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category of elasticity you found in part b (either perfectly elastic or perfectly inelastic supply). d. What would likely be true of the availability of inputs for a firm with the supply curve you drew in part c? Explain 481 What you will learn in this Module: • The meaning of consumer surplus and its relationship to the demand curve • The meaning of producer surplus and its relationship to the supply curve Module 49 Consumer and Producer Surplus There is a lively market in second-hand college textbooks. At the end of each term, some students who took a course decide that the money they can make by selling their used books is worth more to them than keeping the books. And some students who are taking the course next term prefer to buy a somewhat battered but less expensive used textbook rather than pay full price for a new one. Textbook publishers and authors are not happy about these transactions because they cut into sales of new books. But both the students who sell used books and those who buy them clearly benefit from the existence of the market. That is why many college bookstores facilitate their trade, buying used textbooks and selling them alongside the new books. But can we put a number on what used textbook buyers and sellers gain from these transactions? Can we answer the question “How much do the buyers and sellers of textbooks gain from the existence of the used-book market?” Yes, we can. In this module we will see how to measure benefits, such as those to buyers of used textbooks, from being able to purchase a good—known as consumer surplus. And we will see that there is a corresponding measure, producer surplus, of the benefits sellers receive from being able to sell a good. The concepts of consumer surplus and producer surplus are useful for analyzing a wide variety of economic issues. They let us calculate how much benefit producers and consumers receive from the existence of a market. They also allow us to calculate how the welfare of consumers and producers is affected by changes in market prices. Such calculations play a crucial role in evaluating many economic policies. What information do we need to calculate consumer and producer surplus? Surprisingly, all we need are the demand and supply curves for a good. That is, the supply and demand model isn’t just a model of how a competitive market works—it’s also a model of how much consumers and producers gain from participating in that market. So our first step will be to learn how consumer and producer surplus can be derived from the demand and supply curves. We will then see how these
concepts can be applied to actual economic issues. 482 Consumer Surplus and the Demand Curve First-year college students are often surprised by the prices of the textbooks required for their classes. The College Board estimates that in 2006-2007 students at four-year schools spent, on average, $942 for books and supplies. But at the end of the semester, students might again be surprised to find out that they can sell back at least some of the textbooks they used for the semester for a percentage of the purchase price (offsetting some of the cost of textbooks). The ability to purchase used textbooks at the start of the semester and to sell back used textbooks at the end of the semester is beneficial to students on a budget. In fact, the market for used textbooks is a big business in terms of dollars and cents—approximately $1.9 billion in 2004– 2005. This market provides a convenient starting point for us to develop the concepts of consumer and producer surplus. We’ll use the concepts of consumer and producer surplus to understand exactly how buyers and sellers benefit from a competitive market and how big those benefits are. In addition, these concepts assist in the analysis of what happens when competitive markets don’t work well or there is interference in the market. So let’s begin by looking at the market for used textbooks, starting with the buyers. The key point, as we’ll see in a minute, is that the demand curve is derived from their tastes or preferences—and that those same preferences also determine how much they gain from the opportunity to buy used books. Willingness to Pay and the Demand Curve A used book is not as good as a new book—it will be battered and coffee-stained, may include someone else’s highlighting, and may not be completely up to date. How much this bothers you depends on your preferences. Some potential buyers would prefer to buy the used book even if it is only slightly cheaper than a new one, while others would buy the used book only if it is considerably cheaper. Let’s define a potential buyer’s willingness to pay as the maximum price at which he or she would buy a good, in this case a used textbook. An individual won’t buy the good if it costs more than this amount but is eager to do so if it costs less. If the price is just equal to an individual’s willingness to pay, he or she is indifferent between buying and not buying. For the sake of simplicity, we
’ll assume that the individual buys the good in this case. The table in Figure 49.1 on the next page shows five potential buyers of a used book that costs $100 new, listed in order of their willingness to pay. At one extreme is Aleisha, who will buy a second-hand book even if the price is as high as $59. Brad is less willing to have a used book and will buy one only if the price is $45 or less. Claudia is willing to pay only $35 and Darren, only $25. Edwina, who really doesn’t like the idea of a used book, will buy one only if it costs no more than $10. How many of these five students will actually buy a used book? It depends on the price. If the price of a used book is $55, only Aleisha buys one; if the price is $40, Aleisha and Brad both buy used books, and so on. So the information in the table can be used to construct the demand schedule for used textbooks. We can use this demand schedule to derive the market demand curve shown in Figure 49.1. Because we are considering only a small number of consumers, this curve doesn’t look like the smooth demand curves we have seen previously, for markets that contained hundreds or thousands of consumers. This demand curve is step-shaped, with alternating horizontal and vertical segments. Each horizontal segment—each step—corresponds to one potential buyer’s willingness to pay. However, we’ll see shortly that for the analysis of consumer surplus it doesn’t matter whether the demand curve is step-shaped, as in this figure, or whether there are many consumers, making the curve smooth. A consumer’s willingness to pay for a good is the maximum price at which he or she would buy that good 483 f i g u r e 49.1 The Demand Curve for Used Textbooks Potential buyers Willingness to pay Aleisha Brad Claudia Darren Edwina $59 45 35 25 10 Price of book $59 Aleisha 45 35 25 10 Brad Claudia Darren Edwina 0 1 2 3 4 D 5 Quantity of books With only five potential consumers in this market, the demand curve is step-shaped. Each step represents one consumer, and its height indicates that consumer’s willingness to pay—the maximum price at which each will buy a used textbook—as indicated in the table. Aleisha has the highest willingness to pay at
$59, Brad has the next highest at $45, and so on down to Edwina with the lowest willingness to pay at $10. At a price of $59, the quantity demanded is one (Aleisha); at a price of $45, the quantity demanded is two (Aleisha and Brad); and so on until you reach a price of $10, at which all five students are willing to purchase a book. Willingness to Pay and Consumer Surplus Suppose that the campus bookstore makes used textbooks available at a price of $30. In that case Aleisha, Brad, and Claudia will buy books. Do they gain from their purchases, and if so, how much? The answer, shown in Table 49.1, is that each student who purchases a book does achieve a net gain but that the amount of the gain differs among students. Aleisha would have been willing to pay $59, so her net gain is $59 − $30 = $29. Brad would have been willing to pay $45, so his net gain is $45 − $30 = $15. Claudia would t a b l e 49.1 Consumer Surplus When the Price of a Used Textbook Is $30 Potential buyer Aleisha Brad Claudia Darren Edwina All buyers Willingness to pay Price paid Individual consumer surplus = Willingness to pay − Price paid $59 45 35 25 10 $30 30 30 — — $29 15 5 — — Total consumer surplus = $49 484 Individual consumer surplus is the net gain to an individual buyer from the purchase of a good. It is equal to the difference between the buyer’s willingness to pay and the price paid. Total consumer surplus is the sum of the individual consumer surpluses of all the buyers of a good in a market. The term consumer surplus is often used to refer to both individual and to total consumer surplus have been willing to pay $35, so her net gain is $35 − $30 = $5. Darren and Edwina, however, won’t be willing to buy a used book at a price of $30, so they neither gain nor lose. The net gain that a buyer achieves from the purchase of a good is called that buyer’s individual consumer surplus. What we learn from this example is that whenever a buyer pays a price less than his or her willingness to pay, the buyer achieves some individual consumer surplus. The sum of the individual consumer surpluses achieved by all the buyers of a good
is known as the total consumer surplus achieved in the market. In Table 49.1, the total consumer surplus is the sum of the individual consumer surpluses achieved by Aleisha, Brad, and Claudia: $29 + $15 + $5 = $49. Economists often use the term consumer surplus to refer to both individual and total consumer surplus. We will follow this practice; it will always be clear in context whether we are referring to the consumer surplus achieved by an individual or by all buyers. Total consumer surplus can be represented graphically. Figure 49.2 reproduces the demand curve from Figure 49.1. Each step in that demand curve is one book wide and represents one consumer. For example, the height of Aleisha’s step is $59, her willingness to pay. This step forms the top of a rectangle, with $30—the price she actually pays for a book—forming the bottom. The area of Aleisha’s rectangle, ($59 − $30) × 1 = $29, is her consumer surplus from purchasing one book at $30. So the individual consumer surplus Aleisha gains is the area of the dark blue rectangle shown in Figure 49.2. In addition to Aleisha, Brad and Claudia will also each buy a book when the price is $30. Like Aleisha, they benefit from their purchases, though not as much, because they each have a lower willingness to pay. Figure 49.2 also shows the consumer surplus gained by Brad and Claudia; again, this can be measured by the areas of the appropriate rectangles. Darren and Edwina, because they do not buy books at a price of $30, receive no consumer surplus. The total consumer surplus achieved in this market is just the sum of the individual consumer surpluses received by Aleisha, Brad, and Claudia. So total consumer surplus is equal to the combined area of the three rectangles—the entire shaded area in Figure 49.2. Another way to say this is that total consumer surplus is equal to the area below the demand curve but above the price. f i g u r e 49.2 Consumer Surplus in the Used-Textbook Market At a price of $30, Aleisha, Brad, and Claudia each buy a book but Darren and Edwina do not. Aleisha, Brad, and Claudia get individual consumer surpluses equal to the difference between their willingness to pay and the price, illustrated by the areas of the shaded rectangles. Both Darren
and Edwina have a willingness to pay less than $30, so they are unwilling to buy a book in this market; they receive zero consumer surplus. The total consumer surplus is given by the entire shaded area—the sum of the individual consumer surpluses of Aleisha, Brad, and Claudia— equal to $29 + $15 + $5 = $49. Price of book $59 Aleisha Aleisha’s consumer surplus: $59 − $30 = $29 Brad’s consumer surplus: $45 − $30 = $15 Brad Claudia’s consumer surplus: $35 − $30 = $5 Claudia Darren Price 45 35 30 25 10 0 1 2 3 4 Edwina D 5 Quantity of books 485 This is worth repeating as a general principle: The total consumer surplus generated by purchases of a good at a given price is equal to the area below the demand curve but above that price. The same principle applies regardless of the number of consumers. When we consider large markets, this graphical representation becomes particularly helpful. Consider, for example, the sales of personal computers to millions of potential buyers. Each potential buyer has a maximum price that he or she is willing to pay. With so many potential buyers, the demand curve will be smooth, like the one shown in Figure 49.3. f i g u r e 49.3 Consumer Surplus The demand curve for computers is smooth because there are many potential buyers. At a price of $1,500, 1 million computers are demanded. The consumer surplus at this price is equal to the shaded area: the area below the demand curve but above the price. This is the total net gain to consumers generated from buying and consuming computers when the price is $1,500. Price of computer $1,500 0 Consumer surplus Price D 1 million Quantity of computers Suppose that at a price of $1,500, a total of 1 million computers are purchased. How much do consumers gain from being able to buy those 1 million computers? We could answer that question by calculating the individual consumer surplus of each buyer and then adding these numbers up to arrive at a total. But it is much easier just to look at Figure 49.3 and use the fact that total consumer surplus is equal to the shaded area below the demand curve but above the price. How Changing Prices Affect Consumer Surplus It is often important to know how price changes affect consumer surplus. For example, we may want to know the harm to consumers from a frost in Florida
that drives up orange prices or consumers’ gain from the introduction of fish farming that makes salmon steaks less expensive. The same approach we have used to derive consumer surplus can be used to answer questions about how changes in prices affect consumers. Let’s return to the example of the market for used textbooks. Suppose that the bookstore decided to sell used textbooks for $20 instead of $30. By how much would this fall in price increase consumer surplus? The answer is illustrated in Figure 49.4. As shown in the figure, there are two parts to the increase in consumer surplus. The first part, shaded dark blue, is the gain of those who would have bought books even at the higher price of $30. Each of the students who would have bought books at $30—Aleisha, Brad, and Claudia—now pays $10 less, and therefore each gains $10 in consumer surplus from the fall in price to $20. So 486 49.4 Consumer Surplus and a Fall in the Price of Used Textbooks There are two parts to the increase in consumer surplus generated by a fall in price from $30 to $20. The first is given by the dark blue rectangle: each person who would have bought at the original price of $30—Aleisha, Brad, and Claudia— receives an increase in consumer surplus equal to the total reduction in price, $10. So the area of the dark blue rectangle corresponds to an amount equal to 3 × $10 = $30. The second part is given by the light blue area: the increase in consumer surplus for those who would not have bought at the original price of $30 but who buy at the new price of $20—namely, Darren. Darren’s willingness to pay is $25, so he now receives consumer surplus of $5. The total increase in consumer surplus is 3 × $10 + $5 = $35, represented by the sum of the shaded areas. Likewise, a rise in price from $20 to $30 would decrease consumer surplus by an amount equal to the sum of the shaded areas. Price of book $59 Aleisha Increase in Aleisha’s consumer surplus 45 35 30 25 20 10 Increase in Brad’s consumer surplus Brad Increase in Claudia’s consumer surplus Claudia Darren Original price New price Edwina Darren’s consumer surplus 0 1 2 3 4 D 5 Quantity of books the dark blue area represents the $10 × 3 = $30 increase in consumer surplus to
those three buyers. The second part, shaded light blue, is the gain to those who would not have bought a book at $30 but are willing to pay more than $20. In this case that gain goes to Darren, who would not have bought a book at $30 but does buy one at $20. He gains $5—the difference between his willingness to pay of $25 and the new price of $20. So the light blue area represents a further $5 gain in consumer surplus. The total increase in consumer surplus is the sum of the shaded areas, $35. Likewise, a rise in price from $20 to $30 would decrease consumer surplus by an amount equal to the sum of the shaded areas. Figure 49.4 illustrates that when the price of a good falls, the area under the demand curve but above the price—the total consumer surplus—increases. Figure 49.5 on the next page shows the same result for the case of a smooth demand curve for personal computers. Here we assume that the price of computers falls from $5,000 to $1,500, leading to an increase in the quantity demanded from 200,000 to 1 million units. As in the used-textbook example, we divide the gain in consumer surplus into two parts. The dark blue rectangle in Figure 49.5 corresponds to the dark blue area in Figure 49.4: it is the gain to the 200,000 people who would have bought computers even at the higher price of $5,000. As a result of the price reduction, each receives additional surplus of $3,500. The light blue triangle in Figure 49.5 corresponds to the light blue area in Figure 49.4: it is the gain to people who would not have bought the good at the higher price but are willing to do so at a price of $1,500. For example, the light blue triangle includes the gain to someone who would have been willing to pay $2,000 for a computer and therefore gains $500 in consumer surplus when it is possible to buy a computer for only $1,500. As before, the total gain in consumer surplus is the sum of the shaded areas, the increase in the area under the demand curve but above the price. What would happen if the price of a good were to rise instead of fall? We would do the same analysis in reverse. Suppose, for example, that for some reason the price of 487 f i g u r e 49.5
A Fall in the Price Increases Consumer Surplus A fall in the price of a computer from $5,000 to $1,500 leads to an increase in the quantity demanded and an increase in consumer surplus. The change in total consumer surplus is given by the sum of the shaded areas: the total area below the demand curve and between the old and new prices. Here, the dark blue area represents the increase in consumer surplus for the 200,000 consumers who would have bought a computer at the original price of $5,000; they each receive an increase in consumer surplus of $3,500. The light blue area represents the increase in consumer surplus for those willing to buy at a price equal to or greater than $1,500 but less than $5,000. Similarly, a rise in the price of a computer from $1,500 to $5,000 generates a decrease in consumer surplus equal to the sum of the two shaded areas. Price of computer $5,000 1,500 Increase in consumer surplus to original buyers Consumer surplus gained by new buyers D 0 200,000 1 million Quantity of computers computers rises from $1,500 to $5,000. This would lead to a fall in consumer surplus equal to the sum of the shaded areas in Figure 49.5. This loss consists of two parts. The dark blue rectangle represents the loss to consumers who would still buy a computer, even at a price of $5,000. The light blue triangle represents the loss to consumers who decide not to buy a computer at the higher price. fy i A Matter of Life and Death Each year about 4,000 people in the United States die while waiting for a kidney transplant. In 2009, some 80,000 were on the waiting list. Since the number of those in need of a kidney far exceeds availability, what is the best way to allocate available organs? A market isn’t feasible. For understandable reasons, the sale of human body parts is illegal in this country. So the task of establishing a protocol for these situations has fallen to the nonprofit group United Network for Organ Sharing (UNOS). Under current UNOS guidelines, a donated kidney goes to the person who has been waiting the longest. According to this system, an available kidney would go to a 75-year-old who has been waiting for 2 years instead of to a 25-year-old who has been waiting 6 months, even though the 25-year-old will likely live longer and benefit from the transplanted organ
