9, and air cargo have driven down transportation costs. Innovations in computing and telecommunications have made it easier and cheaper to manage long-distance economic connections of production and sales. Many valuable products and services in the modern economy can take the form of information—for example: computer software; financial advice; travel planning; music, books and movies; and blueprints for designing a building. These products and many others can be transported over telephones and computer networks at ever-lower costs. Finally, international agreements and treaties between countries have encouraged greater trade. Table 1.2 presents one measure of globalization. It shows the percentage of domestic economic production that was exported for a selection of countries from 2010 to 2015, according to an entity known as The World Bank. Exports are the goods and services that one produces domestically and sells abroad. Imports are the goods and services that one produces abroad and then sells domestically. Gross domestic product (GDP) measures the size of total production in an economy. Thus, the ratio of exports divided by GDP measures what share of a country’s total economic production is sold in other countries. Country 2010 2011 2012 2013 2014 2015 Higher Income Countries United States Belgium Canada France Middle Income Countries Brazil Mexico South Korea 12.4 76.2 29.1 26.0 10.9 29.9 49.4 13.6 81.4 30.7 27.8 11.9 31.2 55.7 13.6 82.2 30.0 28.1 12.6 32.6 56.3 13.5 82.8 30.1 28.3 12.6 31.7 53.9 13.5 84.0 31.7 29.0 11.2 32.3 50.3 12.6 84.4 31.5 30.0 13.0 35.3 45.9 Table 1.2 The Extent of Globalization (exports/GDP) (Source: http://databank.worldbank.org/data/) 22 Chapter 1 \| Welcome to Economics! Country 2010 2011 2012 2013 2014 2015 Lower Income Countries Chad China India Nigeria 36.8 29.4 22.0 25.3 38.9 28.5 23.9 31.3 36.9 27.3 24.0 31.4 32.2 26
.4 24.8 18.0 34.2 23.9 22.9 18.4 29.8 22.4 - - Table 1.2 The Extent of Globalization (exports/GDP) (Source: http://databank.worldbank.org/data/) In recent decades, the export/GDP ratio has generally risen, both worldwide and for the U.S. economy. Interestingly, the share of U.S. exports in proportion to the U.S. economy is well below the global average, in part because large economies like the United States can contain more of the division of labor inside their national borders. However, smaller economies like Belgium, Korea, and Canada need to trade across their borders with other countries to take full advantage of division of labor, specialization, and economies of scale. In this sense, the enormous U.S. economy is less affected by globalization than most other countries. Table 1.2 indicates that many medium and low income countries around the world, like Mexico and China, have also experienced a surge of globalization in recent decades. If an astronaut in orbit could put on special glasses that make all economic transactions visible as brightly colored lines and look down at Earth, the astronaut would see the planet covered with connections. Despite the rise in globalization over the last few decades, in recent years we've seen significant pushback against globalization from people across the world concerned about loss of jobs, loss of political sovereignty, and increased economic inequality. Prominent examples of this pushback include the 2016 vote in Great Britain to exit the European Union (i.e. Brexit), and the election of Donald J. Trump for President of the United States. Hopefully, you now have an idea about economics. Before you move to any other chapter of study, be sure to read the very important appendix to this chapter called The Use of Mathematics in Principles of Economics. It is essential that you learn more about how to read and use models in economics. Decisions... Decisions in the Social Media Age The world we live in today provides nearly instant access to a wealth of information. Consider that as recently as the late 1970s, the Farmer’s Almanac, along with the Weather Bureau of the U.S. Department of Agriculture, were the primary sources American farmers used to determine when to plant and harvest their crops. Today, farmers are more likely to access, online, weather forecasts from the National Oceanic and Atmospheric Administration or watch the Weather Channel. After all, knowing the upcoming forecast
could drive when to harvest crops. Consequently, knowing the upcoming weather could change the amount of crop harvested. Some relatively new information forums, such as Facebook, are rapidly changing how information is distributed; hence, influencing decision making. In 2014, the Pew Research Center reported that 71% of online adults use Facebook. This social media forum posts topics ranging from the National Basketball Association, to celebrity singers and performers, to farmers. Information helps us make decisions as simple as what to wear today to how many reporters the media should send to cover a crash. Each of these decisions is an economic decision. After all, resources are scarce. If the media send ten reporters to cover an accident, they are not available to cover other stories or complete other tasks. Information provides the necessary knowledge to make the best possible decisions on how to utilize scarce resources. Welcome to the world of economics! This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 1 \| Welcome to Economics! 23 KEY TERMS circular flow diagram a diagram that views the economy as consisting of households and firms interacting in a goods and services market and a labor market command economy an economy where economic decisions are passed down from government authority and where the government owns the resources division of labor the way in which different workers divide required tasks to produce a good or service economics the study of how humans make choices under conditions of scarcity economies of scale when the average cost of producing each individual unit declines as total output increases exports products (goods and services) made domestically and sold abroad fiscal policy economic policies that involve government spending and taxes globalization the trend in which buying and selling in markets have increasingly crossed national borders goods and services market a market in which firms are sellers of what they produce and households are buyers gross domestic product (GDP) measure of the size of total production in an economy imports products (goods and services) made abroad and then sold domestically labor market the market in which households sell their labor as workers to business firms or other employers macroeconomics the branch of economics that focuses on broad issues such as growth, unemployment, inflation, and trade balance market interaction between potential buyers and sellers; a combination of demand and supply market economy an economy where economic decisions are decentralized, private individuals own resources, and businesses supply goods and services based on demand microeconomics the branch of economics that focuses on actions of particular agents within the economy, like households, workers, and business firms model see theory monetary policy policy that involves altering the level of interest rates
, the availability of credit in the economy, and the extent of borrowing private enterprise system where private individuals or groups of private individuals own and operate the means of production (resources and businesses) scarcity when human wants for goods and services exceed the available supply specialization when workers or firms focus on particular tasks for which they are well-suited within the overall production process theory a representation of an object or situation that is simplified while including enough of the key features to help us understand the object or situation traditional economy typically an agricultural economy where things are done the same as they have always been done underground economy a market where the buyers and sellers make transactions in violation of one or more 24 Chapter 1 \| Welcome to Economics! government regulations KEY CONCEPTS AND SUMMARY 1.1 What Is Economics, and Why Is It Important? Economics seeks to solve the problem of scarcity, which is when human wants for goods and services exceed the available supply. A modern economy displays a division of labor, in which people earn income by specializing in what they produce and then use that income to purchase the products they need or want. The division of labor allows individuals and firms to specialize and to produce more for several reasons: a) It allows the agents to focus on areas of advantage due to natural factors and skill levels; b) It encourages the agents to learn and invent; c) It allows agents to take advantage of economies of scale. Division and specialization of labor only work when individuals can purchase what they do not produce in markets. Learning about economics helps you understand the major problems facing the world today, prepares you to be a good citizen, and helps you become a well-rounded thinker. 1.2 Microeconomics and Macroeconomics Microeconomics and macroeconomics are two different perspectives on the economy. The microeconomic perspective focuses on parts of the economy: individuals, firms, and industries. The macroeconomic perspective looks at the economy as a whole, focusing on goals like growth in the standard of living, unemployment, and inflation. Macroeconomics has two types of policies for pursuing these goals: monetary policy and fiscal policy. 1.3 How Economists Use Theories and Models to Understand Economic Issues Economists analyze problems differently than do other disciplinary experts. The main tools economists use are economic theories or models. A theory is not an illustration of the answer to a problem. Rather, a theory is a tool for determining the answer. 1.4 How To Organize Economies: An Overview of Economic Systems We can organize societies as traditional, command, or