for a longer period of time. To address this issue, UNOS is devising a new set of guidelines based on a concept it calls “net benefit.” According to these new guidelines, kidneys would be allocated on the basis of who will receive the greatest net benefit, where net benefit is measured as the expected increase in lifespan from the transplant. And age is by far the biggest predictor of how long someone will live after a transplant. For example, a typical 25-year-old diabetic will gain an extra 8.7 years of life from a transplant, but a typical 55-year-old diabetic will gain only 3.6 extra years. Under the current system, based on waiting times, transplants lead to about 44,000 extra years of life for recipients; under the new system, that number would jump to 55,000 extra years. The share of kidneys going to those in their 20s would triple; the share going to those 60 and older would be halved. What does this have to do with consumer surplus? As you may have guessed, the UNOS 488 concept of “net benefit” is a lot like individual consumer surplus—the individual consumer surplus generated from getting a new kidney. In essence, UNOS has devised a system that allocates donated kidneys according to who gets the greatest individual consumer surplus. In terms of results, then, its proposed “net benefit” system operates a lot like a competitive market Producer Surplus and the Supply Curve Just as some buyers of a good would have been willing to pay more for their purchase than the price they actually pay, some sellers of a good would have been willing to sell it for less than the price they actually receive. We can therefore carry out an analysis of producer surplus and the supply curve that is almost exactly parallel to that of consumer surplus and the demand curve. Cost and Producer Surplus Consider a group of students who are potential sellers of used textbooks. Because they have different preferences, the various potential sellers differ in the price at which they are willing to sell their books. The table in Figure 49.6 shows the prices at which several different students would be willing to sell. Andrew is willing to sell the book as long as he can get at least $5; Betty won’t sell unless she can get at least $15; Carlos requires $25; Donna requires $35; Engelbert $45. f i g u r e 49.6 The Supply Curve for Used Textbooks Price of book $45 35 25
15 5 0 S Engelbert Donna Carlos Potential sellers Andrew Betty Carlos Donna Engelbert Cost $5 15 25 35 45 Betty Andrew 1 2 3 4 5 Quantity of books The supply curve illustrates sellers’ cost, the lowest price at which a potential seller is willing to sell the good, and the quantity supplied at that price. Each of the five students has one book to sell and each has a different cost, as indicated in the accompanying table. At a price of $5 the quantity supplied is one (Andrew), at $15 it is two (Andrew and Betty), and so on until you reach $45, the price at which all five students are willing to sell. The lowest price at which a potential seller is willing to sell is called the seller’s cost. So Andrew’s cost is $5, Betty’s is $15, and so on. Using the term cost, which people normally associate with the monetary cost of producing a good, may sound a little strange when applied to sellers of used textbooks. The students don’t have to manufacture the books, so it doesn’t cost the student who sells a book anything to make that book available for sale, does it? Yes, it does. A student who sells a book won’t have it later, as part of his or her personal collection. So there is an opportunity cost to selling a textbook, even if the owner has completed the course for which it was required. And remember that one of the basic principles of economics is that the true measure of the cost of doing something is A seller’s cost is the lowest price at which he or she is willing to sell a good 489 Individual producer surplus is the net gain to an individual seller from selling a good. It is equal to the difference between the price received and the seller’s cost. Total producer surplus in a market is the sum of the individual producer surpluses of all the sellers of a good in a market. Economists use the term producer surplus to refer both to individual and to total producer surplus. always its opportunity cost. That is, the real cost of something is what you must give up to get it. So it is good economics to talk of the minimum price at which someone will sell a good as the “cost” of selling that good, even if he or she doesn’t spend any money to make the good available for sale. Of course, in most real-world markets the sellers are also those who
produce the good and therefore do spend money to make the good available for sale. In this case the cost of making the good available for sale includes monetary costs, but it may also include other opportunity costs. Getting back to the example, suppose that Andrew sells his book for $30. Clearly he has gained from the transaction: he would have been willing to sell for only $5, so he has gained $25. This net gain, the difference between the price he actually gets and his cost—the minimum price at which he would have been willing to sell—is known as his individual producer surplus. Just as we derived the demand curve from the willingness to pay of different consumers, we can derive the supply curve from the cost of different producers. The stepshaped curve in Figure 49.6 shows the supply curve implied by the costs shown in the accompanying table. At a price less than $5, none of the students are willing to sell; at a price between $5 and $15, only Andrew is willing to sell, and so on. As in the case of consumer surplus, we can add the individual producer surpluses of sellers to calculate the total producer surplus, the total net gain to all sellers in the market. Economists use the term producer surplus to refer to either total or individual producer surplus. Table 49.2 shows the net gain to each of the students who would sell a used book at a price of $30: $25 for Andrew, $15 for Betty, and $5 for Carlos. The total producer surplus is $25 + $15 + $5 = $45. t a b l e 49.2 Producer Surplus When the Price of a Used Textbook Is $30 Potential seller Andrew Betty Carlos Donna Engelbert All sellers Cost Price received Individual producer surplus = Price received − Cost $5 15 25 35 45 $30 30 30 — — $25 15 5 — — Total producer surplus = $45 As with consumer surplus, the producer surplus gained by those who sell books can be represented graphically. Figure 49.7 reproduces the supply curve from Figure 49.6. Each step in that supply curve is one book wide and represents one seller. The height of Andrew’s step is $5, his cost. This forms the bottom of a rectangle, with $30, the price he actually receives for his book, forming the top. The area of this rectangle, ($30 − $5) × 1 = $25, is his producer surplus. So the producer surplus Andrew gains
from selling his book is the area of the dark red rectangle shown in the figure. Let’s assume that the campus bookstore is willing to buy all the used copies of this book that students are willing to sell at a price of $30. Then, in addition to Andrew, Betty and Carlos will also sell their books. They will also benefit from their sales, though not as much as Andrew, because they have higher costs. Andrew, as we have seen, gains $25. Betty gains a smaller amount: since her cost is $15, she gains only $15. Carlos gains even less, only $5. 490 49.7 Producer Surplus in the UsedTextbook Market At a price of $30, Andrew, Betty, and Carlos each sell a book but Donna and Engelbert do not. Andrew, Betty, and Carlos get individual producer surpluses equal to the difference between the price and their cost, illustrated here by the shaded rectangles. Donna and Engelbert each have a cost that is greater than the price of $30, so they are unwilling to sell a book and so receive zero producer surplus. The total producer surplus is given by the entire shaded area, the sum of the individual producer surpluses of Andrew, Betty, and Carlos, equal to $25 + $15 + $5 = $45. Price of book $45 35 30 25 15 5 0 S Engelbert Donna Carlos Betty Andrew Price Carlos’s producer surplus Andrew’s producer surplus Betty’s producer surplus 1 2 3 4 5 Quantity of books Again, as with consumer surplus, we have a general rule for determining the total producer surplus from sales of a good: The total producer surplus from sales of a good at a given price is the area above the supply curve but below that price. This rule applies both to examples like the one shown in Figure 49.7, where there are a small number of producers and a step-shaped supply curve, and to more realistic examples, where there are many producers and the supply curve is more or less smooth. Consider, for example, the supply of wheat. Figure 49.8 shows how producer surplus depends on the price per bushel. Suppose that, as shown in f i g u r e 49.8 Producer Surplus Here is the supply curve for wheat. At a price of $5 per bushel, farmers supply 1 million bushels. The producer surplus at this price is equal to the shaded area: the area above the supply curve but
below the price. This is the total gain to producers—farmers in this case—from supplying their product when the price is $5. Price of wheat (per bushel) $5 Producer surplus Price 0 1 million Quantity of wheat (bushels 491 the figure, the price is $5 per bushel and farmers supply 1 million bushels. What is the benefit to the farmers from selling their wheat at a price of $5? Their producer surplus is equal to the shaded area in the figure—the area above the supply curve but below the price of $5 per bushel. How Changing Prices Affect Producer Surplus As in the case of consumer surplus, a change in price alters producer surplus. However, although a fall in price increases consumer surplus, it reduces producer surplus. Similarly, a rise in price reduces consumer surplus but increases producer surplus. To see this, let’s first consider a rise in the price of the good. Producers of the good will experience an increase in producer surplus, though not all producers gain the same amount. Some producers would have produced the good even at the original price; they will gain the entire price increase on every unit they produce. Other producers will enter the market because of the higher price; they will gain only the difference between the new price and their cost. Figure 49.9 is the supply counterpart of Figure 49.5. It shows the effect on producer surplus of a rise in the price of wheat from $5 to $7 per bushel. The increase in producer surplus is the sum of the shaded areas, which consists of two parts. First, there is a dark red rectangle corresponding to the gains to those farmers who would have supplied wheat even at the original $5 price. Second, there is an additional light red triangle that corresponds to the gains to those farmers who would not have supplied wheat at the original price but are drawn into the market by the higher price. f i g u r e 49.9 A Rise in the Price Increases Producer Surplus A rise in the price of wheat from $5 to $7 leads to an increase in the quantity supplied and an increase in producer surplus. The change in total producer surplus is given by the sum of the shaded areas: the total area above the supply curve but between the old and new prices. The dark red area represents the gain to the farmers who would have supplied 1 million bushels at the original price of $5; they each receive an increase in producer surplus of $2 for
each of those bushels. The triangular light red area represents the increase in producer surplus achieved by the farmers who supply the additional 500,000 bushels because of the higher price. Similarly, a fall in the price of wheat generates a reduction in producer surplus equal to the sum of the shaded areas. Increase in producer surplus to original sellers Producer surplus gained by new sellers S Price of wheat (per bushel) $7 5 0 1 million 1.5 million Quantity of wheat (bushels) If the price were to fall from $7 to $5 per bushel, the story would run in reverse. The sum of the shaded areas would now be the decline in producer surplus, the decrease in the area above the supply curve but below the price. The loss would consist of two parts, the loss to farmers who would still grow wheat at a price of $5 (the dark red rectangle) and the loss to farmers who decide to no longer grow wheat because of the lower price (the light red triangle). 492 49 AP R e v i e w Solutions appear at the back of the book. Check Your Understanding 1. Consider the market for cheese-stuffed jalapeno peppers. There are two consumers, Casey and Josey, and their willingness to pay for each pepper is given in the accompanying table. (Neither is willing to consume more than 4 peppers at any price.) Use the table (i) to construct the demand schedule for peppers for prices of $0.00, $0.10, and so on, up to $0.90, and (ii) to calculate the total consumer surplus when the price of a pepper is $0.40. 2. Again consider the market for cheese-stuffed jalapeno peppers. There are two producers, Cara and Jamie, and their costs of producing each pepper are given in the accompanying table. (Neither is willing to produce more than 4 peppers at any price.) Use the table (i) to construct the supply schedule for peppers for prices of $0.00, $0.10, and so on, up to $0.90, and (ii) to calculate the total producer surplus when the price of a pepper is $0.70. Quantity of peppers 1st pepper 2nd pepper 3rd pepper 4th pepper Casey’s willingness to pay $0.90 0.70 0.50 0.30 Josey’s willingness to pay $0.80 0.60 0.40
0.30 Quantity of peppers 1st pepper 2nd pepper 3rd pepper 4th pepper Cara’s cost $0.10 0.10 0.40 0.60 Jamie’s cost $0.30 0.50 0.70 0.90 Tackle the Test: Multiple-Choice Questions 1. Refer to the graph below. What is the value of consumer surplus 2. Refer to the graph below. What is the value of producer surplus when the market price is $40? when the market price is $60 Price $80 40 0 a. $400 b. $800 c. $4,000 d. $8,000 e. $16,000 Price $60 20 0 a. $100 b. $150 c. $1,000 d. $1,500 e. $3,000 D 200 Quantity S 50 Quantity 3. Other things equal, a rise in price will result in which of the following? a. Producer surplus will rise; consumer surplus will rise. b. Producer surplus will fall; consumer surplus will fall. c. Producer surplus will rise; consumer surplus will fall. d. Producer surplus will fall; consumer surplus will rise. e. Producer surplus will not change; consumer surplus will rise 493 4. Consumer surplus is found as the area a. above the supply curve and below the price. b. below the demand curve and above the price. c. above the demand curve and below the price. d. below the supply curve and above the price. e. below the supply curve and above the demand curve. 5. Allocating kidneys to those with the highest net benefit (where net benefit is measured as the expected increase in lifespan from a transplant) is an attempt to maximize a. consumer surplus. b. producer surplus. c. profit. d. equity. e. respect for elders. Tackle the Test: Free-Response Questions 1. Refer to the graph provided. Price $80 40 10 0 Answer (6 points) 1 point: $4,000 1 point: $3,000 S 1 point: Consumer surplus will increase. 1 point: An increase in supply lowers the equilibrium price, which causes consumer surplus to increase. 1 point: Producer surplus will decrease. 1 point: A decrease in demand decreases the equilibrium price, which causes producer surplus to decrease. 2. Draw a correctly labeled graph showing a competitive market in equilibrium. On your graph, clearly indicate and label the area of consumer surplus and the area of producer surplus. 200 D Qu
antity a. Calculate consumer surplus. b. Calculate producer surplus. c. If supply increases, what will happen to consumer surplus? Explain. d. If demand decreases, what will happen to producer surplus? Explain. 494 Module 50 Efficiency and Deadweight Loss Consumer Surplus, Producer Surplus, and Efficiency Markets are a remarkably effective way to organize economic activity: under the right conditions, they can make society as well off as possible given the available resources. The concepts of consumer and producer surplus can help us deepen our understanding of why this is so. The Gains from Trade Let’s return to the market for used textbooks, but now consider a much bigger market— say, one at a large state university. There are many potential buyers and sellers, so the market is competitive. Let’s line up incoming students who are potential buyers of a book in order of their willingness to pay, so that the entering student with the highest willingness to pay is potential buyer number 1, the student with the next highest willingness to pay is number 2, and so on. Then we can use their willingness to pay to derive a demand curve like the one in Figure 50.1 on the next page. Similarly, we can line up outgoing students, who are potential sellers of the book, in order of their cost, starting with the student with the lowest cost, then the student with the next lowest cost, and so on, to derive a supply curve like the one shown in the same figure. As we have drawn the curves, the market reaches equilibrium at a price of $30 per book, and 1,000 books are bought and sold at that price. The two shaded triangles show the consumer surplus (blue) and the producer surplus (red) generated by this market. The sum of consumer and producer surplus is known as total surplus. The striking thing about this picture is that both consumers and producers gain— that is, both consumers and producers are better off because there is a market in this good. But this should come as no surprise—it illustrates another core principle of economics: There are gains from trade. These gains from trade are the reason everyone is better off participating in a market economy than they would be if each individual tried to be self-sufficient. What you will learn in this Module: • The meaning and importance of total surplus and how it can be used to illustrate efficiency in markets • How taxes affect total surplus and can create deadweight loss Total surplus is the total net gain to consumers and producers from trading
in a market. It is the sum of producer and consumer surplus 495 f i g u r e 50. 1 Total Surplus In the market for used textbooks, the equilibrium price is $30 and the equilibrium quantity is 1,000 books. Consumer surplus is given by the blue area, the area below the demand curve but above the price. Producer surplus is given by the red area, the area above the supply curve but below the price. The sum of the blue and the red areas is total surplus, the total benefit to society from the production and consumption of the good. Price of book Equilibrium price $30 Consumer surplus Producer surplus E S D 0 1,000 Quantity of books Equilibrium quantity But are we as well off as we could be? This brings us to the question of the efficiency of markets. The Efficiency of Markets A market is efficient if, once the market has produced its gains from trade, there is no way to make some people better off without making other people worse off. Note that market equilibrium is just one way of deciding who consumes a good and who sells a good. To better understand how markets promote efficiency, let’s examine some alternatives. Consider the example of kidney transplants discussed earlier in an FYI box. There is not a market for kidneys, and available kidneys currently go to whoever has been on the waiting list the longest. Of course, those who have been waiting the longest aren’t necessarily those who would benefit the most from a new kidney. Similarly, imagine a committee charged with improving on the market equilibrium by deciding who gets and who gives up a used textbook. The committee’s ultimate goal would be to bypass the market outcome and come up with another arrangement that would increase total surplus. Let’s consider three approaches the committee could take: 1. It could reallocate consumption among consumers. 2. It could reallocate sales among sellers. 3. It could change the quantity traded. The Reallocation of Consumption Among Consumers The committee might try to increase total surplus by selling books to different consumers. Figure 50.2 shows why this will result in lower surplus compared to the market equilibrium outcome. Points A and B show the positions on the demand curve of two potential buyers of used books, Ana and Bob. As we can see from the figure, Ana is willing to pay $35 for a book, but Bob is willing to pay only $25. Since the market equilibrium price is $30, under the market outcome Ana gets a book and Bob does not
. Now suppose the committee reallocates consumption. This would mean taking the book away from Ana and giving it to Bob. Since the book is worth $35 to Ana but only $25 to Bob, this change reduces total consumer surplus by $35 − $25 = $10. Moreover, this result 496 50.2 Reallocating Consumption Lowers Consumer Surplus Ana (point A) has a willingness to pay of $35. Bob (point B) has a willingness to pay of only $25. At the market equilibrium price of $30, Ana purchases a book but Bob does not. If we rearrange consumption by taking a book from Ana and giving it to Bob, consumer surplus declines by $10 and, as a result, total surplus declines by $10. The market equilibrium generates the highest possible consumer surplus by ensuring that those who consume the good are those who most value it. Price of book $35 30 25 Loss in consumer surplus if the book is taken from Ana and given to Bob,000 Quantity of books doesn’t depend on which two students we pick. Every student who buys a book at the market equilibrium price has a willingness to pay of $30 or more, and every student who doesn’t buy a book has a willingness to pay of less than $30. So reallocating the good among consumers always means taking a book away from a student who values it more and giving it to one who values it less. This necessarily reduces total consumer surplus. The Reallocation of Sales Among Sellers The committee might try to increase total surplus by altering who sells their books, taking sales away from sellers who would have sold their books in the market equilibrium and instead compelling those who would not have sold their books in the market equilibrium to sell them. Figure 50.3 shows why this will result in lower surplus. Here points X and Y show the positions on the supply f i g u r e 50.3 Reallocating Sales Lowers Producer Surplus Yvonne (point Y ) has a cost of $35, $10 more than Xavier (point X ), who has a cost of $25. At the market equilibrium price of $30, Xavier sells a book but Yvonne does not. If we rearrange sales by preventing Xavier from selling his book and compelling Yvonne to sell hers, producer surplus declines by $10 and, as a result, total surplus declines by $10. The market equilibrium generates the highest possible producer surplus by assuring that those who sell the
good are those who most value the right to sell it. Price of book $35 30 25 S E X Y Loss in producer surplus if Yvonne is made to sell the book instead of Xavier D 0 1,000 Quantity of books 497 curve of Xavier, who has a cost of $25, and Yvonne, who has a cost of $35. At the equilibrium market price of $30, Xavier would sell his book but Yvonne would not sell hers. If the committee reallocated sales, forcing Xavier to keep his book and Yvonne to sell hers, total producer surplus would be reduced by $35 − $25 = $10. Again, it doesn’t matter which two students we choose. Any student who sells a book at the market equilibrium price has a lower cost than any student who keeps a book. So reallocating sales among sellers necessarily increases total cost and reduces total producer surplus. Changes in the Quantity Traded The committee might try to increase total surplus by compelling students to trade either more books or fewer books than the market equilibrium quantity. Figure 50.4 shows why this will result in lower surplus. It shows all four students: potential buyers Ana and Bob, and potential sellers Xavier and Yvonne. To reduce sales, the committee will have to prevent a transaction that would have occurred in the market equilibrium—that is, prevent Xavier from selling to Ana. Since Ana is willing to pay $35 and Xavier’s cost is $25, preventing this transaction reduces total surplus by $35 − $25 = $10. Once again, this result doesn’t depend on which two students we pick: any student who would have sold the book in the market equilibrium has a cost of $30 or less, and any student who would have purchased the book in the market equilibrium has a willingness to pay of $30 or more. So preventing any sale that would have occurred in the market equilibrium necessarily reduces total surplus. f i g u r e 50.4 Changing the Quantity Lowers Total Surplus If Xavier (point X ) were prevented from selling his book to someone like Ana (point A), total surplus would fall by $10, the difference between Ana’s willingness to pay ($35) and Xavier’s cost ($25). This means that total surplus falls whenever fewer than 1,000 books—the equilibrium quantity—are transacted. Likewise, if Yvonne (point Y ) were compelled to sell her book to someone like Bob (point B
), total surplus would also fall by $10, the difference between Yvonne’s cost ($35) and Bob’s willingness to pay ($25). This means that total surplus falls whenever more than 1,000 books are transacted. These two examples show that at market equilibrium, all mutually beneficial transactions—and only mutually beneficial transactions—occur. Price of book $35 30 25 Loss in total surplus if the transaction between Ana and Xavier is prevented A X E Y B S Loss in total surplus if the transaction between Yvonne and Bob is forced D 0 1,000 Quantity of books Finally, the committee might try to increase sales by forcing Yvonne, who would not have sold her book in the market equilibrium, to sell it to someone like Bob, who would not have bought a book in the market equilibrium. Because Yvonne’s cost is $35, but Bob is only willing to pay $25, this transaction reduces total surplus by $10. And once again it doesn’t matter which two students we pick—anyone who wouldn’t have bought the book has a willingness to pay of less than $30, and anyone who wouldn’t have sold has a cost of more than $30. The key point to remember is that once this market is in equilibrium, there is no way to increase the gains from trade. Any other outcome reduces total surplus. We can summarize our results by stating that an efficient market performs four important functions: 498. It allocates consumption of the good to the potential buyers who most value it, as indicated by the fact that they have the highest willingness to pay. 2. It allocates sales to the potential sellers who most value the right to sell the good, as indicated by the fact that they have the lowest cost. 3. It ensures that every consumer who makes a purchase values the good more than every seller who makes a sale, so that all transactions are mutually beneficial. 4. It ensures that every potential buyer who doesn’t make a purchase values the good less than every potential seller who doesn’t make a sale, so that no mutually beneficial transactions are missed. There are three caveats, however. First, although a market may be efficient, it isn’t necessarily fair. In fact, fairness, or equity, is often in conflict with efficiency. We’ll discuss this next. The second caveat is that markets sometimes fail. Under some well- defined conditions, markets can fail
to deliver efficiency. When this occurs, markets no longer maximize total surplus. We’ll take a closer look at market failures in later modules. Third, even when the market equilibrium maximizes total surplus, this does not mean that it results in the best outcome for every individual consumer and producer. Other things equal, each buyer would like to pay a lower price and each seller would like to receive a higher price. So if the government were to intervene in the market—say, by lowering the price below the equilibrium price to make consumers happy or by raising the price above the equilibrium price to make producers happy—the outcome would no longer be efficient. Although some people would be happier, society as a whole would be worse off because total surplus would be lower. Equity and Efficiency It’s easy to get carried away with the idea that markets are always good and that economic policies that interfere with efficiency are bad. But that would be misguided because there is another factor to consider: society cares about equity, or what’s “fair.” There is often a trade-off between equity and efficiency: policies that promote equity often come at the cost of decreased efficiency, and policies that promote efficiency often result in decreased equity. So it’s important to realize that a society’s choice to sacrifice some efficiency for the sake of equity, however it defines equity, may well be a valid one. And it’s important to understand that fairness, unlike efficiency, can be very hard to define. Fairness is a concept about which well-intentioned people often disagree. In fact, the debate about equity and efficiency is at the core of most debates about taxation. Proponents of taxes that redistribute income from the rich to the poor often argue for the fairness of such redistributive taxes. Opponents of taxation often argue that phasing out certain taxes would make the economy more efficient. Because taxes are ultimately paid out of income, economists classify taxes according to how they vary with the income of individuals. A tax that rises more than in proportion to income, so that high-income taxpayers pay a larger percentage of their income than low-income taxpayers, is a progressive tax. A tax that rises less than in proportion to income, so that high-income taxpayers pay a smaller percentage of their income than low-income taxpayers, is a regressive tax. A tax that rises in proportion to income, so that all taxpayers pay the same percentage of their income, is a proportional tax. The U.S.
tax system contains a mixture of progressive and regressive taxes, though it is somewhat progressive overall. The Effects of Taxes on Total Surplus To understand the economics of taxes, it’s helpful to look at a simple type of tax known as an excise tax—a tax charged on each unit of a good or service that is sold. Most tax revenue in the United States comes from other kinds of taxes, but excise taxes progressive tax rises more than in proportion to income. A regressive tax rises less than in proportion to income. A proportional tax rises in proportion to income. An excise tax is a tax on sales of a particular good or service 499 are common. For example, there are excise taxes on gasoline, cigarettes, and foreignmade trucks, and many local governments impose excise taxes on services such as hotel room rentals. The lessons we’ll learn from studying excise taxes apply to other, more complex taxes as well. The Effect of an Excise Tax on Quantities and Prices Suppose that the supply and demand for hotel rooms in the city of Potterville are as shown in Figure 50.5. We’ll make the simplifying assumption that all hotel rooms are the same. In the absence of taxes, the equilibrium price of a room is $80 per night and the equilibrium quantity of hotel rooms rented is 10,000 per night. f i g u r e 50.5 The Supply and Demand for Hotel Rooms in Potterville In the absence of taxes, the equilibrium price of hotel rooms is $80 a night, and the equilibrium number of rooms rented is 10,000 per night, as shown by point E. The supply curve, S, shows the quantity supplied at any given price, pre-tax. At a price of $60 a night, hotel owners are willing to supply 5,000 rooms, as shown by point B. But post-tax, hotel owners are willing to supply the same quantity only at a price of $100: $60 for themselves plus $40 paid to the city as tax. Price of hotel room Equilibrium price $140 120 100 80 60 40 20 0 E B S D 5,000 10,000 Equilibrium quantity 15,000 Quantity of hotel rooms Now suppose that Potterville’s government imposes an excise tax of $40 per night on hotel rooms—that is, every time a room is rented for the night, the owner of the hotel must pay the city $40. For example, if a customer pays $80, $40 is collected as a tax,
leaving the hotel owner with only $40. As a result, hotel owners are less willing to supply rooms at any given price. What does this imply about the supply curve for hotel rooms in Potterville? To answer this question, we must compare the incentives of hotel owners pre-tax (before the tax is levied) to their incentives post-tax (after the tax is levied). From Figure 50.5 we know that pre-tax, hotel owners are willing to supply 5,000 rooms per night at a price of $60 per room. But after the $40 tax per room is levied, they are willing to supply the same amount, 5,000 rooms, only if they receive $100 per room—$60 for themselves plus $40 paid to the city as tax. In other words, in order for hotel owners to be willing to supply the same quantity post-tax as they would have pre-tax, they must receive an additional $40 per room, the amount of the tax. This implies that the post-tax supply curve shifts up by the amount of the tax compared to the pre-tax supply curve. At every quantity supplied, the supply price—the price that producers must receive to produce a given quantity—has increased by $40. 500 The upward shift of the supply curve caused by the tax is shown in Figure 50.6, where S1 is the pre-tax supply curve and S2 is the post-tax supply curve. As you can see, the market equilibrium moves from E, at the equilibrium price of $80 per room and 10,000 rooms rented each night, to A, at a market price of $100 per room and only 5,000 rooms rented each night. A is, of course, on both the demand curve D and the new supply curve S2. In this case, $100 is the demand price of 5,000 rooms—but in effect hotel owners receive only $60, when you account for the fact that they have to pay the $40 tax. From the point of view of hotel owners, it is as if they were on their original supply curve at point B. f i g u r e 50.6 An Excise Tax Imposed on Hotel Owners A $40 per room tax imposed on hotel owners shifts the supply curve from S1 to S2, an upward shift of $40. The equilibrium price of hotel rooms rises from $80 to $100 a night, and the equilibrium quantity of rooms rented falls from 10,000 to 5,
000. Although hotel owners pay the tax, they actually bear only half the burden: the price they receive net of tax falls only $20, from $80 to $60. Guests who rent rooms bear the other half of the burden because the price they pay rises by $20, from $80 to $100. Price of hotel room Excise tax = $40 per room $140 120 100 80 60 40 20 0 Supply curve shifts upward by the amount of the tax. A B E S2 S1 D 5,000 10,000 15,000 Quantity of hotel rooms Let’s check this again. How do we know that 5,000 rooms will be supplied at a price of $100? Because the price net of tax is $60, and according to the original supply curve, 5,000 rooms will be supplied at a price of $60, as shown by point B in Figure 50.6. An excise tax drives a wedge between the price paid by consumers and the price received by producers. As a result of this wedge, consumers pay more and producers receive less. In our example, consumers—people who rent hotel rooms—end up paying $100 a night, $20 more than the pre-tax price of $80. At the same time, producers—the hotel owners—receive a price net of tax of $60 per room, $20 less than the pre-tax price. In addition, the tax creates missed opportunities: 5,000 potential consumers who would have rented hotel rooms—those willing to pay $80 but not $100 per night—are discouraged from renting rooms. Correspondingly, 5,000 rooms that would have been made available by hotel owners when they receive $80 are not offered when they receive only $60. Like a quota on sales as discussed in Module 9, this tax leads to inefficiency by distorting incentives and creating missed opportunities for mutually beneficial transactions. It’s important to recognize that as we’ve described it, Potterville’s hotel tax is a tax on the hotel owners, not their guests—it’s a tax on the producers, not the consumers. Yet the price received by producers, net of tax, is down by only $20, half the amount of the tax, and the price paid by consumers is up by $20. In effect, half the tax is being paid by consumers 501 What would happen if the city levied a tax on consumers instead of producers? That is, suppose that instead of requiring
hotel owners to pay $40 a night for each room they rent, the city required hotel guests to pay $40 for each night they stayed in a hotel. The answer is shown in Figure 50.7. If a hotel guest must pay a tax of $40 per night, then the price for a room paid by that guest must be reduced by $40 in order for the quantity of hotel rooms demanded post-tax to be the same as that demanded pre-tax. So the demand curve shifts downward, from D1 to D2, by the amount of the tax. At every quantity demanded, the demand price—the price that consumers must be offered to demand a given quantity—has fallen by $40. This shifts the equilibrium from E to B, where the market price of hotel rooms is $60 and 5,000 hotel rooms are bought and sold. In effect, hotel guests pay $100 when you include the tax. So from the point of view of guests, it is as if they were on their original demand curve at point A. f i g u r e 50.7 An Excise Tax Imposed on Hotel Guests A $40 per room tax imposed on hotel guests shifts the demand curve from D1 to D2, a downward shift of $40. The equilibrium price of hotel rooms falls from $80 to $60 a night, and the quantity of rooms rented falls from 10,000 to 5,000. Although in this case the tax is officially paid by consumers, while in Figure 50.6 the tax was paid by producers, the outcome is the same: after taxes, hotel owners receive $60 per room but guests pay $100. This illustrates a general principle: The incidence of an excise tax doesn’t depend on whether consumers or producers officially pay the tax. Price of hotel room Excise tax = $40 per room $140 120 100 80 60 40 20 0 Demand curve shifts downward by the amount of the tax. E A B S D1 D2 5,000 10,000 15,000 Quantity of hotel rooms If you compare Figures 50.6 and 50.7, you will notice that the effects of the tax are the same even though different curves are shifted. In each case, consumers pay $100 per unit (including the tax, if it is their responsibility), producers receive $60 per unit (after paying the tax, if it is their responsibility), and 5,000 hotel rooms are bought and sold. In fact, it doesn’t matter who officially pays the
tax—the equilibrium outcome is the same. This example illustrates a general principle of tax incidence, a measure of who really pays a tax: the burden of a tax cannot be determined by looking at who writes the check to the government. In this particular case, a $40 tax on hotel rooms brings about a $20 increase in the price paid by consumers and a $20 decrease in the price received by producers. Regardless of whether the tax is levied on consumers or producers, the incidence of the tax is the same. As we will see next, the burden of a tax depends on the price elasticities of supply and demand. Price Elasticities and Tax Incidence We’ve just learned that the incidence of an excise tax doesn’t depend on who officially pays it. In the example shown in Figures 50.5 through 50.7, a tax on hotel rooms falls equally on consumers and producers, no matter on whom the tax is Tax incidence is the distribution of the tax burden. 502 levied. But it’s important to note that this 50–50 split between consumers and producers is a result of our assumptions in this example. In the real world, the incidence of an excise tax usually falls unevenly between consumers and producers: one group bears more of the burden than the other. What determines how the burden of an excise tax is allocated between consumers and producers? The answer depends on the shapes of the supply and the demand curves. More specifically, the incidence of an excise tax depends on the price elasticity of supply and the price elasticity of demand. We can see this by looking first at a case in which consumers pay most of an excise tax, and then at a case in which producers pay most of the tax. When an Excise Tax Is Paid Mainly by Consumers Figure 50.8 shows an excise tax that falls mainly on consumers: an excise tax on gasoline, which we set at $1 per gallon. (There really is a federal excise tax on gasoline, though it is actually only about $0.18 per gallon in the United States. In addition, states impose excise taxes between $0.08 and $0.37 per gallon.) According to Figure 50.8, in the absence of the tax, gasoline would sell for $2 per gallon 50.8 An Excise Tax Paid Mainly by Consumers The relatively steep demand curve here reflects a low price elasticity of demand for gasoline. The relatively flat supply curve reflects a high price elasticity of supply. The pretax price of a gallon