market-oriented economies. Most societies are a mix. The last few decades have seen globalization evolve as a result of growth in commercial and financial networks that cross national borders, making businesses and workers from different economies increasingly interdependent. SELF-CHECK QUESTIONS 1. What is scarcity? Can you think of two causes of scarcity? 2. Residents of the town of Smithfield like to consume hams, but each ham requires 10 people to produce it and takes a month. If the town has a total of 100 people, what is the maximum amount of ham the residents can consume in a month? 3. A consultant works for $200 per hour. She likes to eat vegetables, but is not very good at growing them. Why does it make more economic sense for her to spend her time at the consulting job and shop for her vegetables? 4. A computer systems engineer could paint his house, but it makes more sense for him to hire a painter to do it. Explain why. 5. What would be another example of a “system” in the real world that could serve as a metaphor for micro and macroeconomics? 6. Suppose we extend the circular flow model to add imports and exports. Copy the circular flow diagram onto a sheet of paper and then add a foreign country as a third agent. Draw a rough sketch of the flows of imports, exports, and the payments for each on your diagram. 7. What is an example of a problem in the world today, not mentioned in the chapter, that has an economic dimension? This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 1 \| Welcome to Economics! 25 8. The chapter defines private enterprise as a characteristic of market-oriented economies. What would public enterprise be? Hint: It is a characteristic of command economies. 9. Why might Belgium, France, Italy, and Sweden have a higher export to GDP ratio than the United States? REVIEW QUESTIONS 10. Give the three reasons that explain why the division of increases an economy’s level of production. labor 11. What are three reasons to study economics? How did 15. economics? John Maynard Keynes define 16. Are households primarily buyers or sellers in the goods and services market? In the labor market? 12. What is the difference between microeconomics and macroeconomics? 17. Are firms primarily buyers or sellers in the goods and services market? In the labor market? 13. What are examples
of agents? individual economic 18. What are the three ways that societies can organize themselves economically? What 14. macroeconomics? are the three main goals of 19. What is globalization? How do you think it might have affected the economy over the past decade? CRITICAL THINKING QUESTIONS 20. Suppose you have a team of two workers: one is a baker and one is a chef. Explain why the kitchen can produce more meals in a given period of time if each worker specializes in what they do best than if each worker tries to do everything from appetizer to dessert. 24. Macroeconomics is an aggregate of what happens at the microeconomic level. Would it be possible for what happens at the macro level to differ from how economic agents would react to some stimulus at the micro level? Hint: Think about the behavior of crowds. 21. Why would division of labor without trade not work? 25. Why is it unfair or meaningless to criticize a theory as “unrealistic?” 22. Can you think of any examples of free goods, that is, goods or services that are not scarce? 23. A balanced federal budget and a balance of trade are secondary goals of macroeconomics, while growth in the standard of living (for example) is a primary goal. Why do you think that is so? 26. Suppose, as an economist, you are asked to analyze an issue unlike anything you have ever done before. Also, suppose you do not have a specific model for analyzing that issue. What should you do? Hint: What would a carpenter do in a similar situation? 27. Why do you think that most modern countries’ economies are a mix of command and market types? 28. Can you think of ways that globalization has helped you economically? Can you think of ways that it has not? 26 Chapter 1 \| Welcome to Economics! This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 27 2 \| Choice in a World of Scarcity Figure 2.1 Choices and Tradeoffs In general, the higher the degree, the higher the salary, so why aren’t more people pursuing higher degrees? The short answer: choices and tradeoffs. (Credit: modification of work by “Jim, the Photographer”/Flickr Creative Commons) Choices... To What Degree? In 2015, the median income for workers who hold master's
degrees varies from males to females. The average of the two is $2,951 weekly. Multiply this average by 52 weeks, and you get an average salary of $153,452. Compare that to the median weekly earnings for a full-time worker over 25 with no higher than a bachelor’s degree: $1,224 weekly and $63,648 a year. What about those with no higher than a high school diploma in 2015? They earn just $664 weekly and $34,528 over 12 months. In other words, says the Bureau of Labor Statistics (BLS), earning a bachelor’s degree boosted salaries 54% over what you would have earned if you had stopped your education after high school. A master’s degree yields a salary almost double that of a high school diploma. Given these statistics, we might expect many people to choose to go to college and at least earn a bachelor’s degree. Assuming that people want to improve their material well-being, it seems like they would make those choices that provide them with the greatest opportunity to consume goods and services. As it turns out, the analysis is not nearly as simple as this. In fact, in 2014, the BLS reported that while almost 88% of the population in the United States had a high school diploma, only 33.6% of 25–65 year olds had bachelor’s degrees, and only 7.4% of 25–65 year olds in 2014 had earned a master’s. This brings us to the subject of this chapter: why people make the choices they make and how economists explain those choices. 28 Chapter 2 \| Choice in a World of Scarcity Introduction to Choice in a World of Scarcity In this chapter, you will learn about: • How Individuals Make Choices Based on Their Budget Constraint • The Production Possibilities Frontier and Social Choices • Confronting Objections to the Economic Approach You will learn quickly when you examine the relationship between economics and scarcity that choices involve tradeoffs. Every choice has a cost. In 1968, the Rolling Stones recorded “You Can’t Always Get What You Want.” Economists chuckled, because they had been singing a similar tune for decades. English economist Lionel Robbins (1898–1984), in his Essay on the Nature and Significance of Economic Science in 1932, described not always getting what you want in this way: The time at our disposal is limited. There are only twenty-four hours
in the day. We have to choose between the different uses to which they may be put.... Everywhere we turn, if we choose one thing we must relinquish others which, in different circumstances, we would wish not to have relinquished. Scarcity of means to satisfy given ends is an almost ubiquitous condition of human nature. Because people live in a world of scarcity, they cannot have all the time, money, possessions, and experiences they wish. Neither can society. This chapter will continue our discussion of scarcity and the economic way of thinking by first introducing three critical concepts: opportunity cost, marginal decision making, and diminishing returns. Later, it will consider whether the economic way of thinking accurately describes either how we make choices and how we should make them. 2.1 \| How Individuals Make Choices Based on Their Budget Constraint By the end of this section, you will be able to: • Calculate and graph budget constraints • Explain opportunity sets and opportunity costs • Evaluate the law of diminishing marginal utility • Explain how marginal analysis and utility influence choices Consider the typical consumer’s budget problem. Consumers have a limited amount of income to spend on the things they need and want. Suppose Alphonso has $10 in spending money each week that he can allocate between bus tickets for getting to work and the burgers that he eats for lunch. Burgers cost $2 each, and bus tickets are 50 cents each. We can see Alphonso's budget problem in Figure 2.2. Figure 2.2 The Budget Constraint: Alphonso’s Consumption Choice Opportunity Frontier Each point on the budget constraint represents a combination of burgers and bus tickets whose total cost adds up to Alphonso’s budget of $10. The relative price of burgers and bus tickets determines the slope of the budget constraint. All along the budget set, giving up one burger means gaining four bus tickets. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 29 The vertical axis in the figure shows burger purchases and the horizontal axis shows bus ticket purchases. If Alphonso spends all his money on burgers, he can afford five per week. ($10 per week/$2 per burger = 5 burgers per week.) However, if he does this, he will not be able to afford any bus tickets. Point A in the figure shows the choice (zero bus tickets and five burgers). Alternatively, if Alphonso spends all his
money on bus tickets, he can afford 20 per week. ($10 per week/$0.50 per bus ticket = 20 bus tickets per week.) Then, however, he will not be able to afford any burgers. Point F shows this alternative choice (20 bus tickets and zero burgers). If we connect all the points between A and F, we get Alphonso's budget constraint. This indicates all the combination of burgers and bus tickets Alphonso can afford, given the price of the two goods and his budget amount. If Alphonso is like most people, he will choose some combination that includes both bus tickets and burgers. That is, he will choose some combination on the budget constraint that is between points A and F. Every point on (or inside) the constraint shows a combination of burgers and bus tickets that Alphonso can afford. Any point outside the constraint is not affordable, because it would cost more money than Alphonso has in his budget. The budget constraint clearly shows the tradeoff Alphonso faces in choosing between burgers and bus tickets. Suppose he is currently at point D, where he can afford 12 bus tickets and two burgers. What would it cost Alphonso for one more burger? It would be natural to answer $2, but that’s not the way economists think. Instead they ask, how many bus tickets would Alphonso have to give up to get one more burger, while staying within his budget? Since bus tickets cost 50 cents, Alphonso would have to give up four to afford one more burger. That is the true cost to Alphonso. The Concept of Opportunity Cost Economists use the term opportunity cost to indicate what one must give up to obtain what he or she desires. The idea behind opportunity cost is that the cost of one item is the lost opportunity to do or consume something else. In short, opportunity cost is the value of the next best alternative. For Alphonso, the opportunity cost of a burger is the four bus tickets he would have to give up. He would decide whether or not to choose the burger depending on whether the value of the burger exceeds the value of the forgone alternative—in this case, bus tickets. Since people must choose, they inevitably face tradeoffs in which they have to give up things they desire to obtain other things they desire more. View this website (http://openstaxcollege.org/l/linestanding) for an example of opportunity cost—paying someone else to wait in line for you. A fundamental principle of economics is that every choice has
an opportunity cost. If you sleep through your economics class, the opportunity cost is the learning you miss from not attending class. If you spend your income on video games, you cannot spend it on movies. If you choose to marry one person, you give up the opportunity to marry anyone else. In short, opportunity cost is all around us and part of human existence. The following Work It Out feature shows a step-by-step analysis of a budget constraint calculation. Read through it to understand another important concept—slope—that we further explain in the appendix The Use of Mathematics in Principles of Economics. 30 Chapter 2 \| Choice in a World of Scarcity Understanding Budget Constraints Budget constraints are easy to understand if you apply a little math. The appendix The Use of Mathematics in Principles of Economics explains all the math you are likely to need in this book. Therefore, if math is not your strength, you might want to take a look at the appendix. Step 1: The equation for any budget constraint is: Budget = P1 × Q1 + P2 × Q2 where P and Q are the price and quantity of items purchased (which we assume here to be two items) and Budget is the amount of income one has to spend. Step 2. Apply the budget constraint equation to the scenario. In Alphonso’s case, this works out to be: Budget = P1 × Q1 + P2 × Q2 $10 budget = $2 per burger × quantity of burgers + $0.50 per bus ticket × quantity of bus tickets $10 = $2 × Qburgers + $0.50 × Qbus tickets Step 3. Using a little algebra, we can turn this into the familiar equation of a line: y = b + mx For Alphonso, this is: Step 4. Simplify the equation. Begin by multiplying both sides of the equation by 2: $10 = $2 × Qburgers + $0.50 × Qbus tickets 2 × 10 = 2 × 2 × Qburgers + 2 × 0.5 × Qbus tickets 20 = 4 × Qburgers + 1 × Qbus tickets Step 5. Subtract one bus ticket from both sides: 20 – Qbus tickets = 4 × Qburgers Divide each side by 4 to yield the answer: 5 – 0.25 × Qbus tickets = Qburgers or Qburgers = 5 – 0.25 × Qbus tickets Step 6. Notice that this equation fits the budget constraint in
Figure 2.2. The vertical intercept is 5 and the slope is –0.25, just as the equation says. If you plug 20 bus tickets into the equation, you get 0 burgers. If you plug other numbers of bus tickets into the equation, you get the results (see Table 2.1), which are the points on Alphonso’s budget constraint. Point Quantity of Burgers (at $2) Quantity of Bus Tickets (at 50 cents) A B C D 5 4 3 2 Table 2.1 0 4 8 12 This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 31 Point Quantity of Burgers (at $2) Quantity of Bus Tickets (at 50 cents) E F 1 0 Table 2.1 16 20 Step 7. Notice that the slope of a budget constraint always shows the opportunity cost of the good which is on the horizontal axis. For Alphonso, the slope is −0.25, indicating that for every bus ticket he buys, he must give up 1/4 burger. To phrase it differently, for every four tickets he buys, Alphonso must give up 1 burger. There are two important observations here. First, the algebraic sign of the slope is negative, which means that the only way to get more of one good is to give up some of the other. Second, we define the slope as the price of bus tickets (whatever is on the horizontal axis in the graph) divided by the price of burgers (whatever is on the vertical axis), in this case $0.50/$2 = 0.25. If you want to determine the opportunity cost quickly, just divide the two prices. Identifying Opportunity Cost In many cases, it is reasonable to refer to the opportunity cost as the price. If your cousin buys a new bicycle for $300, then $300 measures the amount of “other consumption” that he has forsaken. For practical purposes, there may be no special need to identify the specific alternative product or products that he could have bought with that $300, but sometimes the price as measured in dollars may not accurately capture the true opportunity cost. This problem can loom especially large when costs of time are involved. For example, consider a boss who decides that all employees will attend a two-day retreat to “build team spirit.” The out-of-pocket monetary cost of the event may involve hiring
an outside consulting firm to run the retreat, as well as room and board for all participants. However, an opportunity cost exists as well: during the two days of the retreat, none of the employees are doing any other work. Attending college is another case where the opportunity cost exceeds the monetary cost. The out-of-pocket costs of attending college include tuition, books, room and board, and other expenses. However, in addition, during the hours that you are attending class and studying, it is impossible to work at a paying job. Thus, college imposes both an out-of-pocket cost and an opportunity cost of lost earnings. What is the opportunity cost associated with increased airport security measures? After the terrorist plane hijackings on September 11, 2001, many steps were proposed to improve air travel safety. For example, the federal government could provide armed “sky marshals” who would travel inconspicuously with the rest of the passengers. The cost of having a sky marshal on every flight would be roughly $3 billion per year. Retrofitting all U.S. planes with reinforced cockpit doors to make it harder for terrorists to take over the plane would have a price tag of $450 million. Buying more sophisticated security equipment for airports, like three-dimensional baggage scanners and cameras linked to face recognition software, could cost another $2 billion. However, the single biggest cost of greater airline security does not involve spending money. It is the opportunity cost of additional waiting time at the airport. According to the United States Department of Transportation (DOT), there were 895.5 million systemwide (domestic and international) scheduled service passengers in 2015. Since the 9/11 hijackings, security screening has become more intensive, and consequently, the procedure takes longer than in the past. Say that, on average, each air passenger spends 32 Chapter 2 \| Choice in a World of Scarcity an extra 30 minutes in the airport per trip. Economists commonly place a value on time to convert an opportunity cost in time into a monetary figure. Because many air travelers are relatively high-paid business people, conservative estimates set the average price of time for air travelers at $20 per hour. By these backof-the-envelope calculations, the opportunity cost of delays in airports could be as much as 800 million × 0.5 hours × $20/hour, or $8 billion per year. Clearly, the opportunity costs of waiting time can be just as important as costs that involve direct spending
. In some cases, realizing the opportunity cost can alter behavior. Imagine, for example, that you spend $8 on lunch every day at work. You may know perfectly well that bringing a lunch from home would cost only $3 a day, so the opportunity cost of buying lunch at the restaurant is $5 each day (that is, the $8 buying lunch costs minus the $3 your lunch from home would cost). Five dollars each day does not seem to be that much. However, if you project what that adds up to in a year—250 days a year × $5 per day equals $1,250, the cost, perhaps, of a decent vacation. If you describe the opportunity cost as “a nice vacation” instead of “$5 a day,” you might make different choices. Marginal Decision-Making and Diminishing Marginal Utility The budget constraint framework helps to emphasize that most choices in the real world are not about getting all of one thing or all of another; that is, they are not about choosing either the point at one end of the budget constraint or else the point all the way at the other end. Instead, most choices involve marginal analysis, which means examining the benefits and costs of choosing a little more or a little less of a good. People naturally compare costs and benefits, but often we look at total costs and total benefits, when the optimal choice necessitates comparing how costs and benefits change from one option to another. You might think of marginal analysis as “change analysis.” Marginal analysis is used throughout economics. We now turn to the notion of utility. People desire goods and services for the satisfaction or utility those goods and services provide. Utility, as we will see in the chapter on Consumer Choices, is subjective but that does not make it less real. Economists typically assume that the more of some good one consumes (for example, slices of pizza), the more utility one obtains. At the same time, the utility a person receives from consuming the first unit of a good is typically more than the utility received from consuming the fifth or the tenth unit of that same good. When Alphonso chooses between burgers and bus tickets, for example, the first few bus rides that he chooses might provide him with a great deal of utility—perhaps they help him get to a job interview or a doctor’s appointment. However, later bus rides might provide much less utility—they may only serve to kill time on a rainy day
. Similarly, the first burger that Alphonso chooses to buy may be on a day when he missed breakfast and is ravenously hungry. However, if Alphonso has a burger every single day, the last few burgers may taste pretty boring. The general pattern that consumption of the first few units of any good tends to bring a higher level of utility to a person than consumption of later units is a common pattern. Economists refer to this pattern as the law of diminishing marginal utility, which means that as a person receives more of a good, the additional (or marginal) utility from each additional unit of the good declines. In other words, the first slice of pizza brings more satisfaction than the sixth. The law of diminishing marginal utility explains why people and societies rarely make all-or-nothing choices. You would not say, “My favorite food is ice cream, so I will eat nothing but ice cream from now on.” Instead, even if you get a very high level of utility from your favorite food, if you ate it exclusively, the additional or marginal utility from those last few servings would not be very high. Similarly, most workers do not say: “I enjoy leisure, so I’ll never work.” Instead, workers recognize that even though some leisure is very nice, a combination of all leisure and no income is not so attractive. The budget constraint framework suggests that when people make choices in a world of scarcity, they will use marginal analysis and think about whether they would prefer a little more or a little less. A rational consumer would only purchase additional units of some product as long as the marginal utility exceeds the opportunity cost. Suppose Alphonso moves down his budget constraint from Point A to Point B to Point C and further. As he consumes more bus tickets, the marginal utility of bus tickets will diminish, while the opportunity cost, that is, the marginal utility of foregone burgers, will increase. Eventually, the opportunity cost will exceed the marginal utility of an additional bus ticket. If Alphonso is rational, he won’t purchase more bus tickets once the marginal utility just equals the opportunity cost. While we can’t (yet) say exactly how many bus tickets Alphonso will buy, that number is unlikely to be the most he can afford, 20. Sunk Costs In the budget constraint framework, all decisions involve what will happen next: that is, what quantities of goods will This OpenStax book is available for free at http://cnx.org/content/col12