of gasoline is $2.00, and a tax of $1.00 per gallon is imposed. The price paid by consumers rises by $0.95 to $2.95, reflecting the fact that most of the burden of the tax falls on consumers. Only a small portion of the tax is borne by producers: the price they receive falls by only $0.05 to $1.95. Price of gasoline (per gallon) $2.95 Excise tax = $1 per gallon 2.00 1.95 Tax burden falls mainly on consumers. S D 0 Quantity of gasoline (gallons) Two key assumptions are reflected in the shapes of the supply and demand curves in Figure 50.8. First, the price elasticity of demand for gasoline is assumed to be very low, so the demand curve is relatively steep. Recall that a low price elasticity of demand means that the quantity demanded changes little in response to a change in price. Second, the price elasticity of supply of gasoline is assumed to be very high, so the supply curve is relatively flat. A high price elasticity of supply means that the quantity supplied changes a lot in response to a change in price. We have just learned that an excise tax drives a wedge, equal to the size of the tax, between the price paid by consumers and the price received by producers. This wedge drives the price paid by consumers up and the price received by producers down. But as we can see from Figure 50.8, in this case those two effects are very unequal in size. The price received by producers falls only slightly, from $2.00 to $1.95, but the price paid by consumers rises by a lot, from $2.00 to $2.95. This means that consumers bear the greater share of the tax burden. This example illustrates another general principle of taxation: When the price elasticity of demand is low and the price elasticity of supply is high, the burden of an excise tax falls 503 mainly on consumers. Why? A low price elasticity of demand means that consumers have few substitutes and so little alternative to buying higher-priced gasoline. In contrast, a high price elasticity of supply results from the fact that producers have many production substitutes for their gasoline (that is, other uses for the crude oil from which gasoline is refined). This gives producers much greater flexibility in refusing to accept lower prices for their gasoline. And, not surprisingly, the party with the least flexibility—in this case, consumers—gets stuck paying
most of the tax. This is a good description of how the burden of the main excise taxes actually collected in the United States today, such as those on cigarettes and alcoholic beverages, is allocated between consumers and producers. When an Excise Tax Is Paid Mainly by Producers Figure 50.9 shows an example of an excise tax paid mainly by producers, a $5.00 per day tax on downtown parking in a small city. In the absence of the tax, the market equilibrium price of parking is $6.00 per day. f i g u r e 50.9 An Excise Tax Paid Mainly by Producers The relatively flat demand curve here reflects a high price elasticity of demand for downtown parking, and the relatively steep supply curve results from a low price elasticity of supply. The pre-tax price of a daily parking space is $6.00 and a tax of $5.00 is imposed. The price received by producers falls a lot, to $1.50, reflecting the fact that they bear most of the tax burden. The price paid by consumers rises a small amount, $0.50, to $6.50, so they bear very little of the burden. Price of parking space $6.50 6.00 Excise tax = $5 per parking space 1.50 0 S D Tax burden falls mainly on producers. Quantity of parking spaces We’ve assumed in this case that the price elasticity of supply is very low because the lots used for parking have very few alternative uses. This makes the supply curve for parking spaces relatively steep. The price elasticity of demand, however, is assumed to be high: consumers can easily switch from the downtown spaces to other parking spaces a few minutes’ walk from downtown, spaces that are not subject to the tax. This makes the demand curve relatively flat. The tax drives a wedge between the price paid by consumers and the price received by producers. In this example, however, the tax causes the price paid by consumers to rise only slightly, from $6.00 to $6.50, but the price received by producers falls a lot, from $6.00 to $1.50. In the end, a consumer bears only $0.50 of the $5 tax burden, with a producer bearing the remaining $4.50. Again, this example illustrates a general principle: When the price elasticity of demand is high and the price elasticity of supply is low, the burden of an excise tax falls mainly
on producers. A real-world example is a tax on purchases of existing houses. In many American towns, house prices in desirable locations have risen as well-off outsiders have moved in and purchased homes from the less well-off original occupants, a phenomenon called gentrification. Some of these towns have imposed taxes on house sales intended to extract money from the new arrivals. But this ignores the fact that the price elasticity of demand for houses in a particular town is often high because potential buyers 504 can choose to move to other towns. Furthermore, the price elasticity of supply is often low because most sellers must sell their houses due to job transfers or to provide funds for their retirement. So taxes on home purchases are actually paid mainly by the less well-off sellers—not, as town officials imagine, by wealthy buyers. The Benefits and Costs of Taxation When a government is considering whether to impose a tax or how to design a tax system, it has to weigh the benefits of a tax against its costs. We may not think of a tax as something that provides benefits, but governments need money to provide things people want, such as streets, schools, national defense, and health care for those unable to afford it. The benefit of a tax is the revenue it raises for the government to pay for these services. Unfortunately, this benefit comes at a cost—a cost that is normally larger than the amount consumers and producers pay. Let’s look first at what determines how much money a tax raises and then at the costs a tax imposes The Revenue from an Excise Tax How much revenue does the government collect from an excise tax? In our hotel tax example, the revenue is equal to the area of the shaded rectangle in Figure 50.10 50.10 The Revenue from an Excise Tax The revenue from a $40 excise tax on hotel rooms is $200,000, equal to the tax rate, $40—the size of the wedge that the tax drives between the supply price and the demand price—multiplied by the number of rooms rented, 5,000. This is equal to the area of the shaded rectangle. Price of hotel room Excise tax = $40 per room $140 120 100 80 60 40 20 0 Area = tax revenue A B E S D 5,000 10,000 Quantity of hotel rooms 15,000 To see why this area represents the revenue collected by a $40 tax on hotel rooms, notice that the height of the rectangle is $40, equal to the tax per room. It
is also, as we’ve seen, the size of the wedge that the tax drives between the supply price (the price received by producers) and the demand price (the price paid by consumers). Meanwhile, the width of the rectangle is 5,000 rooms, equal to the equilibrium quantity of rooms given the $40 tax. With that information, we can make the following calculations. The tax revenue collected is: Tax revenue = $40 per room × 5,000 rooms = $200,000 505 The area of the shaded rectangle is: Area = Height × Width = $40 per room × 5,000 rooms = $200,000, or Tax revenue = Area of shaded rectangle This is a general principle: The revenue collected by an excise tax is equal to the area of a rectangle with the height of the tax wedge between the supply price and the demand price and the width of the quantity sold under the tax. The Costs of Taxation What is the cost of a tax? You might be inclined to answer that it is the amount of money taxpayers pay to the government—the tax revenue collected. But suppose the government uses the tax revenue to provide services that taxpayers want. Or suppose that the government simply hands the tax revenue back to taxpayers. Would we say in those cases that the tax didn’t actually cost anything? No—because a tax, like a quota, prevents mutually beneficial transactions from occurring. Consider Figure 50.10 once more. Here, with a $40 tax on hotel rooms, guests pay $100 per room but hotel owners receive only $60 per room. Because of the wedge created by the tax, we know that some transactions didn’t occur that would have occurred without the tax. More specifically, we know from the supply and demand curves that there are some potential guests who would be willing to pay up to $90 per night and some hotel owners who would be willing to supply rooms if they received at least $70 per night. If these two sets of people were allowed to trade with each other without the tax, they would engage in mutually beneficial transactions—hotel rooms would be rented. But such deals would be illegal because the $40 tax would not be paid. In our example, 5,000 potential hotel room rentals that would have occurred in the absence of the tax, to the mutual benefit of guests and hotel owners, do not take place because of the tax. So an excise tax imposes costs over and above the tax revenue collected in the form of inefficiency, which occurs
because the tax discourages mutually beneficial transactions. You may recall from Module 9 that the cost to society of this kind of inefficiency—the value of the forgone mutually beneficial transactions—is called the deadweight loss. While all real-world taxes impose some deadweight loss, a badly designed tax imposes a larger deadweight loss than a well-designed one. To measure the deadweight loss from a tax, we turn to the concepts of producer and consumer surplus. Figure 50.11 shows the effects of an excise tax on consumer and producer surplus. In the absence of the tax, the equilibrium is at E and the equilibrium price and quantity are PE and QE, respectively. An excise tax drives a wedge equal to the amount of the tax between the price received by producers and the price paid by consumers, reducing the quantity sold. In this case, with a tax of T dollars per unit, the quantity sold falls to QT. The price paid by consumers rises to PC, the demand price of the reduced quantity, QT, and the price received by producers falls to PP, the supply price of that quantity. The difference between these prices, PC − PP, is equal to the excise tax, T. Using the concepts of producer and consumer surplus, we can show exactly how much surplus producers and consumers lose as a result of the tax. We learned previously that a fall in the price of a good generates a gain in consumer surplus that is equal to the sum of the areas of a rectangle and a triangle. Similarly, a price increase causes a loss to consumers that is represented by the sum of the areas of a rectangle and a triangle. So it’s not surprising that in the case of an excise tax, the rise in the price paid by consumers causes a loss equal to the sum of the areas of a rectangle and a triangle: the dark blue rectangle labeled A and the area of the light blue triangle labeled B in Figure 50.11. The deadweight loss (from a tax) is the decrease in total surplus resulting from the tax, minus the tax revenues generated. 506 50.11 A Tax Reduces Consumer and Producer Surplus Before the tax, the equilibrium price and quantity are PE and QE, respectively. After an excise tax of T per unit is imposed, the price to consumers rises to PC and consumer surplus falls by the sum of the dark blue rectangle, labeled A, and the light blue triangle, labeled B. The tax also causes the price to producers to fall to PP ; producer surplus falls
by the sum of the dark red rectangle, labeled C, and the light red triangle, labeled F. The government receives revenue from the tax, QT × T, which is given by the sum of the areas A and C. Areas B and F represent the losses to consumer and producer surplus that are not collected by the government as revenue; they are the deadweight loss to society of the tax. Price PC PE PP Excise tax = T Fall in consumer surplus due to tax A C B F E Fall in producer surplus due to tax S D QT QE Quantity Meanwhile, the fall in the price received by producers leads to a fall in producer surplus. This, too, is equal to the sum of the areas of a rectangle and a triangle. The loss in producer surplus is the sum of the areas of the dark red rectangle labeled C and the light red triangle labeled F in Figure 50.11. Of course, although consumers and producers are hurt by the tax, the government gains revenue. The revenue the government collects is equal to the tax per unit sold, T, multiplied by the quantity sold, QT. This revenue is equal to the area of a rectangle QT wide and T high. And we already have that rectangle in the figure: it is the sum of rectangles A and C. So the government gains part of what consumers and producers lose from an excise tax. But a portion of the loss to producers and consumers from the tax is not offset by a gain to the government—specifically, the two triangles B and F. The deadweight loss caused by the tax is equal to the combined area of these two triangles. It represents the total surplus lost to society because of the tax—that is, the amount of surplus that would have been generated by transactions that now do not take place because of the tax. Figure 50.12 on the next page is a version of Figure 50.11 that leaves out rectangles A (the surplus shifted from consumers to the government) and C (the surplus shifted from producers to the government) and shows only the deadweight loss, drawn here as a triangle shaded yellow. The base of that triangle is equal to the tax wedge, T; the height of the triangle is equal to the reduction in the quantity transacted due to the tax, QE − QT. Clearly, the larger the tax wedge and the larger the reduction in the quantity transacted, the greater the inefficiency from the tax. But also note an important, contrasting point: if the excise
tax somehow didn’t reduce the quantity bought and sold in this market—if QT remained equal to QE after the tax was levied—the yellow triangle would disappear and the deadweight loss from the tax would be zero. So if a tax does not discourage transactions, it causes no deadweight loss. In this case, the tax simply shifts surplus straight from consumers and producers to the government. Using a triangle to measure deadweight loss is a technique used in many economic applications. For example, triangles are used to measure the deadweight loss produced by types of taxes other than excise taxes. They are also used to measure the deadweight loss produced by monopoly, another kind of market distortion. And deadweight-loss triangles are often used to evaluate the benefits and costs of public policies besides taxation— such as whether to impose stricter safety standards on a product 507 f i g u r e 50.12 The Deadweight Loss of a Tax A tax leads to a deadweight loss because it creates inefficiency: some mutually beneficial transactions never take place because of the tax, namely the transactions QE − QT. The yellow area here represents the value of the deadweight loss: it is the total surplus that would have been gained from the QE − QT transactions. If the tax had not discouraged transactions—had the number of transactions remained at QE —no deadweight loss would have been incurred. Price PC PE PP Excise tax = T Deadweight loss E S D QT QE Quantity In considering the total amount of inefficiency caused by a tax, we must also take into account something not shown in Figure 50.12: the resources actually used by the government to collect the tax, and by taxpayers to pay it, over and above the amount of the tax. These lost resources are called the administrative costs of the tax. The most familiar administrative cost of the U.S. tax system is the time individuals spend filling out their income tax forms or the money they spend on accountants to prepare their tax forms for them. (The latter is considered an inefficiency from the point of view of society because accountants could instead be performing other, non-tax-related services.) Included in the administrative costs that taxpayers incur are resources used to evade the tax, both legally and illegally. The costs of operating the Internal Revenue Service, the arm of the federal government tasked with collecting the federal income tax, are actually quite small in comparison to the administrative costs paid by taxpayers. The total inefficiency caused by a tax
is the sum of its deadweight loss and its administrative costs. Some extreme forms of taxation, such as the poll tax instituted by the government of British Prime Minister Margaret Thatcher in 1989, are notably unfair but very efficient. A poll tax is an example of a lump-sum tax, a tax that is the same for everyone regardless of any actions people take. The poll tax in Britain was widely perceived as much less fair than the tax structure it replaced, in which local taxes were proportional to property values. Under the old system, the highest local taxes were paid by the people with the most expensive houses. Because these people tended to be wealthy, they were also best able to bear the burden. But the old system definitely distorted incentives to engage in mutually beneficial transactions and created deadweight loss. People who were considering home improvements knew that such improvements, by making their property more valuable, would increase their tax bills. The result, surely, was that some home improvements that would have taken place without the tax did not take place because of it. In contrast, a lump-sum tax does not distort incentives. Because under a lump-sum tax people have to pay the same amount of tax regardless of their actions, it does not cause them to substitute untaxed goods for a good whose price has been artificially inflated by a tax, as occurs with an excise tax. So lump-sum taxes, although unfair, are better than other taxes at promoting economic efficiency. The administrative costs of a tax are the resources used by government to collect the tax, and by taxpayers to pay (or to evade) it, over and above the amount collected. A lump-sum tax is a tax of a fixed amount paid by all taxpayers. 508 50 AP R e v i e w Solutions appear at the back of the book. Check Your Understanding 1. Using the tables in Check Your Understanding Module 49, find the equilibrium price and quantity in the market for cheese-stuffed jalapeno peppers. What is the total surplus in the equilibrium in this market, and who receives it? 2. Consider the market for butter, shown in the accompanying figure. The government imposes an excise tax of $0.30 per pound of butter. What is the price paid by consumers post-tax? What is the price received by producers post-tax? What is the quantity of butter sold? How is the incidence of the tax allocated between consumers and producers? Show this on the figure. Price of butter (per pound) $1.40 1.30 1.
20 1.10 1.00 0.90 0.80 0.70 0.60 0 6 S E D 9 8 7 11 Quantity of butter (millions of pounds) 13 12 10 14 3. The accompanying table shows five consumers’ willingness to pay for one can of diet soda each as well as five producers’ costs of selling one can of diet soda each. Each consumer buys at most one can of soda; each producer sells at most one can of soda. The government asks your advice about the effects of an excise tax of $0.40 per can of diet soda. Assume that there are no administrative costs from the tax. Consumer Willingness to Pay $0.70 0.60 0.50 0.40 0.30 Producer Cost $0.10 0.20 0.30 0.40 0.50 Ana Bernice Chizuko Dagmar Ella a. Without the excise tax, what is the equilibrium price and Zhang Yves Xavier Walter Vern the equilibrium quantity of soda? b. The excise tax raises the price paid by consumers post-tax to $0.60 and lowers the price received by producers post-tax to $0.20. With the excise tax, what is the quantity of soda sold? c. Without the excise tax, how much individual consumer surplus does each of the consumers gain? How much individual consumer surplus does each consumer gain with the tax? How much total consumer surplus is lost as a result of the tax? d. Without the excise tax, how much individual producer surplus does each of the producers gain? How much individual producer surplus does each producer gain with the tax? How much total producer surplus is lost as a result of the tax? e. How much government revenue does the excise tax create? f. What is the deadweight loss from the imposition of this excise tax? Tackle the Test: Multiple-Choice Questions 1. At market equilibrium in a competitive market, which of the following is necessarily true? I. Consumer surplus is maximized. II. Producer surplus is maximized. III. Total surplus is maximized. a. I only b. II only c. III only d. I, II, and III e. None of the above a. I only b. II only c. III only d. I and II only I, II, and III e. 2. When a competitive market is in equilibrium, total surplus can be increased by I. reallocating consumption among consumers. II. reallocating sales among sellers
. III. changing the quantity traded. 3. Which of the following is true regarding equity and efficiency in competitive markets? a. Competitive markets ensure equity and efficiency. b. There is often a trade-off between equity and efficiency. c. Competitive markets lead to neither equity nor efficiency. d. There is generally agreement about the level of equity and efficiency in a market. e. None of the above 509 4. An excise tax imposed on sellers in a market will result in which 5. An excise tax will be paid mainly by producers when of the following? I. an upward shift of the supply curve II. a downward shift of the demand curve III. deadweight loss a. I only b. II only c. III only d. I and III only I, II, and III e. Tackle the Test: Free-Response Questions 1. Refer to the graph provided. Assume the government has imposed an excise tax of $60 on producers in this market. Price $120 90 60 30 0 S D 1,000 2,000 3,000 Quantity a. What quantity will be sold in the market? b. What price will consumers pay in the market? c. By how much will consumer surplus change as a result of the tax? d. By how much will producer surplus change as a result of the tax? e. How much revenue will the government collect from this excise tax? f. Calculate the deadweight loss created by the tax. it is imposed on producers. it is imposed on consumers. a. b. c. the price elasticity of supply is low and the price elasticity of demand is high. d. the price elasticity of supply is high and the price elasticity of demand is low. e. the price elasticity of supply is perfectly elastic. Answer (8 points) 1 point: 1,000 1 point: $90 1 point: Consumer surplus will decrease by $45,000, from $60,000 before the tax to $15,000 after the tax. 1 point: Producer surplus will decrease by $45,000, from $60,000 before the tax to $15,000 after the tax. 1 point: $60 × 1,000 = $60,000 1 point: $30,000 2. Draw a correctly labeled graph of a competitive market in equilibrium. Use your graph to illustrate the effect of an excise tax imposed on consumers. Indicate each of the following on your graph: a. the equilibrium price and quantity without the tax
, labeled PE and Q E b. the quantity sold in the market post-tax, labeled QT c. the price paid by consumers post-tax, labeled PC d. the price received by producers post-tax, labeled PP e. the tax revenue generated by the tax, labeled “Tax revenue” f. The deadweight loss resulting from the tax, labeled “DWL.” 510 Module 51 Utility Maximization We have used the demand curve to study consumer responsiveness to changes in prices and discovered its usefulness in predicting how consumers will gain from the availability of goods and services in a market. But where does the demand curve come from? In other words, what lies behind the demand curve? The demand curve represents the tastes, preferences, and resulting choices of individual consumers. Its shape reflects the additional satisfaction, or utility, people receive from consuming more and more of a good or service. Utility: It’s All About Getting Satisfaction When analyzing consumer behavior, we’re looking into how people pursue their needs and wants and the subjective feelings that motivate purchases. Yet there is no simple way to measure subjective feelings. How much satisfaction do I get from my third cookie? Is it less or more than the satisfaction you receive from your third cookie? Does it even make sense to ask that question? Luckily, we don’t need to make comparisons between your feelings and mine. The analysis of consumer behavior that follows requires only the assumption that individuals try to maximize some personal measure of the satisfaction gained from consumption. That measure of satisfaction is known as utility, a concept we use to understand behavior but don’t expect to measure in practice. Utility and Consumption We can think of consumers as using consumption to “produce” utility, much in the same way that producers use inputs to produce output. As consumers, we do not make explicit calculations of the utility generated by consumption choices, but we must make choices, and we usually base them on at least a rough attempt to achieve greater satisfaction. I can have either soup or salad with my dinner. Which will I enjoy more? I can go to Disney World this year or put the money toward buying a new car. Which will make me happier? These are the types of questions that go into utility maximization. The concept of utility offers a way to study choices that are made in a more or less rational way. What you will learn in this Module: • How consumers make choices about the purchase of goods and services • Why consumers’ general
goal is to maximize utility • Why the principle of diminishing marginal utility applies to the consumption of most goods and services • How to use marginal analysis to find the optimal consumption bundle Utility is a measure of personal satisfaction 511 A util is a unit of utility. How do we measure utility? For the sake of simplicity, it is useful to suppose that we can measure utility in hypothetical units called—what else?—utils. A utility function shows the relationship between a consumer’s utility and the combination of goods and services—the consumption bundle—he or she consumes. Figure 51.1 illustrates a utility function. It shows the total utility that Cassie, who likes fried clams, gets from an all-you-can-eat clam dinner. We suppose that her consumption bundle consists of a side of coleslaw, which comes with the meal, plus a number of clams to be determined. The table that accompanies the figure shows how Cassie’s total utility depends on the number of clams; the curve in panel (a) of the figure shows that same information graphically. Cassie’s utility function slopes upward over most of the range shown, but it gets flatter as the number of clams consumed increases. And in this example it eventually turns downward. According to the information in the table in Figure 51.1, nine clams is a clam too far. Adding that additional clam actually makes Cassie worse off: it would lower her total utility. If she’s rational, of course, Cassie will realize that and not consume the ninth clam. f i g u r e 51.1 Cassie’s Total Utility and Marginal Utility (a) Cassie’s Utility Function Total utility (utils) 70 60 50 40 30 20 10 0 Marginal utility per clam (utils) 16 14 12 10 8 6 4 2 0 –2 Utility function Quantity of clams Total utility (utils) Marginal utility per clam (utils Quantity of clams (b) Cassie’s Marginal Utility Curve Marginal utility curve 1 2 3 4 5 6 7 8 9 Quantity of clams 15 28 39 48 55 60 63 64 63 15 13 11 9 7 5 3 1 –1 Panel (a) shows how Cassie’s total utility depends on her consumption of fried clams. It increases until it reaches its maximum utility level of 64 utils at 8 clams consumed and decreases after that. Marginal utility is calculated in the table. Panel (
b) shows the marginal utility curve, which slopes downward due to diminishing marginal utility. That is, each additional clam gives Cassie less utility than the previous clam. 512 The marginal utility of a good or service is the change in total utility generated by consuming one additional unit of that good or service. The marginal utility curve shows how marginal utility depends on the quantity of a good or service consumed. According to the principle of diminishing marginal utility, each successive unit of a good or service consumed adds less to total utility than does the previous unit So when Cassie chooses how many clams to consume, she will make this decision by considering the change in her total utility from consuming one more clam. This illustrates the general point: to maximize total utility, consumers must focus on marginal utility. The Principle of Diminishing Marginal Utility In addition to showing how Cassie’s total utility depends on the number of clams she consumes, the table in Figure 51.1 also shows the marginal utility generated by consuming each additional clam—that is, the change in total utility from consuming one additional clam. The marginal utility curve is constructed by plotting points at the midpoint between the numbered quantities since marginal utility is found as consumption levels change. For example, when consumption rises from 1 to 2 clams, marginal utility is 13. Therefore, we place the point corresponding to marginal utility of 13 halfway between 1 and 2 clams. The marginal utility curve slopes downward because each successive clam adds less to total utility than the previous clam. This is reflected in the table: marginal utility falls from a high of 15 utils for the first clam consumed to −1 for the ninth clam consumed. The fact that the ninth clam has negative marginal utility means that consuming it actually reduces total utility. (Restaurants that offer allyou-can-eat meals depend on the proposition that you can have too much of a good thing.) Not all marginal utility curves eventually become negative. But it is generally accepted that marginal utility curves do slope downward—that consumption of most goods and services is subject to diminishing marginal utility The basic idea behind the principle of diminishing marginal utility is that the additional satisfaction a consumer gets from one more unit of a good or service declines as the amount of that good or service consumed rises. Or, to put it slightly differently, the more of a good or service you consume, the closer you are to being satiated—reaching a point at which an additional unit of the good adds nothing to your satisfaction. For someone who almost never gets to eat a banana
, the occasional banana is a marvelous treat (as it was in Eastern Europe before the fall of communism, when bananas were very hard to find). For someone who eats them all the time, a banana is just, well, a banana. fyi Is Marginal Utility Really Diminishing? Are all goods really subject to diminishing marginal utility? Of course not; there are a number of goods for which, at least over some range, marginal utility is surely increasing. For example, there are goods that require some experience to enjoy. The first time you do it, downhill skiing involves a lot more fear than enjoyment—or so they say: two of the authors have never tried it! It only becomes a pleasurable activity if you do it enough to become reasonably competent. And even some less strenuous forms of consumption take practice; people who are not accustomed to drinking coffee say it has a bitter taste and can’t understand its appeal. (The authors, on the other hand, regard coffee as one of the basic food groups.) Another example would be goods that only deliver positive utility if you buy enough. The great Victorian economist Alfred Marshall, who more or less invented the supply and demand model, gave the example of wallpaper: buying only enough to do half a room is worse than useless. If you need two rolls of wallpaper to fin- ish a room, the marginal utility of the second roll is larger than the marginal utility of the first roll. So why does it make sense to assume dimin- ishing marginal utility? For one thing, most goods don’t suffer from these qualifications: nobody needs to learn to like ice cream. Also, although most people don’t ski and some people don’t drink coffee, those who do ski or drink coffee do enough of it that the marginal utility of one more ski run or one more cup is less than that of the last. So in the relevant range of consumption, marginal utility is still diminishing 513 The principle of diminishing marginal utility doesn’t always apply, but it does apply in the great majority of cases, enough to serve as a foundation for our analysis of consumer behavior. Budgets and Optimal Consumption The principle of diminishing marginal utility explains why most people eventually reach a limit, even at an all-you-can-eat buffet where the cost of another clam is measured only in future indigestion. Under ordinary circumstances, however, it costs some additional resources to consume more of a good, and consumers must take that cost into account
when making choices. What do we mean by cost? As always, the fundamental measure of cost is opportunity cost. Because the amount of money a consumer can spend is limited, a decision to consume more of one good is also a decision to consume less of some other good. Budget Constraints and Budget Lines Consider Sammy, whose appetite is exclusively for clams and potatoes. (There’s no accounting for tastes.) He has a weekly income of $20 and since, given his appetite, more of either good is better than less, he spends all of it on clams and potatoes. We will assume that clams cost $4 per pound and potatoes cost $2 per pound. What are his possible choices? Whatever Sammy chooses, we know that the cost of his consumption bundle cannot exceed the amount of money he has to spend. That is, (51-1) Expenditure on clams + Expenditure on potatoes ≤ Total income Consumers always have limited income, which constrains how much they can consume. So the requirement illustrated by Equation 51-1—that a consumer must choose a consumption bundle that costs no more than his or her income—is known as the consumer’s budget constraint. It’s a simple way of saying that a consumer can’t spend more than the total amount of income available to him or her. In other words, consumption bundles are affordable when they obey the budget constraint. We call the set of all of Sammy’s affordable consumption bundles his consumption possibilities. In general, whether or not a particular consumption bundle is included in a consumer’s consumption possibilities depends on the consumer’s income and the prices of goods and services. Figure 51.2 shows Sammy’s consumption possibilities. The quantity of clams in his consumption bundle is measured on the horizontal axis and the quantity of potatoes on the vertical axis. The downward-sloping line connecting points A through F shows which consumption bundles are affordable and which are not. Every bundle on or inside this line (the shaded area) is affordable; every bundle outside this line is unaffordable. As an example of one of the points, let’s look at point C, representing 2 pounds of clams and 6 pounds of potatoes, and check whether it satisfies Sammy’s budget constraint. The cost of bundle C is 6 pounds of potatoes × $2 per pound + 2 pounds of clams × $4 per pound = $12 + $8 = $20. So bundle C
does indeed satisfy Sammy’s budget constraint: it costs no more than his weekly income of $20. In fact, bundle C costs exactly as much as Sammy’s income. By doing the arithmetic, you can check that all the other points lying on the downward-sloping line are also bundles at which Sammy spends all of his income. The downward-sloping line has a special name, the budget line. It shows all the consumption bundles available to Sammy when he spends all of his income. It’s downward-sloping because when Sammy is spending all of his income, say by consuming at point A on the budget line, then in order to consume more clams he must consume fewer potatoes—that is, he must move to a point like B. In other words, when A budget constraint limits the cost of a consumer’s consumption bundle to no more than the consumer’s income. A consumer’s consumption possibilities is the set of all consumption bundles that are affordable, given the consumer’s income and prevailing prices. A consumer’s budget line shows the consumption bundles available to a consumer who spends all of his or her income. 514 51.2 The Budget Line Quantity of potatoes (pounds) 10 A 8 6 4 2 0 Unaffordable consumption bundles B C Affordable consumption bundles D E Affordable consumption bundles that cost all of Sammy’s income Consumption bundle Quantity of clams (pounds) Quantity of potatoes (pounds 10 Sammy’s budget line, BL Quantity of clams (pounds) The budget line represents all the possible combinations of quantities of potatoes and clams that Sammy can purchase if he spends all of his income. Also, it is the boundary between the set of affordable consumption bundles (the consumption possibilities) and the unaffordable ones. Given that clams cost $4 per pound and potatoes cost $2 per pound, if Sammy spends all of his income on clams (bundle F ), he can purchase 5 pounds of clams; if he spends all of his income on potatoes (bundle A), he can purchase 10 pounds of potatoes Sammy is on his budget line, the opportunity cost of consuming more clams is consuming fewer potatoes, and vice versa. As Figure 51.2 indicates, any consumption bundle that lies above the budget line is unaffordable. Do we need to consider the other bundles in Sammy’s consumption possibilities, the ones that lie within the shaded region in Figure 51.2 bounded by the
budget line? The answer is, for all practical situations, no: as long as Sammy doesn’t get satiated— that is, as long as his marginal utility from consuming either good is always positive— and he doesn’t get any utility from saving income rather than spending it, then he will always choose to consume a bundle that lies on his budget line. Given that $20 per week budget, next we can consider the culinary dilemma of what point on his budget line Sammy will choose. The Optimal Consumption Bundle Because Sammy’s budget constrains him to a consumption bundle somewhere along the budget line, a choice to consume a given quantity of clams also determines his potato consumption, and vice versa. We want to find the consumption bundle—represented by a point on the budget line—that maximizes Sammy’s total utility. This bundle is Sammy’s optimal consumption bundle. Table 51.1 on the next page shows how much utility Sammy gets from different levels of consumption of clams and potatoes, respectively. According to the table, Sammy has a healthy appetite; the more of either good he consumes, the higher his utility. But because he has a limited budget, he must make a trade-off: the more pounds of clams he consumes, the fewer pounds of potatoes, and vice versa. That is, he must choose a point on his budget line. A consumer’s optimal consumption bundle is the consumption bundle that maximizes the consumer’s total utility given his or her budget constraint 515 t a b l e 51.1 Sammy’s Utility from Clam and Potato Consumption Utility from clam consumption Utility from potato consumption Quantity of clams (pounds) Utility from clams (utils) Quantity of potatoes (pounds) Utility from potatoes (utils) 0 1 2 3 4 5 0 15 25 31 34 36 10 0 11.5 21.4 29.8 36.8 42.5 47.0 50.5 53.2 55.2 56.7 Table 51.2 shows how his total utility varies for the different consumption bundles along his budget line. Each of six possible consumption bundles, A through F from Figure 51.2, is given in the first column. The second column shows the level of clam consumption corresponding to each choice. The third column shows the utility Sammy gets from consuming those clams. The fourth column shows the quantity of potatoes Sammy can afford given the level of clam consumption; this quantity goes down as his clam consumption goes