170/1.7 Chapter 2 \| Choice in a World of Scarcity 33 you consume, how many hours will you work, or how much will you save. These decisions do not look back to past choices. Thus, the budget constraint framework assumes that sunk costs, which are costs that were incurred in the past and cannot be recovered, should not affect the current decision. Consider the case of Selena, who pays $8 to see a movie, but after watching the film for 30 minutes, she knows that it is truly terrible. Should she stay and watch the rest of the movie because she paid for the ticket, or should she leave? The money she spent is a sunk cost, and unless the theater manager is sympathetic, Selena will not get a refund. However, staying in the movie still means paying an opportunity cost in time. Her choice is whether to spend the next 90 minutes suffering through a cinematic disaster or to do something—anything—else. The lesson of sunk costs is to forget about the money and time that is irretrievably gone and instead to focus on the marginal costs and benefits of current and future options. For people and firms alike, dealing with sunk costs can be frustrating. It often means admitting an earlier error in judgment. Many firms, for example, find it hard to give up on a new product that is doing poorly because they spent so much money in creating and launching the product. However, the lesson of sunk costs is to ignore them and make decisions based on what will happen in the future. From a Model with Two Goods to One of Many Goods The budget constraint diagram containing just two goods, like most models used in this book, is not realistic. After all, in a modern economy people choose from thousands of goods. However, thinking about a model with many goods is a straightforward extension of what we discussed here. Instead of drawing just one budget constraint, showing the tradeoff between two goods, you can draw multiple budget constraints, showing the possible tradeoffs between many different pairs of goods. In more advanced classes in economics, you would use mathematical equations that include many possible goods and services that can be purchased, together with their quantities and prices, and show how the total spending on all goods and services is limited to the overall budget available. The graph with two goods that we presented here clearly illustrates that every choice has an opportunity cost, which is the point that does carry over to the real world. 2.2 \| The Production Possibilities Frontier and Social Choices By the end of this
section, you will be able to: Interpret production possibilities frontier graphs • • Contrast a budget constraint and a production possibilities frontier • Explain the relationship between a production possibilities frontier and the law of diminishing returns • Contrast productive efficiency and allocative efficiency • Define comparative advantage Just as individuals cannot have everything they want and must instead make choices, society as a whole cannot have everything it might want, either. This section of the chapter will explain the constraints society faces, using a model called the production possibilities frontier (PPF). There are more similarities than differences between individual choice and social choice. As you read this section, focus on the similarities. Because society has limited resources (e.g., labor, land, capital, raw materials) at any point in time, there is a limit to the quantities of goods and services it can produce. Suppose a society desires two products, healthcare and education. The production possibilities frontier in Figure 2.3 illustrates this situation. 34 Chapter 2 \| Choice in a World of Scarcity Figure 2.3 A Healthcare vs. Education Production Possibilities Frontier This production possibilities frontier shows a tradeoff between devoting social resources to healthcare and devoting them to education. At A all resources go to healthcare and at B, most go to healthcare. At D most resources go to education, and at F, all go to education. Figure 2.3 shows healthcare on the vertical axis and education on the horizontal axis. If the society were to allocate all of its resources to healthcare, it could produce at point A. However, it would not have any resources to produce education. If it were to allocate all of its resources to education, it could produce at point F. Alternatively, the society could choose to produce any combination of healthcare and education on the production possibilities frontier. In effect, the production possibilities frontier plays the same role for society as the budget constraint plays for Alphonso. Society can choose any combination of the two goods on or inside the PPF. However, it does not have enough resources to produce outside the PPF. Most importantly, the production possibilities frontier clearly shows the tradeoff between healthcare and education. Suppose society has chosen to operate at point B, and it is considering producing more education. Because the PPF is downward sloping from left to right, the only way society can obtain more education is by giving up some healthcare. That is the tradeoff society faces. Suppose it considers moving from point B to point C. What would the opportunity cost be for the additional education? The opportunity cost would be the
healthcare society has to forgo. Just as with Alphonso’s budget constraint, the slope of the production possibilities frontier shows the opportunity cost. By now you might be saying, “Hey, this PPF is sounding like the budget constraint.” If so, read the following Clear It Up feature. What’s the difference between a budget constraint and a PPF? There are two major differences between a budget constraint and a production possibilities frontier. The first is the fact that the budget constraint is a straight line. This is because its slope is given by the relative prices of the two goods, which from the point of view of an individual consumer, are fixed, so the slope doesn't change. In contrast, the PPF has a curved shape because of the law of the diminishing returns. Thus, the slope is different at various points on the PPF. The second major difference is the absence of specific numbers on the axes of the PPF. There are no specific numbers because we do not know the exact amount of resources this imaginary economy has, nor do we know how many resources it takes to produce healthcare and how many resources it takes to produce education. If this were a real world example, that data would be available. Whether or not we have specific numbers, conceptually we can measure the opportunity cost of additional education as society moves from point B to point C on the PPF. We measure the additional education by the horizontal distance between B and C. The foregone healthcare is given by the vertical distance between B and C. The slope of the PPF between B and C is (approximately) the vertical distance (the “rise”) over the horizontal distance (the “run”). This is the opportunity cost of the additional education. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 35 The Shape of the PPF and the Law of Diminishing Returns The budget constraints that we presented earlier in this chapter, showing individual choices about what quantities of goods to consume, were all straight lines. The reason for these straight lines was that the relative prices of the two goods in the consumption budget constraint determined the slope of the budget constraint. However, we drew the production possibilities frontier for healthcare and education as a curved line. Why does the PPF have a different shape? To understand why the PPF is curved, start by considering point A at the top
left-hand side of the PPF. At point A, all available resources are devoted to healthcare and none are left for education. This situation would be extreme and even ridiculous. For example, children are seeing a doctor every day, whether they are sick or not, but not attending school. People are having cosmetic surgery on every part of their bodies, but no high school or college education exists. Now imagine that some of these resources are diverted from healthcare to education, so that the economy is at point B instead of point A. Diverting some resources away from A to B causes relatively little reduction in health because the last few marginal dollars going into healthcare services are not producing much additional gain in health. However, putting those marginal dollars into education, which is completely without resources at point A, can produce relatively large gains. For this reason, the shape of the PPF from A to B is relatively flat, representing a relatively small drop-off in health and a relatively large gain in education. Now consider the other end, at the lower right, of the production possibilities frontier. Imagine that society starts at choice D, which is devoting nearly all resources to education and very few to healthcare, and moves to point F, which is devoting all spending to education and none to healthcare. For the sake of concreteness, you can imagine that in the movement from D to F, the last few doctors must become high school science teachers, the last few nurses must become school librarians rather than dispensers of vaccinations, and the last few emergency rooms are turned into kindergartens. The gains to education from adding these last few resources to education are very small. However, the opportunity cost lost to health will be fairly large, and thus the slope of the PPF between D and F is steep, showing a large drop in health for only a small gain in education. The lesson is not that society is likely to make an extreme choice like devoting no resources to education at point A or no resources to health at point F. Instead, the lesson is that the gains from committing additional marginal resources to education depend on how much is already being spent. If on the one hand, very few resources are currently committed to education, then an increase in resources used can bring relatively large gains. On the other hand, if a large number of resources are already committed to education, then committing additional resources will bring relatively smaller gains. This pattern is common enough that economists have given it a name: the law of diminishing returns, which holds that as
additional increments of resources are added to a certain purpose, the marginal benefit from those additional increments will decline. (The law of diminishing marginal utility that we introduced in the last section is a more specific case of the law of diminishing returns.) When government spends a certain amount more on reducing crime, for example, the original gains in reducing crime could be relatively large. However, additional increases typically cause relatively smaller reductions in crime, and paying for enough police and security to reduce crime to nothing at all would be tremendously expensive. The curvature of the production possibilities frontier shows that as we add more resources to education, moving from left to right along the horizontal axis, the original gains are fairly large, but gradually diminish. Thus, the slope of the PPF is relatively flat. By contrast, as we add more resources to healthcare, moving from bottom to top on the vertical axis, the original gains are fairly large, but again gradually diminish. Thus, the slope of the PPF is relatively steep. In this way, the law of diminishing returns produces the outward-bending shape of the production possibilities frontier. Productive Efficiency and Allocative Efficiency The study of economics does not presume to tell a society what choice it should make along its production possibilities frontier. In a market-oriented economy with a democratic government, the choice will involve a mixture of decisions by individuals, firms, and government. However, economics can point out that some choices are unambiguously better than others. This observation is based on the concept of efficiency. In everyday usage, efficiency refers to lack of waste. An inefficient machine operates at high cost, while an efficient machine operates at lower cost, because it is not wasting energy or materials. An inefficient organization operates with long delays and high costs, while an efficient organization meets schedules, is focused, and performs within budget. The production possibilities frontier can illustrate two kinds of efficiency: productive efficiency and allocative efficiency. Figure 2.4 illustrates these ideas using a production possibilities frontier between healthcare and 36 education. Chapter 2 \| Choice in a World of Scarcity Figure 2.4 Productive and Allocative Efficiency Productive efficiency means it is impossible to produce more of one good without decreasing the quantity that is produced of another good. Thus, all choices along a given PPF like B, C, and D display productive efficiency, but R does not. Allocative efficiency means that the particular mix of goods being produced—that is, the specific choice along the production possibilities frontier—represents the allocation that society most desires. Productive efficiency means that,
given the available inputs and technology, it is impossible to produce more of one good without decreasing the quantity that is produced of another good. All choices on the PPF in Figure 2.4, including A, B, C, D, and F, display productive efficiency. As a firm moves from any one of these choices to any other, either healthcare increases and education decreases or vice versa. However, any choice inside the production possibilities frontier is productively inefficient and wasteful because it is possible to produce more of one good, the other good, or some combination of both goods. For example, point R is productively inefficient because it is possible at choice C to have more of both goods: education on the horizontal axis is higher at point C than point R (E2 is greater than E1), and healthcare on the vertical axis is also higher at point C than point R (H2 is great than H1). We can show the particular mix of goods and services produced—that is, the specific combination of selected healthcare and education along the production possibilities frontier—as a ray (line) from the origin to a specific point on the PPF. Output mixes that had more healthcare (and less education) would have a steeper ray, while those with more education (and less healthcare) would have a flatter ray. Allocative efficiency means that the particular combination of goods and services on the production possibility curve that a society produces represents the combination that society most desires. How to determine what a society desires can be a controversial question, and is usually a discussion in political science, sociology, and philosophy classes as well as in economics. At its most basic, allocative efficiency means producers supply the quantity of each product that consumers demand. Only one of the productively efficient choices will be the allocatively efficient choice for society as a whole. Why Society Must Choose In Welcome to Economics! we learned that every society faces the problem of scarcity, where limited resources conflict with unlimited needs and wants. The production possibilities curve illustrates the choices involved in this dilemma. Every economy faces two situations in which it may be able to expand consumption of all goods. In the first case, a society may discover that it has been using its resources inefficiently, in which case by improving efficiency and producing on the production possibilities frontier, it can have more of all goods (or at least more of some and less of none). In the second case, as resources grow over a period of years (e.g., more labor and more capital), the economy grows.
As it does, the production possibilities frontier for a society will tend to shift outward and society will be able to afford more of all goods. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 37 However, improvements in productive efficiency take time to discover and implement, and economic growth happens only gradually. Thus, a society must choose between tradeoffs in the present. For government, this process often involves trying to identify where additional spending could do the most good and where reductions in spending would do the least harm. At the individual and firm level, the market economy coordinates a process in which firms seek to produce goods and services in the quantity, quality, and price that people want. However, for both the government and the market economy in the short term, increases in production of one good typically mean offsetting decreases somewhere else in the economy. The PPF and Comparative Advantage While every society must choose how much of each good or service it should produce, it does not need to produce every single good it consumes. Often how much of a good a country decides to produce depends on how expensive it is to produce it versus buying it from a different country. As we saw earlier, the curvature of a country’s PPF gives us information about the tradeoff between devoting resources to producing one good versus another. In particular, its slope gives the opportunity cost of producing one more unit of the good in the x-axis in terms of the other good (in the y-axis). Countries tend to have different opportunity costs of producing a specific good, either because of different climates, geography, technology, or skills. Suppose two countries, the US and Brazil, need to decide how much they will produce of two crops: sugar cane and wheat. Due to its climatic conditions, Brazil can produce quite a bit of sugar cane per acre but not much wheat. Conversely, the U.S. can produce large amounts of wheat per acre, but not much sugar cane. Clearly, Brazil has a lower opportunity cost of producing sugar cane (in terms of wheat) than the U.S. The reverse is also true: the U.S. has a lower opportunity cost of producing wheat than Brazil. We illustrate this by the PPFs of the two countries in Figure 2.5. Figure 2.5 Production Possibility Frontier for the U.S. and Brazil The U.S. PPF is flatter
than the Brazil PPF implying that the opportunity cost of wheat in terms of sugar cane is lower in the U.S. than in Brazil. Conversely, the opportunity cost of sugar cane is lower in Brazil. The U.S. has comparative advantage in wheat and Brazil has comparative advantage in sugar cane. When a country can produce a good at a lower opportunity cost than another country, we say that this country has a comparative advantage in that good. Comparative advantage is not the same as absolute advantage, which is when a country can produce more of a good. Comparative advantage is not the same as absolute advantage, which is when a country can produce more of a good. In our example, Brazil has an absolute advantage in sugar cane and the U.S. has an absolute advantage in wheat. One can easily see this with a simple observation of the extreme production points in the PPFs of the two countries. If Brazil devoted all of its resources to producing wheat, it would be producing at point A. If however it had devoted all of its resources to producing sugar cane instead, it would be producing a much larger 38 Chapter 2 \| Choice in a World of Scarcity amount than the U.S., at point B. The slope of the PPF gives the opportunity cost of producing an additional unit of wheat. While the slope is not constant throughout the PPFs, it is quite apparent that the PPF in Brazil is much steeper than in the U.S., and therefore the opportunity cost of wheat generally higher in Brazil. In the chapter on International Trade you will learn that countries’ differences in comparative advantage determine which goods they will choose to produce and trade. When countries engage in trade, they specialize in the production of the goods in which they have comparative advantage, and trade part of that production for goods in which they do not have comparative advantage. With trade, manufacturers produce goods where the opportunity cost is lowest, so total production increases, benefiting both trading parties. 2.3 \| Confronting Objections to the Economic Approach By the end of this section, you will be able to: • Analyze arguments against economic approaches to decision-making • • Contrast normative statements and positive statements Interpret a tradeoff diagram It is one thing to understand the economic approach to decision-making and another thing to feel comfortable applying it. The sources of discomfort typically fall into two categories: that people do not act in the way that fits the economic way of thinking, and that even if people did act that way, they should try not to