up because he is sliding down the budget line. The fifth column shows the utility he gets from consuming those potatoes. And the final column shows his total utility. In this example, Sammy’s total utility is the sum of the utility he gets from clams and the utility he gets from potatoes. Figure 51.3 gives a visual representation of the data shown in Table 51.2. Panel (a) shows Sammy’s budget line, to remind us that when he decides to consume more clams he is also deciding to consume fewer potatoes. Panel (b) then shows how his total utility depends on that choice. The horizontal axis in panel (b) has two sets of labels: it shows both the quantity of clams, increasing from left to right, and the quantity of t a b l e 51.2 Sammy’s Budget and Total Utility Consumption bundle Quantity of clams (pounds) Utility from clams (utils) Quantity of potatoes (pounds) Utility from potatoes (utils) Total utility (utils 15 25 31 34 36 10 8 6 4 2 0 56.7 53.2 47.0 36.8 21.4 0 56.7 68.2 72.0 67.8 55.4 36.0 516 51.3 Optimal Consumption Bundle Panel (a) shows Sammy’s budget line and his six possible consumption bundles. Panel (b) shows how his total utility is affected by his consumption bundle, which must lie on his budget line. The quantity of clams is measured from left to right on the horizontal axis, and the quantity of potatoes is measured from right to left. His total utility is maximized at bundle C, where he consumes 2 pounds of clams and 6 pounds of potatoes. This is Sammy’s optimal consumption bundle. Quantity of potatoes (pounds) 10 8 6 4 2 0 (a) Sammy’s Budget Line A B The optimal consumption bundle... C D E 1 2 F 5 4 Quantity of clams (pounds) 3 BL (b) Sammy's Utility Function B C D... maximizes total utility given the budget constraint. 1 8 2 3 Quantity of clams (pounds) 6 4 Quantity of potatoes (pounds) E 4 2 Utility function F 5 0 Total utility (utils) 80 A 70 60 50 40 30 20 10 0 10 potatoes, increasing from right to left. The reason we can use the same axis to represent consumption of both goods is, of course,
that he is constrained by the budget line: the more pounds of clams Sammy consumes, the fewer pounds of potatoes he can afford, and vice versa. Clearly, the consumption bundle that makes the best of the trade-off between clam consumption and potato consumption, the optimal consumption bundle, is the one that maximizes Sammy’s total utility. That is, Sammy’s optimal consumption bundle puts him at the top of the total utility curve. As always, we can find the top of the curve by direct observation. We can see from Figure 51.3 that Sammy’s total utility is maximized at point C—that his optimal consumption bundle contains 2 pounds of clams and 6 pounds of potatoes. But we know that we usually gain more insight into “how much” problems when we use marginal analysis. So in the next section we turn to representing and solving the optimal consumption choice problem with marginal analysis 517 The marginal utility per dollar spent on a good or service is the additional utility from spending one more dollar on that good or service. Spending the Marginal Dollar As we’ve just seen, we can find Sammy’s optimal consumption choice by finding the total utility he receives from each consumption bundle on his budget line and then choosing the bundle at which total utility is maximized. But we can use marginal analysis instead, turning Sammy’s problem of finding his optimal consumption choice into a “how much” problem. How do we do this? By thinking about choosing an optimal consumption bundle as a problem of how much to spend on each good. That is, to find the optimal consumption bundle with marginal analysis we ask the question of whether Sammy can make himself better off by spending a little bit more of his income on clams and less on potatoes, or by doing the opposite—spending a little bit more on potatoes and less on clams. In other words, the marginal decision is a question of how to spend the marginal dollar—how to allocate an additional dollar between clams and potatoes in a way that maximizes utility. Our first step in applying marginal analysis is to ask if Sammy is made better off by spending an additional dollar on either good; and if so, by how much is he better off. To answer this question we must calculate the marginal utility per dollar spent on either clams or potatoes—how much additional utility Sammy gets from spending an additional dollar on either good. Marginal Utility per Dollar We’ve already introduced the concept of marginal utility,
the additional utility a consumer gets from consuming one more unit of a good or service; now let’s see how this concept can be used to derive the related measure of marginal utility per dollar. Table 51.3 shows how to calculate the marginal utility per dollar spent on clams and potatoes, respectively. t a b l e 51.3 Sammy’s Marginal Utility per Dollar (a) Clams (price of clams = $4 per pound) (b) Potatoes (price of potatoes = $2 per pound) Quantity of clams (pounds) Utility from clams (utils) Marginal utility per pound of clams (utils) Marginal utility per dollar (utils) Quantity of potatoes (pounds) Utility from potatoes (utils) 0 1 2 3 4 5 0 15 25 31 34 36 15 10 6 3 2 3.75 2.50 1.50 0.75 0.50 10 0 11.5 21.4 29.8 36.8 42.5 47.0 50.5 53.2 55.2 56.7 Marginal utility per pound of potatoes (utils) 11.5 9.9 8.4 7.0 5.7 4.5 3.5 2.7 2.0 1.5 Marginal utility per dollar (utils) 5.75 4.95 4.20 3.50 2.85 2.25 1.75 1.35 1.00 0.75 518 In panel (a) of the table, the first column shows different possible amounts of clam consumption. The second column shows the utility Sammy derives from each amount of clam consumption; the third column then shows the marginal utility, the increase in utility Sammy gets from consuming an additional pound of clams. Panel (b) provides the same information for potatoes. The next step is to derive marginal utility per dollar for each good. To do this, we just divide the marginal utility of the good by its price in dollars. To see why we divide by the price, compare the third and fourth columns of panel (a). Consider what happens if Sammy increases his clam consumption from 2 pounds to 3 pounds. This raises his total utility by 6 utils. But he must spend $4 for that additional pound, so the increase in his utility per additional dollar spent on clams is 6 utils/$4 = 1.5 utils per dollar. Similarly, if he increases his clam consumption from 3 pounds to 4 pounds, his marginal utility is 3 utils
but his marginal utility per dollar is 3 utils/$4 = 0.75 utils per dollar. Notice that because of diminishing marginal utility, Sammy’s marginal utility per pound of clams falls as the quantity of clams he consumes rises. As a result, his marginal utility per dollar spent on clams also falls as the quantity of clams he consumes rises. So the last column of panel (a) shows how Sammy’s marginal utility per dollar spent on clams depends on the quantity of clams he consumes. Similarly, the last column of panel (b) shows how his marginal utility per dollar spent on potatoes depends on the quantity of potatoes he consumes. Again, marginal utility per dollar spent on each good declines as the quantity of that good consumed rises because of diminishing marginal utility. We will use the symbols MUC and MUP to represent the marginal utility per pound of clams and potatoes, respectively. And we will use the symbols PC and PP to represent the price of clams (per pound) and the price of potatoes (per pound). Then the marginal utility per dollar spent on clams is MUC/PC and the marginal utility per dollar spent on potatoes is MUP/PP. In general, the additional utility generated from an additional dollar spent on a good is equal to: (51-2) Marginal utility per dollar spent on a good = Marginal utility of one unit of the good/Price of one unit of the good = MUgood/Pgood Next we’ll see how this concept helps us determine a consumer’s optimal consumption bundle using marginal analysis. Optimal Consumption Let’s consider Figure 51.4 on the next page. As in Figure 51.3, we can measure both the quantity of clams and the quantity of potatoes on the horizontal axis due to the budget constraint. Along the horizontal axis of Figure 51.4—also as in Figure 51.3—the quantity of clams increases as you move from left to right, and the quantity of potatoes increases as you move from right to left. The curve labeled MUC/PC in Figure 51.4 shows Sammy’s marginal utility per dollar spent on clams as derived in Table 51.3. Likewise, the curve labeled MUP/PP shows his marginal utility per dollar spent on potatoes. Notice that the two curves, MUC/PC and MUP/PP, cross at the optimal consumption bundle, point C, consisting of 2 pounds of clams and 6 pounds of
potatoes. Moreover, Figure 51.4 illustrates an important feature of Sammy’s optimal consumption bundle: when Sammy consumes 2 pounds of clams and 6 pounds of potatoes, his marginal utility per dollar spent is the same, 2, for both goods. That is, at the optimal consumption bundle, MUC/PC = MUP/PP = 2. This isn’t an accident. Consider another one of Sammy’s possible consumption bundles—say, B in Figure 51.3, at which he consumes 1 pound of clams and 8 pounds of potatoes. The marginal utility per dollar spent on each good is shown by points BC and BP in Figure 51.4. At that consumption bundle, Sammy’s marginal utility per 519 f i g u r e 51.4 Marginal Utility per Dollar Sammy’s optimal consumption bundle is at point C, where his marginal utility per dollar spent on clams, MUC /PC, is equal to his marginal utility per dollar spent on potatoes, MUP /PP. This illustrates the optimal consumption rule: at the optimal consumption bundle, the marginal utility per dollar spent on each good and service is the same. At any other consumption bundle on Sammy’s budget line, such as bundle B in Figure 51.3, represented here by points BC and BP, consumption is not optimal: Sammy can increase his utility at no additional cost by reallocating his spending. Marginal utility per dollar (utils) 6 5 4 3 2 1 MUP/PP At the optimal consumption bundle, the marginal utility per dollar spent on clams is equal to the marginal utility per dollar spent on potatoes. BC BP C 2 3 4 Quantity of clams (pounds) 2 Quantity of potatoes (pounds) 6 4 MUC/PC 5 0 0 10 1 8 dollar spent on clams would be approximately 3, but his marginal utility per dollar spent on potatoes would be only approximately 1. This shows that he has made a mistake: he is consuming too many potatoes and not enough clams. How do we know this? If Sammy’s marginal utility per dollar spent on clams is higher than his marginal utility per dollar spent on potatoes, he has a simple way to make himself better off while staying within his budget: spend $1 less on potatoes and $1 more on clams. By spending an additional dollar on clams, he adds about 3 utils to his total utility; meanwhile, by spending $1 less on potatoes, he subtracts only
about 1 util from his total utility. Because his marginal utility per dollar spent is higher for clams than for potatoes, reallocating his spending toward clams and away from potatoes would increase his total utility. On the other hand, if his marginal utility per dollar spent on potatoes is higher, he can increase his utility by spending less on clams and more on potatoes. So if Sammy has in fact chosen his optimal consumption bundle, his marginal utility per dollar spent on clams and potatoes must be equal. This is a general principle, known as the optimal consumption rule: when a consumer maximizes utility in the face of a budget constraint, the marginal utility per dollar spent on each good or service in the consumption bundle is the same. That is, for any two goods C and P, the optimal consumption rule says that at the optimal consumption bundle (51-3) MUC PC = MUP PP The optimal consumption rule says that in order to maximize utility, a consumer must equate the marginal utility per dollar spent on each good and service in the consumption bundle. It’s easiest to understand this rule using examples in which the consumption bundle contains only two goods, but it applies no matter how many goods or services a consumer buys: the marginal utilities per dollar spent for each and every good or service in the optimal consumption bundle are equal. The main reason for studying consumer behavior is to look behind the market demand curve. In Module 46 we explained how the substitution effect leads consumers to buy less of a good when its price increases. We used the substitution effect to explain, 520 in general, why the individual demand curve obeys the law of demand. Marginal analysis adds clarity to the utility-maximizing behavior of individuals and explains more precisely how an increase in price leads to less marginal utility per dollar and therefore a decrease in the quantity demanded. M o d u l e 51 AP R e v i e w Solutions appear at the back of the book. Check Your Understanding 1. Explain why a rational consumer who has diminishing marginal utility for a good would not consume an additional unit when it generates negative marginal utility, even when that unit is free. 2. In the following two examples, find all the consumption bundles that lie on the consumer’s budget line. Illustrate these consumption possibilities in a diagram, and draw the budget line through them. a. The consumption bundle consists of movie tickets and buckets of popcorn. The price of each ticket is $10.00, the price of each bucket of popcorn is $5.00
, and the consumer’s income is $20.00. In your diagram, put movie tickets on the vertical axis and buckets of popcorn on the horizontal axis. b. The consumption bundle consists of underwear and socks. The price of each pair of underwear is $4.00, the price of each pair of socks is $2.00, and the consumer’s income is $12.00. In your diagram, put pairs of socks on the vertical axis and pairs of underwear on the horizontal axis. 3. In Table 51.3 you can see that the marginal utility per dollar spent on clams and the marginal utility per dollar spent on potatoes are equal when Sammy increases his consumption of clams from 3 pounds to 4 pounds and his consumption of potatoes from 9 pounds to 10 pounds. Explain why this is not Sammy’s optimal consumption bundle. Illustrate your answer using a budget line like the one in Figure 51.3. Tackle the Test: Multiple-Choice Questions 1. Generally, each successive unit of a good consumed will cause 4. A consumer is spending all of her income and receiving 100 utils from the last unit of good A and 80 utils from the last unit of good B. If the price of good A is $2 and the price of good B is $1, to maximize total utility the consumer should buy a. more of good A. b. more of good B. c. less of good B. d. more of both goods. less of both goods. e. 5. The optimal consumption bundle is always represented by a point a. inside the consumer’s budget line. b. outside the consumer’s budget line. c. at the highest point on the consumer’s budget line. d. on the consumer’s budget line. e. at the horizontal intercept of the consumer’s budget line. increase at an increasing rate. increase at a decreasing rate. increase at a constant rate. marginal utility to a. b. c. d. decrease. e. either increase or decrease. 2. Assume there are two goods, good X and good Y. Good X costs $5 and good Y costs $10. If your income is $200, which of the following combinations of good X and good Y is on your budget line? a. 0 units of good X and 18 units of good Y b. 0 units of good X and 20 units of good Y c. 20 units of good X and 0 units of good
Y d. 10 units of good X and 12 units of good Y e. all of the above 3. The optimal consumption rule states that total utility is maximized when all income is spent and a. MU/P is equal for all goods. b. MU is equal for all goods. c. P/MU is equal for all goods. d. MU is as high as possible for all goods. e. The amount spent on each good is equal 521 Tackle the Test: Free-Response Questions 1. Refer to the table provided. Assume you have $20 to spend. Snacks (price = $4) Drinks (price = $2) Quantity 1 2 3 4 5 Total Utility (utils) 15 25 31 34 36 Quantity 1 2 3 4 5 6 7 8 Total Utility (utils) 12 21 29 36 42 47 50 52 a. Draw a correctly labeled budget line. b. Determine the marginal utility and the marginal utility per dollar spent on the fourth drink. c. What is the optimal consumption rule? d. How many drinks and snacks should you purchase to maximize your total utility? Answer (6 points) Quantity of snacks 5 0 10 Quantity of drinks 1 point: Graph with “Quantity of snacks” and “Quantity of drinks” as axis labels. 1 point: Straight budget line with intercepts at 5 snacks and 0 drinks and at 0 snacks and 10 drinks. 1 point: MU = 7 utils 1 point: MU/P = 3.5 utils per dollar 1 point: Total utility is maximized when the marginal utility per dollar is equal for all goods. 1 point: 6 drinks, 2 snacks 2. Assume you have an income of $100. The price of good X is $5, and the price of good Y is $20. a. Draw a correctly labeled budget line with “Quantity of good X” on the horizontal axis and “Quantity of good Y” on the vertical axis. Be sure to correctly label the horizontal and vertical intercepts. b. With your current consumption bundle, you receive 100 utils from consuming your last unit of good X and 400 utils from consuming your last unit of good Y. Are you maximizing your total utility? Explain. c. What will happen to the total and marginal utility you receive from consuming good X if you decide to consume another unit of good X? Explain. S e c t i o n 9 Review Summary 1. Changes in the price of a good affect the quantity consumed
as a result of the substitution effect, and in some cases the income effect. Most goods absorb only a small share of a consumer’s spending; for these goods, only the substitution effect—buying less of the good that has become relatively more expensive and more of the good that has become relatively cheaper—is significant. The income effect becomes substantial when there is a change in the price of a good that absorbs a large share of a consumer’s spending, thereby changing the purchasing power of the consumer’s income. 2. Many economic questions depend on the size of consumer or producer responses to changes in prices or other variables. Elasticity is a general measure of responsiveness that can be used to answer such questions. 3. The price elasticity of demand—the percent change in the quantity demanded divided by the percent change in the price (dropping the minus sign)—is a measure of the responsiveness of the quantity demanded to changes in the price. In practical calculations, it is usually best to use the midpoint method, which calculates percent changes in prices and quantities based on the average of the initial and final values. 4. Demand can fall anywhere in the range from perfectly inelastic, meaning the quantity demanded is unaffected by the price, to perfectly elastic, meaning there is a unique price at which consumers will buy as much 522 or as little as they are offered. When demand is perfectly inelastic, the demand curve is a vertical line; when it is perfectly elastic, the demand curve is a horizontal line. 5. The price elasticity of demand is classified according to whether it is more or less than 1. If it is greater than 1, demand is elastic; if it is less than 1, demand is inelastic; if it is exactly 1, demand is unit-elastic. This classification determines how total revenue, the total value of sales, changes when the price changes. If demand is elastic, total revenue falls when the price increases and rises when the price decreases. If demand is inelastic, total revenue rises when the price increases and falls when the price decreases. 6. The price elasticity of demand depends on whether there are close substitutes for the good in question, whether the good is a necessity or a luxury, the share of income spent on the good, and the length of time that has elapsed since the price change. 7. The cross-price elasticity of demand measures the effect of a change in one good’s price on the quantity of another good demanded. The
cross-price elasticity of demand can be positive, in which case the goods are substitutes, or negative, in which case they are complements. 8. The income elasticity of demand is the percent change in the quantity of a good demanded when a consumer’s income changes divided by the percent change in income. The income elasticity of demand indicates how intensely the demand for a good responds to changes in income. It can be negative; in that case the good is an inferior good. Goods with positive income elasticities of demand are normal goods. If the income elasticity is greater than 1, a good is income-elastic; if it is positive and less than 1, the good is income-inelastic. 9. The price elasticity of supply is the percent change in the quantity of a good supplied divided by the percent change in the price. If the quantity supplied does not change at all, we have an instance of perfectly inelastic supply; the supply curve is a vertical line. If the quantity supplied is zero below some price but infinite above that price, we have an instance of perfectly elastic supply; the supply curve is a horizontal line. 10. The price elasticity of supply depends on the availability of resources to expand production and on time. It is higher when inputs are available at relatively low cost and when more time has elapsed since the price change. 11. The willingness to pay of each individual consumer determines the shape of the demand curve. When price is less than or equal to the willingness to pay, the potential consumer purchases the good. The difference between willingness to pay and price is the net gain to the consumer, the individual consumer surplus. 12. Total consumer surplus in a market, which is the sum of all individual consumer surpluses in a market, is equal to the area below the market demand curve but Section 9 Summary above the price. A rise in the price of a good reduces consumer surplus; a fall in the price increases consumer surplus. The term consumer surplus is often used to refer to both individual and total consumer surplus. 13. The cost of each potential producer of a good, the lowest price at which he or she is willing to supply a unit of that good, determines the supply curve. If the price of a good is above a producer’s cost, a sale generates a net gain to the producer, known as the individual producer surplus. 14. Total producer surplus in a market, the sum of the individual producer surpluses in a market, is equal to the
area above the market supply curve but below the price. A rise in the price of a good increases producer surplus; a fall in the price reduces producer surplus. The term producer surplus is often used to refer to both individual and total producer surplus. 15. Total surplus, the total gain to society from the pro- duction and consumption of a good, is the sum of consumer and producer surplus. 16. Usually, markets are efficient and achieve the maximum total surplus. Any possible reallocation of consumption or sales, or change in the quantity bought and sold, reduces total surplus. However, society also cares about equity. So government intervention in a market that reduces efficiency but increases equity can be a valid choice by society. 17. A tax that rises more than in proportion to income is a progressive tax. A tax that rises less than in proportion to income is a regressive tax. A taxes that rises in proportion to income is, you guessed it, a proportional tax. 18. An excise tax—a tax on the purchase or sale of a good— raises the price paid by consumers and reduces the price received by producers, driving a wedge between the two. The incidence of the tax—how the burden of the tax is divided between consumers and producers—does not depend on who officially pays the tax. 19. The incidence of an excise tax depends on the price elasticities of supply and demand. If the price elasticity of demand is higher than the price elasticity of supply, the tax falls mainly on producers; if the price elasticity of supply is higher than the price elasticity of demand, the tax falls mainly on consumers. 20. The tax revenue generated by a tax depends on the tax rate and on the number of units sold with the tax. Excise taxes cause inefficiency in the form of deadweight loss because they discourage some mutually beneficial transactions. Taxes also impose administrative costs: resources used to collect the tax, to pay it (over and above the amount of the tax), and to evade it. 21. An excise tax generates revenue for the government but lowers total surplus. The loss in total surplus exceeds the tax revenue, resulting in a deadweight loss to society. This deadweight loss is represented by a triangle, the area of which equals the value of the transactions S u m m a r y 523 discouraged by the tax. The greater the elasticity of demand or supply, or both, the larger the deadweight loss from a tax. If either demand or supply is perfectly inelastic, there
is no deadweight loss from a tax. 22. A lump-sum tax is a tax of a fixed amount paid by all taxpayers. Because a lump-sum tax does not depend on the behavior of taxpayers, it does not discourage mutually beneficial transactions and therefore causes no deadweight loss. 23. Consumers maximize a measure of satisfaction called utility. We measure utility in hypothetical units called utils. 24. A good’s or service’s marginal utility is the additional utility generated by consuming one more unit of the good or service. We usually assume that the principle of diminishing marginal utility holds: consumption of another unit of a good or service yields less addi- tional utility than the previous unit. As a result, the marginal utility curve slopes downward. 25. A budget constraint limits a consumer’s spending to no more than his or her income. It defines the consumer’s consumption possibilities, the set of all affordable consumption bundles. A consumer who spends all of his or her income will choose a consumption bundle on the budget line. An individual chooses the consumption bundle that maximizes total utility, the optimal consumption bundle. 26. We use marginal analysis to find the optimal consumption bundle by analyzing how to allocate the marginal dollar. According to the optimal consumption rule, with the optimal consumption bundle, the marginal utility per dollar spent on each good and service—the marginal utility of a good divided by its price—is the same. Key Terms Substitution effect, p. 458 Income effect, p. 459 Perfectly inelastic supply, p. 478 Perfectly elastic supply, p. 479 Price elasticity of demand, p. 460 Willingness to pay, p. 483 Tax incidence, p. 502 Deadweight loss, p. 506 Administrative costs, p. 508 Midpoint method, p. 462 Individual consumer surplus, p. 485 Lump-sum tax, p. 508 Individual producer surplus, p. 490 Marginal utility curve, p. 513 Perfectly inelastic demand, p. 466 Total consumer surplus, p. 485 Perfectly elastic demand, p. 467 Consumer surplus, p. 485 Elastic demand, p. 467 Inelastic demand, p. 467 Unit-elastic demand, p. 467 Total revenue, p. 468 Cost, p. 489 Total producer surplus, p. 490 Producer surplus, p. 490 Cross-price elasticity of demand, p. 475 Total surplus, p.
495 Income elasticity of demand, p. 476 Income-elastic demand, p. 476 Income-inelastic demand, p. 476 Price elasticity of supply, p. 477 Progressive tax, p. 499 Regressive tax, p. 499 Proportional tax, p. 499 Excise tax, p. 499 Problems Utility, p. 511 Util, p. 512 Marginal utility, p. 513 Principle of diminishing marginal utility, p. 513 Budget constraint, p. 514 Consumption possibilities, p. 514 Budget line, p. 514 Optimal consumption bundle, p. 515 Marginal utility per dollar, p. 518 Optimal consumption rule, p. 520 1. Nile.com, the online bookseller, wants to increase its total revenue. One strategy is to offer a 10% discount on every book it sells. Nile.com knows that its customers can be divided into two distinct groups according to their likely responses to the discount. The accompanying table shows how the two groups respond to the discount. Group A (sales per week) Group B (sales per week) 1.55 million 1.50 million 1.65 million 1.70 million Volume of sales before the 10% discount Volume of sales after the 10% discount a. Using the midpoint method, calculate the price elasticities of demand for group A and group B. b. Explain how the discount will affect total revenue from each group. c. Suppose Nile.com knows which group each customer be- longs to when he or she logs on and can choose whether or not to offer the 10% discount. If Nile.com wants to increase its total revenue, should discounts be offered to group A or to group B, to neither group, or to both groups? 2. Do you think the price elasticity of demand for Ford sportutility vehicles (SUVs) will increase, decrease, or remain the same when each of the following events occurs? Explain your answer. 524. Other car manufacturers, such as General Motors, decide to make and sell SUVs. b. SUVs produced in foreign countries are banned from the American market. c. Due to ad campaigns, Americans believe that SUVs are much safer than ordinary passenger cars. d. The time period over which you measure the elasticity lengthens. During that longer time, new models such as four-wheel-drive cargo vans appear. 3. The accompanying table gives part of the supply schedule for
personal computers in the United States. Price per computer Quantity of computers supplied $1,100 900 12,000 8,000 a. Using the midpoint method, calculate the price elasticity of supply when the price increases from $900 to $1,100. b. Suppose firms produce 1,000 more computers at any given price due to improved technology. As price increases from $900 to $1,100, is the price elasticity of supply now greater than, less than, or the same as it was in part a? c. Suppose a longer time period under consideration means that the quantity supplied at any given price is 20% higher than the figures given in the table. As price increases from $900 to $1,100, is the price elasticity of supply now greater than, less than, or the same as it was in part a? 4. The accompanying table lists the cross-price elasticities of demand for several goods, where the percent quantity change is measured for the first good of the pair, and the percent price change is measured for the second good. Good Air-conditioning units and kilowatts of electricity Coke and Pepsi High-fuel-consuming sport-utility vehicles (SUVs) and gasoline McDonald’s burgers and Burger King burgers Butter and margarine Cross-price elasticities of demand −0.34 +0.63 −0.28 +0.82 +1.54 a. Explain the sign of each of the cross-price elasticities. What does it imply about the relationship between the two goods in question? b. Compare the absolute values of the cross-price elasticities and explain their magnitudes. For example, why is the cross-price elasticity of McDonald’s burgers and Burger King burgers less than the cross-price elasticity of butter and margarine? c. Use the information in the table to calculate how a 5% increase in the price of Pepsi affects the quantity of Coke demanded. Section 9 Summary d. Use the information in the table to calculate how a 10% decrease in the price of gasoline affects the quantity of SUVs demanded. 5. The accompanying table shows the price and yearly quantity sold of souvenir T-shirts in the town of Crystal Lake according to the average income of the tourists visiting. Quantity of T-shirts demanded when average tourist income is $20,000 Quantity of T-shirts demanded when average tourist income is $30,000 3,000 2,400 1,600 800 5,000 4,200
3,000 1,800 Price of T-shirt $4 5 6 7 a. Using the midpoint method, calculate the price elasticity of demand when the price of a T-shirt rises from $5 to $6 and the average tourist income is $20,000. Also calculate it when the average tourist income is $30,000. b. Using the midpoint method, calculate the income elasticity of demand when the price of a T-shirt is $4 and the average tourist income increases from $20,000 to $30,000. Also calculate it when the price is $7. 6. In each of the following cases, do you think the price elasticity of supply is (i) perfectly elastic; (ii) perfectly inelastic; (iii) elastic, but not perfectly elastic; or (iv) inelastic, but not perfectly inelastic? Explain using a diagram. a. An increase in demand this summer for luxury cruises leads to a huge jump in the sales price of a cabin on the Queen Mary 2. b. The price of a kilowatt of electricity is the same during periods of high electricity demand as during periods of low electricity demand. c. Fewer people want to fly during February than during any other month. The airlines cancel about 10% of their flights as ticket prices fall about 20% during this month. d. Owners of vacation homes in Maine rent them out during the summer. Due to a soft economy, a 30% decline in the price of a vacation rental leads more than half of homeowners to occupy their vacation homes themselves during the summer. 7. Worldwide, the average coffee grower has increased the amount of acreage under cultivation over the past few years. The result has been that the average coffee plantation produces significantly more coffee than it did 10 to 20 years ago. Unfortunately for the growers, however, this has also been a period in which their total revenues have plunged. In terms of an elasticity, what must be true for these events to have occurred? Illustrate these events with a diagram, indicating the quantity effect and the price effect that gave rise to these events. 8. Determine the amount of consumer surplus generated in each of the following situations. a. Leon goes to the clothing store to buy a new T-shirt, for which he is willing to pay up to $10. He picks out one he S u m m a r y 525 likes with a price tag of exactly $10. When he is paying for it
, he learns that the T-shirt has been discounted by 50%. b. Alberto goes to the CD store hoping to find a used copy of Nirvana’s Greatest Hits for up to $10. The store has one copy selling for $10, which he purchases. c. After soccer practice, Stacey is willing to pay $2 for a bottle of mineral water. The 7-Eleven sells mineral water for $2.25 per bottle, so she declines to purchase it. 9. Determine the amount of producer surplus generated in each of the following situations. a. Gordon lists his old Lionel electric trains on eBay. He sets a minimum acceptable price, known as his reserve price, of $75. After five days of bidding, the final high bid is exactly $75. He accepts the bid. b. So-Hee advertises her car for sale in the used-car section of the student newspaper for $2,000, but she is willing to sell the car for any price higher than $1,500. The best offer she gets is $1,200, which she declines. c. Sanjay likes his job so much that he would be willing to do it for free. However, his annual salary is $80,000. 10. You are the manager of Fun World, a small amusement park. The accompanying diagram shows the demand curve of a typical customer at Fun World. Price of ride $10 5 0 10 D 20 Quantity of rides (per day) 11. The accompanying diagram illustrates a taxi driver’s individual supply curve. (Assume that each taxi ride is the same distance.) Price of taxi ride S $8 4 0 40 80 Quantity of taxi rides a. Suppose the city sets the price of taxi rides at $4 per ride, and at $4 the taxi driver is able to sell as many taxi rides as he desires. What is this taxi driver’s producer surplus? (Recall that the area of a right triangle is 1⁄2 × the height of the triangle × the base of the triangle.) b. Suppose that the city keeps the price of a taxi ride set at $4, but it decides to charge taxi drivers a “licensing fee.” What is the maximum licensing fee the city could extract from this taxi driver? c. Suppose that the city allowed the price of taxi rides to increase to $8 per ride. Again assume that, at this price, the taxi driver sells as many rides as he is willing
to offer. How much producer surplus does an individual taxi driver now get? What is the maximum licensing fee the city could charge this taxi driver? 12. Consider the original market for pizza in Collegetown, illustrated in the accompanying table. Collegetown officials decide to impose an excise tax on pizza of $4 per pizza. Price of pizza Quantity of pizza demanded Quantity of pizza supplied a. Suppose that the price of each ride is $5. At that price, how much consumer surplus does an individual consumer get? (Recall that the area of a right triangle is 1⁄2 × the height of the triangle × the base of the triangle.) b. Suppose that Fun World considers charging an admission fee, even though it maintains the price of each ride at $5. What is the maximum admission fee it could charge? (Assume that all potential customers have enough money to pay the fee.) c. Suppose that Fun World lowered the price of each ride to zero. How much consumer surplus does an individual consumer get? What is the maximum admission fee Fun World could charge? 10. What is the quantity of pizza bought and sold after the imposition of the tax? What is the price paid by consumers? What is the price received by producers? b. Calculate the consumer surplus and the producer surplus after the imposition of the tax. By how much has the 526 imposition of the tax reduced consumer surplus? By how much has it reduced producer surplus? c. How much tax revenue does Collegetown earn from this tax? d. Calculate the deadweight loss from this tax. 13. The state needs to raise money, and the governor has a choice of imposing an excise tax of the same amount on one of two previously untaxed goods: either restaurant meals or gasoline. Both the demand for and the supply of restaurant meals are more elastic than the demand for and the supply of gasoline. If the governor wants to minimize the deadweight loss caused by the tax, which good should be taxed? For each good, draw a diagram that illustrates the deadweight loss from taxation. 14. For each of the following situations, decide whether Al has in- creasing, constant, or diminishing marginal utility. a. The more economics classes Al takes, the more he enjoys the subject. And the more classes he takes, the easier each one gets, making him enjoy each additional class even more than the one before. b. Al likes loud music. In fact, according to him, “the louder, the
better.” Each time he turns the volume up a notch, he adds 5 utils to his total utility. c. Al enjoys watching reruns of the old sitcom Friends. He claims that these episodes are always funny, but he does admit that the more times he sees an episode, the less funny it gets. d. Al loves toasted marshmallows. The more he eats, however, the fuller he gets and the less he enjoys each additional marshmallow. And there is a point at which he becomes satiated: beyond that point, more marshmallows actually make him feel worse rather than better. 15. Use the concept of marginal utility to explain the following: Newspaper vending machines are designed so that once you have paid for one paper, you could take more than one paper at a time. But soda vending machines, once you have paid for one soda, dispense only one soda at a time. 16. Brenda likes to have bagels and coffee for breakfast. The accompanying table shows Brenda’s total utility from various consumption bundles of bagels and coffee. Consumption bundle Quantity of bagels Quantity of coffee (cups) Total utility (utils 28 40 48 54 28 56 54 62 40 66 Section 9 Summary Suppose Brenda knows she will consume 2 cups of coffee for sure. However, she can choose to consume different quantities of bagels: she can choose either 0, 1, 2, 3, or 4 bagels. a. Calculate Brenda’s marginal utility from bagels as she goes from consuming 0 bagel to 1 bagel, from 1 bagel to 2 bagels, from 2 bagels to 3 bagels, and from 3 bagels to 4 bagels. b. Draw Brenda’s marginal utility curve of bagels. Does Brenda have increasing, diminishing, or constant marginal utility of bagels? 17. Bernie loves notebooks and Beyoncé CDs. The accompanying table shows the utility Bernie receives from each product. Quantity of notebooks Utility from notebooks (utils) Quantity of CDs Utility from CDs (utils) 0 2 4 6 8 10 0 70 130 180 220 250 0 1 2 3 4 5 0 80 150 210 260 300 The price of a notebook is $5, the price of a CD is $10, and Bernie has $50 of income to spend. a. Which consumption bundles of notebooks and CDs can Bernie consume if he spends all his income? Illustrate Bernie’s budget line with a diagram, putting notebooks on the horizontal axis and CDs on the vertical axis.