. Let’s consider these arguments in turn. First Objection: People, Firms, and Society Do Not Act Like This The economic approach to decision-making seems to require more information than most individuals possess and more careful decision-making than most individuals actually display. After all, do you or any of your friends draw a budget constraint and mutter to yourself about maximizing utility before you head to the shopping mall? Do members of the U.S. Congress contemplate production possibilities frontiers before they vote on the annual budget? The messy ways in which people and societies operate somehow doesn’t look much like neat budget constraints or smoothly curving production possibilities frontiers. However, the economics approach can be a useful way to analyze and understand the tradeoffs of economic decisions. To appreciate this point, imagine for a moment that you are playing basketball, dribbling to the right, and throwing a bounce-pass to the left to a teammate who is running toward the basket. A physicist or engineer could work out the correct speed and trajectory for the pass, given the different movements involved and the weight and bounciness of the ball. However, when you are playing basketball, you do not perform any of these calculations. You just pass the ball, and if you are a good player, you will do so with high accuracy. Someone might argue: “The scientist’s formula of the bounce-pass requires a far greater knowledge of physics and far more specific information about speeds of movement and weights than the basketball player actually has, so it must be an unrealistic description of how basketball passes actually occur.” This reaction would be wrongheaded. The fact that a good player can throw the ball accurately because of practice and skill, without making a physics calculation, does not mean that the physics calculation is wrong. Similarly, from an economic point of view, someone who shops for groceries every week has a great deal of practice with how to purchase the combination of goods that will provide that person with utility, even if the shopper does not phrase decisions in terms of a budget constraint. Government institutions may work imperfectly and slowly, but in general, a democratic form of government feels pressure from voters and social institutions to make the choices that are most widely preferred by people in that society. Thus, when thinking about the economic actions of groups of people, firms, and society, it is reasonable, as a first approximation, to analyze them with the tools of economic analysis. For more on this, read about behavioral economics in the chapter on Consumer
Choices. Second Objection: People, Firms, and Society Should Not Act This Way The economics approach portrays people as self-interested. For some critics of this approach, even if self-interest is an accurate description of how people behave, these behaviors are not moral. Instead, the critics argue that people should be taught to care more deeply about others. Economists offer several answers to these concerns. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 39 First, economics is not a form of moral instruction. Rather, it seeks to describe economic behavior as it actually exists. Philosophers draw a distinction between positive statements, which describe the world as it is, and normative statements, which describe how the world should be. Positive statements are factual. They may be true or false, but we can test them, at least in principle. Normative statements are subjective questions of opinion. We cannot test them since we cannot prove opinions to be true or false. They just are opinions based on one's values. For example, an economist could analyze a proposed subway system in a certain city. If the expected benefits exceed the costs, he concludes that the project is worthy—an example of positive analysis. Another economist argues for extended unemployment compensation during the Great Depression because a rich country like the United States should take care of its less fortunate citizens—an example of normative analysis. Even if the line between positive and normative statements is not always crystal clear, economic analysis does try to remain rooted in the study of the actual people who inhabit the actual economy. Fortunately however, the assumption that individuals are purely self-interested is a simplification about human nature. In fact, we need to look no further than to Adam Smith, the very father of modern economics to find evidence of this. The opening sentence of his book, The Theory of Moral Sentiments, puts it very clearly: “How selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it except the pleasure of seeing it.” Clearly, individuals are both self-interested and altruistic. Second, we can label self-interested behavior and profit-seeking with other names, such as personal choice and freedom. The ability to make personal choices about buying, working, and saving is an important personal freedom. Some
people may choose high-pressure, high-paying jobs so that they can earn and spend considerable amounts of money on themselves. Others may allocate large portions of their earnings to charity or spend it on their friends and family. Others may devote themselves to a career that can require much time, energy, and expertise but does not offer high financial rewards, like being an elementary school teacher or a social worker. Still others may choose a job that does consume much of their time or provide a high level of income, but still leaves time for family, friends, and contemplation. Some people may prefer to work for a large company; others might want to start their own business. People’s freedom to make their own economic choices has a moral value worth respecting. Is a diagram by any other name the same? When you study economics, you may feel buried under an avalanche of diagrams. Your goal should be to recognize the common underlying logic and pattern of the diagrams, not to memorize each one. This chapter uses only one basic diagram, although we present labels. The consumption budget constraint and the production possibilities frontier for society, as a whole, are the same basic diagram. Figure 2.6 shows an individual budget constraint and a production possibilities frontier for two goods, Good 1 and Good 2. The tradeoff diagram always illustrates three basic themes: scarcity, tradeoffs, and economic efficiency. it with different sets of The first theme is scarcity. It is not feasible to have unlimited amounts of both goods. Even if the budget constraint or a PPF shifts, scarcity remains—just at a different level. The second theme is tradeoffs. As depicted in the budget constraint or the production possibilities frontier, it is necessary to forgo some of one good to gain more of the other good. The details of this tradeoff vary. In a budget constraint we determine, the tradeoff is determined by the relative prices of the goods: that is, the relative price of two goods in the consumption choice budget constraint. These tradeoffs appear as a straight line. However, a curved line represents the tradeoffs in many production possibilities frontiers because the law of diminishing returns holds that as we add resources to an area, the marginal gains tend to diminish. Regardless of the specific shape, tradeoffs remain. The third theme is economic efficiency, or getting the most benefit from scarce resources. All choices on the production possibilities frontier show productive efficiency because in such cases, there is no way to increase the quantity of one good without decreasing the quantity of the other. Similarly, when
an individual makes a choice along a budget constraint, there is no way to increase the quantity of one good without decreasing the quantity of the other. The choice on a production possibilities set that is socially preferred, or the choice on an 40 Chapter 2 \| Choice in a World of Scarcity individual’s budget constraint that is personally preferred, will display allocative efficiency. The basic budget constraint/production possibilities frontier diagram will recur throughout this book. Some examples include using these tradeoff diagrams to analyze trade, environmental protection and economic output, equality of incomes and economic output, and the macroeconomic tradeoff between consumption and investment. Do not allow the different labels to confuse you. The budget constraint/production possibilities frontier diagram is always just a tool for thinking carefully about scarcity, tradeoffs, and efficiency in a particular situation. Figure 2.6 The Tradeoff Diagram Both the individual opportunity set (or budget constraint) and the social production possibilities frontier show the constraints under which individual consumers and society as a whole operate. Both diagrams show the tradeoff in choosing more of one good at the cost of less of the other. Third, self-interested behavior can lead to positive social results. For example, when people work hard to make a living, they create economic output. Consumers who are looking for the best deals will encourage businesses to offer goods and services that meet their needs. Adam Smith, writing in The Wealth of Nations, named this property the invisible hand. In describing how consumers and producers interact in a market economy, Smith wrote: Every individual…generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain. And he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention…By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it. The metaphor of the invisible hand suggests the remarkable possibility that broader social good can emerge from selfish individual actions. Fourth, even people who focus on their own self-interest in the economic part of their life often set aside their own narrow self-interest in other parts of life. For example, you might focus on your own self-interest when asking your employer for a raise or negotiating to buy a car
. Then you might turn around and focus on other people when you volunteer to read stories at the local library, help a friend move to a new apartment, or donate money to a charity. Selfinterest is a reasonable starting point for analyzing many economic decisions, without needing to imply that people never do anything that is not in their own immediate self-interest. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 41 Choices... To What Degree? What have we learned? We know that scarcity impacts all the choices we make. An economist might argue that people do not obtain a bachelor’s or master’s degree because they do not have the resources to make those choices or because their incomes are too low and/or the price of these degrees is too high. A bachelor’s or a master’s degree may not be available in their opportunity set. The price of these degrees may be too high not only because the actual price, college tuition (and perhaps room and board), is too high. An economist might also say that for many people, the full opportunity cost of a bachelor’s or a master’s degree is too high. For these people, they are unwilling or unable to make the tradeoff of forfeiting years of working, and earning an income, to earn a degree. Finally, the statistics we introduced at the start of the chapter reveal information about intertemporal choices. An economist might say that people choose not to obtain a college degree because they may have to borrow money to attend college, and the interest they have to pay on that loan in the future will affect their decisions today. Also, it could be that some people have a preference for current consumption over future consumption, so they choose to work now at a lower salary and consume now, rather than postponing that consumption until after they graduate college. 42 Chapter 2 \| Choice in a World of Scarcity KEY TERMS allocative efficiency when the mix of goods produced represents the mix that society most desires budget constraint all possible consumption combinations of goods that someone can afford, given the prices of goods, when all income is spent; the boundary of the opportunity set comparative advantage when a country can produce a good at a lower cost in terms of other goods; or, when a country has a lower opportunity cost of production invisible hand Adam Smith's concept that individuals' self-interested behavior can lead to positive social outcomes
law of diminishing marginal utility as we consume more of a good or service, the utility we get from additional units of the good or service tends to become smaller than what we received from earlier units law of diminishing returns as we add additional increments of resources to producing a good or service, the marginal benefit from those additional increments will decline marginal analysis examination of decisions on the margin, meaning a little more or a little less from the status quo normative statement statement which describes how the world should be opportunity cost measures cost by what we give up/forfeit in exchange; opportunity cost measures the value of the forgone alternative opportunity set all possible combinations of consumption that someone can afford given the prices of goods and the individual’s income positive statement statement which describes the world as it is production possibilities frontier (PPF) a diagram that shows the productively efficient combinations of two products that an economy can produce given the resources it has available. productive efficiency when it is impossible to produce more of one good (or service) without decreasing the quantity produced of another good (or service) sunk costs costs that we make in the past that we cannot recover utility satisfaction, usefulness, or value one obtains from consuming goods and services KEY CONCEPTS AND SUMMARY 2.1 How Individuals Make Choices Based on Their Budget Constraint Economists see the real world as one of scarcity: that is, a world in which people’s desires exceed what is possible. As a result, economic behavior involves tradeoffs in which individuals, firms, and society must forgo something that they desire to obtain things that they desire more. Individuals face the tradeoff of what quantities of goods and services to consume. The budget constraint, which is the frontier of the opportunity set, illustrates the range of available choices. The relative price of the choices determines the slope of the budget constraint. Choices beyond the budget constraint are not affordable. Opportunity cost measures cost by what we forgo in exchange. Sometimes we can measure opportunity cost in money, but it is often useful to consider time as well, or to measure it in terms of the actual resources that we must forfeit. Most economic decisions and tradeoffs are not all-or-nothing. Instead, they involve marginal analysis, which means they are about decisions on the margin, involving a little more or a little less. The law of diminishing marginal utility points out that as a person receives more of something—whether it is a specific good or another resource—the This OpenStax book is available for free at
http://cnx.org/content/col12170/1.7 Chapter 2 \| Choice in a World of Scarcity 43 additional marginal gains tend to become smaller. Because sunk costs occurred in the past and cannot be recovered, they should be disregarded in making current decisions. 2.2 The Production Possibilities Frontier and Social Choices A production possibilities frontier defines the set of choices society faces for the combinations of goods and services it can produce given the resources available. The shape of the PPF is typically curved outward, rather than straight. Choices outside the PPF are unattainable and choices inside the PPF are wasteful. Over time, a growing economy will tend to shift the PPF outwards. The law of diminishing returns holds that as increments of additional resources are devoted to producing something, the marginal increase in output will become increasingly smaller. All choices along a production possibilities frontier display productive efficiency; that is, it is impossible to use society’s resources to produce more of one good without decreasing production of the other good. The specific choice along a production possibilities frontier that reflects the mix of goods society prefers is the choice with allocative efficiency. The curvature of the PPF is likely to differ by country, which results in different countries having comparative advantage in different goods. Total production can increase if countries specialize in the goods in which they have comparative advantage and trade some of their production for the remaining goods. 2.3 Confronting Objections to the Economic Approach The economic way of thinking provides a useful approach to understanding human behavior. Economists make the careful distinction between positive statements, which describe the world as it is, and normative statements, which describe how the world should be. Even when economics analyzes the gains and losses from various events or policies, and thus draws normative conclusions about how the world should be, the analysis of economics is rooted in a positive analysis of how people, firms, and governments actually behave, not how they should behave. SELF-CHECK QUESTIONS 1. Suppose Alphonso’s town raised the price of bus tickets to $1 per trip (while the price of burgers stayed at $2 and his budget remained $10 per week.) Draw Alphonso’s new budget constraint. What happens to the opportunity cost of bus tickets? 2. Return to the example in Figure 2.4. Suppose there is an improvement in medical technology that enables more healthcare with the same amount of resources. How would this affect the production possibilities curve and, in particular, how would it affect
the opportunity cost of education? 3. Could a nation be producing in a way that is allocatively efficient, but productively inefficient? 4. What are the similarities between a consumer’s budget constraint and society’s production possibilities frontier, not just graphically but analytically? Individuals may not act in the rational, calculating way described by the economic model of decision making, 5. measuring utility and costs at the margin, but can you make a case that they behave approximately that way? 6. Would an op-ed piece in a newspaper urging the adoption of a particular economic policy be a positive or normative statement? 7. Would a research study on the effects of soft drink consumption on children’s cognitive development be a positive or normative statement? REVIEW QUESTIONS 8. Explain why scarcity leads to tradeoffs. 10. What is comparative advantage? 9. Explain why individuals make choices that are directly on the budget constraint, rather than inside the budget constraint or outside it. 11. What does a production possibilities frontier illustrate? 44 Chapter 2 \| Choice in a World of Scarcity 12. Why is a production possibilities frontier typically drawn as a curve, rather than a straight line? 16. What is the difference between a positive and a normative statement? 13. Explain why societies cannot make a choice above their production possibilities frontier and should not make a choice below it. Is 17. the economic model of decision-making intended as a literal description of how individuals, firms, and the governments actually make decisions? 14. What are diminishing marginal returns? 15. What efficiency? is productive efficiency? Allocative CRITICAL THINKING QUESTIONS 19. Suppose Alphonso’s town raises the price of bus tickets from $0.50 to $1 and the price of burgers rises from $2 to $4. Why is the opportunity cost of bus tickets unchanged? Suppose Alphonso’s weekly spending money increases from $10 to $20. How is his budget constraint affected from all three changes? Explain. 20. During the Second World War, Germany’s factories were decimated. It also suffered many human casualties, both soldiers and civilians. How did the war affect Germany’s production possibilities curve? 18. What are four responses to the claim that people should not behave in the way described in this chapter? 21. It is clear that productive inefficiency is a waste since resources are used in a way that produces less goods and services than a nation is capable of. Why is allocative inefficiency
also wasteful? 22. What assumptions about the economy must be true for the invisible hand to work? To what extent are those assumptions valid in the real world? 23. Do economists have any particular expertise at making normative arguments? In other words, they have expertise at making positive statements (i.e., what will happen) about some economic policy, for example, but do they have special expertise to judge whether or not the policy should be undertaken? PROBLEMS information to answer Use this the following 4 questions: Marie has a weekly budget of $24, which she likes to spend on magazines and pies. 26. Draw Marie’s budget constraint with pies on the horizontal axis and magazines on the vertical axis. What is the slope of the budget constraint? 24. If the price of a magazine is $4 each, what is the maximum number of magazines she could buy in a week? If the price of a pie is $12, what is the maximum 25. number of pies she could buy in a week? 27. What is Marie’s opportunity cost of purchasing a pie? This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 3 \| Demand and Supply 45 3 \| Demand and Supply Figure 3.1 Farmer’s Market Organic vegetables and fruits that are grown and sold within a specific geographical region should, in theory, cost less than conventional produce because the transportation costs are less. That is not, however, usually the case. (Credit: Modification of work by Natalie Maynor/Flickr Creative Commons) Why Can We Not Get Enough of Organic? Organic food is increasingly popular, not just in the United States, but worldwide. At one time, consumers had to go to specialty stores or farmers' markets to find organic produce. Now it is available in most grocery stores. In short, organic is part of the mainstream. Ever wonder why organic food costs more than conventional food? Why, say, does an organic Fuji apple cost $1.99 a pound, while its conventional counterpart costs $1.49 a pound? The same price relationship is true for just about every organic product on the market. If many organic foods are locally grown, would they not take less time to get to market and therefore be cheaper? What are the forces that keep those prices from coming down? Turns out those forces have quite a bit to do with this chapter’s topic: demand and supply. Introduction to Demand and Supply In this chapter
, you will learn about: • Demand, Supply, and Equilibrium in Markets for Goods and Services • Shifts in Demand and Supply for Goods and Services • Changes in Equilibrium Price and Quantity: The Four-Step Process 46 Chapter 3 \| Demand and Supply • Price Ceilings and Price Floors An auction bidder pays thousands of dollars for a dress Whitney Houston wore. A collector spends a small fortune for a few drawings by John Lennon. People usually react to purchases like these in two ways: their jaw drops because they think these are high prices to pay for such goods or they think these are rare, desirable items and the amount paid seems right. Visit this website (http://openstaxcollege.org/l/celebauction) to read a list of bizarre items that have been purchased for their ties to celebrities. These examples represent an interesting facet of demand and supply. When economists talk about prices, they are less interested in making judgments than in gaining a practical understanding of what determines prices and why prices change. Consider a price most of us contend with weekly: that of a gallon of gas. Why was the average price of gasoline in the United States $3.71 per gallon in June 2014? Why did the price for gasoline fall sharply to $1.96 per gallon by January 2016? To explain these price movements, economists focus on the determinants of what gasoline buyers are willing to pay and what gasoline sellers are willing to accept. As it turns out, the price of gasoline in June of any given year is nearly always higher than the price in January of that same year. Over recent decades, gasoline prices in midsummer have averaged about 10 cents per gallon more than their midwinter low. The likely reason is that people drive more in the summer, and are also willing to pay more for gas, but that does not explain how steeply gas prices fell. Other factors were at work during those 18 months, such as increases in supply and decreases in the demand for crude oil. This chapter introduces the economic model of demand and supply—one of the most powerful models in all of economics. The discussion here begins by examining how demand and supply determine the price and the quantity sold in markets for goods and services, and how changes in demand and supply lead to changes in prices and quantities. 3.1 \| Demand, Supply, and Equilibrium in Markets for Goods and Services By the end of this section, you will be able to: Identify a demand curve and a supply curve • Explain demand, quantity demanded, and
the law of demand • • Explain supply, quantity supplied, and the law of supply • Explain equilibrium, equilibrium price, and equilibrium quantity First let’s first focus on what economists mean by demand, what they mean by supply, and then how demand and supply interact in a market. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 3 \| Demand and Supply 47 Demand for Goods and Services Economists use the term demand to refer to the amount of some good or service consumers are willing and able to purchase at each price. Demand is fundamentally based on needs and wants—if you have no need or want for something, you won't buy it. While a consumer may be able to differentiate between a need and a want, but from an economist’s perspective they are the same thing. Demand is also based on ability to pay. If you cannot pay for it, you have no effective demand. By this definition, a homeless person probably has no effective demand for shelter. What a buyer pays for a unit of the specific good or service is called price. The total number of units that consumers would purchase at that price is called the quantity demanded. A rise in price of a good or service almost always decreases the quantity demanded of that good or service. Conversely, a fall in price will increase the quantity demanded. When the price of a gallon of gasoline increases, for example, people look for ways to reduce their consumption by combining several errands, commuting by carpool or mass transit, or taking weekend or vacation trips closer to home. Economists call this inverse relationship between price and quantity demanded the law of demand. The law of demand assumes that all other variables that affect demand (which we explain in the next module) are held constant. We can show an example from the market for gasoline in a table or a graph. Economist call a table that shows the quantity demanded at each price, such as Table 3.1, a demand schedule. In this case we measure price in dollars per gallon of gasoline. We measure the quantity demanded in millions of gallons over some time period (for example, per day or per year) and over some geographic area (like a state or a country). A demand curve shows the relationship between price and quantity demanded on a graph like Figure 3.2, with quantity on the horizontal axis and the price per gallon on the vertical axis. (Note that this is an exception to the normal rule in mathematics that the independent variable
(x) goes on the horizontal axis and the dependent variable (y) goes on the vertical. Economics is not math.) Table 3.1 shows the demand schedule and the graph in Figure 3.2 shows the demand curve. These are two ways to describe the same relationship between price and quantity demanded. Price (per gallon) Quantity Demanded (millions of gallons) $1.00 $1.20 $1.40 $1.60 $1.80 $2.00 $2.20 800 700 600 550 500 460 420 Table 3.1 Price and Quantity Demanded of Gasoline 48 Chapter 3 \| Demand and Supply Figure 3.2 A Demand Curve for Gasoline The demand schedule shows that as price rises, quantity demanded decreases, and vice versa. We graph these points, and the line connecting them is the demand curve (D). The downward slope of the demand curve again illustrates the law of demand—the inverse relationship between prices and quantity demanded. Demand curves will appear somewhat different for each product. They may appear relatively steep or flat, or they may be straight or curved. Nearly all demand curves share the fundamental similarity that they slope down from left to right. Demand curves embody the law of demand: As the price increases, the quantity demanded decreases, and conversely, as the price decreases, the quantity demanded increases. Confused about these different types of demand? Read the next Clear It Up feature. Is demand the same as quantity demanded? In economic terminology, demand is not the same as quantity demanded. When economists talk about demand, they mean the relationship between a range of prices and the quantities demanded at those prices, as illustrated by a demand curve or a demand schedule. When economists talk about quantity demanded, they mean only a certain point on the demand curve, or one quantity on the demand schedule. In short, demand refers to the curve and quantity demanded refers to the (specific) point on the curve. Supply of Goods and Services When economists talk about supply, they mean the amount of some good or service a producer is willing to supply at each price. Price is what the producer receives for selling one unit of a good or service. A rise in price almost always leads to an increase in the quantity supplied of that good or service, while a fall in price will decrease the quantity supplied. When the price of gasoline rises, for example, it encourages profit-seeking firms to take several actions: expand exploration for oil reserves; drill for more oil; invest in more pipelines and oil tankers to bring the
oil to plants for refining into gasoline; build new oil refineries; purchase additional pipelines and trucks to ship the gasoline to gas stations; and open more gas stations or keep existing gas stations open longer hours. Economists call this positive relationship between price and quantity supplied—that a higher price leads to a higher quantity supplied and a lower price leads to a lower quantity supplied—the law of supply. The law of supply assumes that all other variables that affect supply (to be explained in the next module) are held constant. Still unsure about the different types of supply? See the following Clear It Up feature. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 3 \| Demand and Supply 49 Is supply the same as quantity supplied? In economic terminology, supply is not the same as quantity supplied. When economists refer to supply, they mean the relationship between a range of prices and the quantities supplied at those prices, a relationship that we can illustrate with a supply curve or a supply schedule. When economists refer to quantity supplied, they mean only a certain point on the supply curve, or one quantity on the supply schedule. In short, supply refers to the curve and quantity supplied refers to the (specific) point on the curve. Figure 3.3 illustrates the law of supply, again using the market for gasoline as an example. Like demand, we can illustrate supply using a table or a graph. A supply schedule is a table, like Table 3.2, that shows the quantity supplied at a range of different prices. Again, we measure price in dollars per gallon of gasoline and we measure quantity supplied in millions of gallons. A supply curve is a graphic illustration of the relationship between price, shown on the vertical axis, and quantity, shown on the horizontal axis. The supply schedule and the supply curve are just two different ways of showing the same information. Notice that the horizontal and vertical axes on the graph for the supply curve are the same as for the demand curve. Figure 3.3 A Supply Curve for Gasoline The supply schedule is the table that shows quantity supplied of gasoline at each price. As price rises, quantity supplied also increases, and vice versa. The supply curve (S) is created by graphing the points from the supply schedule and then connecting them. The upward slope of the supply curve illustrates the law of supply—that a higher price leads to a higher quantity supplied, and vice versa. Price (per gallon) Quantity Supplied (millions of

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.