b. Calculate the marginal utility of each notebook and the marginal utility of each CD. Then calculate the marginal utility per dollar spent on notebooks and the marginal utility per dollar spent on CDs. c. Draw a diagram like Figure 51.4 in which both the marginal utility per dollar spent on notebooks and the marginal utility per dollar spent on CDs are illustrated. Using this diagram and the optimal consumption rule, predict which bundle—from all the bundles on his budget line—Bernie will choose. 18. For each of the following situations, decide whether the bundle Lakshani is considering is optimal or not. If it is not optimal, how could Lakshani improve her overall level of utility? That is, determine which good she should spend more on and which good she should spend less on. a. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater. S u m m a r y 527 b. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and each pencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The last pen would add five times as much to her total utility as the last pencil. c. Lakshani has $50 per season to spend on tickets to football games and tickets to soccer games. Each football ticket costs $10, and each soccer ticket costs $5. She is thinking about buying 3 football tickets and 2 soccer tickets. Her marginal utility from the third football ticket is twice as much as her marginal utility from the second soccer ticket. 528 10 Module 52: Defining Profit Module 53: Profit Maximization Module 54: The Production Function Module 55: Firm Costs Module 56: Long-Run Costs and Economies of Scale Module 57: Introduction to Market Structure Economics by Example: “Could the Future Cost of Energy Change Life as We Know It?” Behind the Supply Curve: Profit, Production, and Costs In Section 9 we examined the factors that affect consumer choice—the demand side of the supply and demand model. In this section we turn our attention to the factors that affect producer choice and the supply side of the supply and demand model. We’ll begin with the concept of profit and examine
profit maximization as the goal of a firm. We will then investigate the firm’s production function, which shows the relationship between the inputs used for production and the output that is produced. Next we’ll consider the costs that influence firms’ decisions about supply. The final module in this section introduces the models of market structure used to understand how the supply side of the economy works 529 What you will learn in this Module: • The difference between explicit and implicit costs and their importance in decision making • The different types of profit, including economic profit, accounting profit, and normal profit • How to calculate profit An explicit cost is a cost that involves actually laying out money. An implicit cost does not require an outlay of money; it is measured by the value, in dollar terms, of benefits that are forgone. Module 52 Defining Profit Understanding Profit The primary goal of most firms is to maximize profit. Other goals, such as maximizing market share or protecting the environment, may also figure into a firm’s mission. But economic models generally start with the assumption that firms attempt to maximize profit. So we will begin with an explanation of how economists define and calculate profit. In the next module we will look at how firms go about maximizing their profit. In general, a firm’s profit equals its total revenue—which is equal to the price of the output times the quantity sold, or P × Q—minus the cost of all the inputs used to produce its output, its total cost. That is, Profit = Total Revenue − Total Cost However, there are different types of costs that may be used to calculate different types of profit. To start the discussion of how to calculate profit, we’ll look at two different types of costs, explicit costs and implicit costs. Explicit versus Implicit Costs Suppose that, after graduating from high school, you have two options: to go to college or to take a job immediately. You would like to continue your education but are concerned about the cost. But what exactly is the cost of attending college? Here is where it is important to remember the concept of opportunity cost: the cost of the time spent getting a degree is what you forgo by not taking a job for the years you go to college. The opportunity cost of additional education, like any cost, can be broken into two parts: the explicit cost and the implicit cost. An explicit cost is a cost that requires an outlay of money. For example, the explicit cost of a year of college includes
tuition. An implicit cost, though, does not involve an outlay of money; instead, it is measured by the value, in dollar terms, of the benefits that are forgone. For example, the implicit cost of a year spent in college includes the income you would have earned if you had taken a job instead. A common mistake, both in economic analysis and in real business situations, is to ignore implicit costs and focus exclusively on explicit costs. But often the implicit cost 530 of an activity is quite substantial—indeed, sometimes it is much larger than the explicit cost. Table 52.1 gives a breakdown of hypothetical explicit and implicit costs associated with spending a year in college instead of taking a job. The explicit cost consists of tuition, books, supplies, and a computer for doing assignments—all of which require you to spend money. The implicit cost is the salary you would have earned if you had taken a job instead. As you can see, the forgone salary is $35,000 and the explicit cost is $19,500, making the implicit cost more than the explicit cost in this example. So ignoring the implicit cost of an action can lead to a seriously misguided decision. The accounting profit of a business is the business’s total revenue minus the explicit cost and depreciation. t a b l e 52.1 Opportunity Cost of an Additional Year of School Explicit cost Implicit cost Tuition Books and supplies Computer Total explicit cost $17,000 1,000 1,500 19,500 Forgone salary $35,000 Total implicit cost 35,000 Total opportunity cost = Total explicit cost + Total implicit cost = $54,500 A slightly different way of looking at the implicit cost in this example can deepen our understanding of opportunity cost. The forgone salary is the cost of using your own resources—your time—in going to college rather than working. The use of your time for more education, despite the fact that you don’t have to spend any money, is still costly to you. This illustrates an important aspect of opportunity cost: in considering the cost of an activity, you should include the cost of using any of your own resources for that activity. You can calculate the cost of using your own resources by determining what they would have earned in their next best alternative use. Accounting Profit versus Economic Profit As the example of going to college suggests, taking account of implicit as well as explicit costs can be very important when making decisions. This is true whether the decisions affect individuals, groups, governments,
or businesses. Consider the case of Babette’s Cajun Café, a small restaurant in New Orleans. This year Babette brought in $100,000 in revenue. Out of that revenue, she paid her expenses: the cost of food ingredients and other supplies, the cost of wages for her employees, and the rent for her restaurant space. This year her expenses were $60,000. We assume that Babette owns her restaurant equipment—items such as appliances and furnishings. The question is: Is Babette’s restaurant profitable? At first it might seem that the answer is obviously yes: she receives $100,000 from her customers and has expenses of only $60,000. Doesn’t this mean that she has a profit of $40,000? Not according to her accountant, who reduces the number by $5,000 for the yearly depreciation (reduction in value) of the restaurant equipment. Depreciation occurs because equipment wears out over time. As a consequence, every few years Babette must replace her appliances and furnishings. The yearly depreciation amount reflects what an accountant estimates to be the reduction in the value of the machines due to wear and tear that year. This leaves $35,000, which is the business’s accounting profit. That is 531 The economic profit of a business is the business’s total revenue minus the opportunity cost of its resources. It is usually less than the accounting profit. The implicit cost of capital is the opportunity cost of the capital used by a business—the income the owner could have realized from that capital if it had been used in its next best alternative way. the accounting profit of a business is its total revenue minus its explicit cost and depreciation. The accounting profit is the number that Babette has to report on her income tax forms and that she would be obliged to report to anyone thinking of investing in her business. Accounting profit is a very useful number, but suppose that Babette wants to decide whether to keep her restaurant open or do something else. To make this decision, she will need to calculate her economic profit—the total revenue she receives minus her opportunity cost, which includes implicit as well as explicit costs. In general, when economists use the simple term profit, they are referring to economic profit. (We adopt this simplification in this book.) Why does Babette’s economic profit differ from her accounting profit? Because she may have an implicit cost over and above the explicit cost her accountant has calculated. Businesses can
face an implicit cost for two reasons. First, a business’s capital—its equipment, buildings, tools, inventory, and financial assets—could have been put to use in some other way. If the business owns its capital, it does not pay any money for its use, but it pays an implicit cost because it does not use the capital in some other way. Second, the owner devotes time and energy to the business that could have been used elsewhere—a particularly important factor in small businesses, whose owners tend to put in many long hours. If Babette had rented her appliances and furnishings instead of owning them, her rent would have been an explicit cost. But because Babette owns her own equipment, she does not pay rent on them and her accountant deducts an estimate of their depreciation in the profit statement. However, this does not account for the opportunity cost of the equipment— what Babette forgoes by owning it. Suppose that instead of using the equipment in her own restaurant, the best alternative Babette has is to sell the equipment for $50,000 and put the money into a bank account where it would earn yearly interest of $3,000. This $3,000 is an implicit cost of running the business. The implicit cost of capital is the opportunity cost of the capital used by a business; it reflects the income that could have been earned if the capital had been used in its next best alternative way. It is just as much a true cost as if Babette had rented her equipment instead of owning it. “I’ve done the numbers, and I will marry you.” Finally, Babette should take into account the opportunity cost of her own time. Suppose that instead of running her own restaurant, she could earn $34,000 as a chef in someone else’s restaurant. That $34,000 is also an implicit cost of her business. Table 52.2, in the column titled Case 1, summarizes the accounting for Babette’s Cajun Café, taking both explicit and implicit costs into account. It turns out, unfortunately, that t a b l e 52.2 Profit at Babette’s Cajun Café Revenue Explicit cost Depreciation Accounting profit Implicit cost of business Case 1 Case 2 $100,000 $100,000 –60,000 –60,000 –5,000 35,000 –5,000 35,000 Income Babette could have earned on capital used in the next best way –
3,000 –3,000 Income Babette could have earned as a chef in someone else’s restaurant –34,000 –30,000 Economic profit –2,000 +2,000 532 fyi s e g a m Farming in the Shadow of Suburbia Beyond the sprawling suburbs, most of New England is covered by dense forest. But this is not the forest primeval: if you hike through the woods, you encounter many stone walls, relics of the region’s agricultural past when stone walls enclosed fields and pastures. In 1880, more than half of New England’s land was farmed; by 2009, the amount was down to 10%. The remaining farms of New England are mainly located close to large metropolitan areas. There farmers get high prices for their produce from city dwellers who are willing to pay a premium for locally grown, extremely fresh fruits and vegetables. But now even these farms are under economic pressure caused by a rise in the implicit cost of farming close to a metropolitan area. As metropolitan areas have expanded during the last two decades, farmers increasingly ask themselves whether they could do better by selling their land to property developers. In 2009, the average value of an acre of farmland in the United States as a whole was $2,100; in Rhode Island, the most densely populated of the New England states, the average was $15,300. The Federal Reserve Bank of Boston has noted that “high land prices put intense pressure on the region’s farms to generate incomes that are substantial enough to justify keeping the land in agriculture.” The important point is that the pressure is intense even if the farmer owns the land because the land is a form of capital used to run the business. Maintaining the land as a farm instead of selling it to a developer constitutes a large implicit cost of capital. A fact provided by the U.S. Department of Agriculture (USDA) helps us put a dollar figure on the portion of the implicit cost of capital due to development pressure for some Rhode Island farms. In 2004, a USDA program designed to prevent development of Rhode Island farmland by paying owners for the “development rights” to their land paid an average of $4,949 per acre for those rights alone. By 2009, the amount had risen to $15,357. About two-thirds of New England’s farms remaining in business earn very little money. They are maintained as “rural residences” by people with other sources
of income—not so much because they are commercially viable, but more out of a personal commitment and the satisfaction these people derive from farm life. Although many businesses have important implicit costs, they can also have important benefits to their owners that go beyond the revenue earned. although the business makes an accounting profit of $35,000, its economic profit is actually negative. This means that Babette would be better off financially if she closed the restaurant and devoted her time and capital to something else. If, however, some of Babette’s cost should fall sufficiently, she could earn a positive economic profit. In that case, she would be better off financially if she continued to operate the restaurant. For instance, consider the column titled Case 2: here we assume that what Babette could earn as a chef employed by someone else has dropped to $30,000 (say, due to a soft labor market). In this case, her economic profit is positive: she is earning more than her explicit and implicit costs and she should keep her restaurant open. In real life, discrepancies between accounting profit and economic profit are extremely common. As the FYI above explains, this is a message that has found a receptive audience among real-world businesses. Normal Profit In the example above, when Babette is earning an economic profit, her total revenue is higher than the sum of her implicit and explicit costs. This means that operating her restaurant makes Babette better off financially than she would be using her resources in any other activity. When Babette earns a negative economic profit (which can also be described as a loss), it means that Babette would be better off financially if she devoted her resources to her next best alternative. As this example illustrates, economic profits signal the best use of resources. A positive economic profit indicates that the current use is the best use of resources. A negative economic profit indicates that there is a better alternative use for resources 533 An economic profit equal to zero is also known as a normal profit. It is an economic profit just high enough to keep a firm engaged in its current activity. But what about an economic profit equal to zero? Most of us would generally think earning zero profit was a bad thing. After all, a firm’s goal is to maximize profit—profit is what firms are after! However, an economic profit equal to zero is not bad at all. An economic profit of zero means that the firm could not do any better using its resources in any alternative activity. Another name for an economic profit of zero is
a normal profit. A firm earning a normal profit is earning just enough to keep it using its resources in its current activity. After all, it can’t do any better in any other activity! M o d u l e 52 AP R e v i e w Solutions appear at the back of the book. Check Your Understanding 1. Karma and Don run a furniture-refinishing business from their home. Which of the following represent an explicit cost of the business and which represent an implicit cost? a. supplies such as paint stripper, varnish, polish, sandpaper, and so on b. basement space that has been converted into a workroom c. wages paid to a part-time helper d. a van that they inherited and use only for transporting furniture e. the job at a larger furniture restorer that Karma gave up in order to run the business 2. a. Suppose you are in business earning an accounting profit of $25,000. What is your economic profit if the implicit cost of your capital is $2,000 and the opportunity cost of your time is $23,000? Explain your answer. b. What does your answer to part a tell you about the advisability of devoting your time and capital to this business? Tackle the Test: Multiple-Choice Questions 1. Which of the following is an example of an implicit cost of going 4. Which of the following is considered when calculating out for lunch? a. the amount of the tip you leave the waiter b. the total bill you charge to your credit card c. the cost of gas to drive to the restaurant d. the value of the time you spent eating lunch e. all of the above economic profit but not accounting profit? implicit cost a. b. explicit cost c. total revenue d. marginal cost e. All of the above are considered when calculating accounting 2. Which of the following is an implicit cost of attending college? profit. a. tuition b. books c. d. lab fees e. forgone salary laptop computer 3. Which of the following is the best definition of accounting profit? Accounting profit equals total revenue minus depreciation and total a. explicit cost only. b. implicit cost only. c. explicit cost plus implicit cost. d. opportunity cost. e. explicit cost plus opportunity cost. 5. You sell T-shirts at your school’s football games. Each shirt costs $5 to make and sells for $10. Each game lasts two hours and you sell 100 shirts per game.
You could always be earning $8 per hour at your other job. Which of the following is correct? Your accounting profit from selling shirts at a game is a. $1,000 and your economic profit is $500. b. $500 and your economic profit is $1,000. c. $500 and your economic profit is $484. d. $484 and your economic profit is $500. e. $500 and your economic profit is also $500. 534 Tackle the Test: Free-Response Questions 1. Your firm is selling 10,000 units of output at a price of $10 per unit. Your firm’s total explicit cost is $70,000. Your firm’s implicit cost of capital is $10,000, and your opportunity cost is $20,000. a. Calculate total revenue. b. Calculate total implicit cost. c. Calculate your accounting profit. d. Calculate your economic profit. e. What does the value of your economic profit calculated in part d tell you? Answer (5 points) 1 point: Total revenue = $100,000 1 point: Total implicit cost = $30,000 1 point: Accounting profit = $30,000 1 point: Economic profit = $0 1 point: Because your firm earns normal profit, there is no better alternative use for your resources. 2. Sunny owns and operates Sunny’s Sno Cone Stand. Use the data in the table provided to answer the questions below. Sunny’s Sno Cone Stand: January $2 Price of Sno Cone 2,000 Sno Cones sold $400 Explicit cost $100 Depreciation $200 Implicit cost of capital a. Calculate Sunny’s Sno Cone Stand’s total revenue for January. b. Calculate Sunny’s Sno Cone Stand’s accounting profit for January. c. What additional information would Sunny need in order to determine whether or not to continue operating the Sno Cone Stand? d. Explain how Sunny would determine whether or not to continue operating the business on the basis of these numbers 535 What you will learn in this Module: • The principle of marginal analysis • How to determine the profit-maximizing level of output using the optimal output rule Module 53 Profit Maximization Maximizing Profit In the previous module we learned about different types of profit, how to calculate profit, and how firms can use profit calculations to make decisions—for instance to determine whether to continue using resources for the
same activity or not. In this module we ask the question: what quantity of output would maximize the producer’s profit? First we will find the profit-maximizing quantity by calculating the total profit at each quantity for comparison. Then we will use marginal analysis to determine the optimal output rule, which turns out to be simple: as our discussion of marginal analysis in Module 1 suggested, a producer should produce up until marginal benefit equals marginal cost. Consider Jennifer and Jason, who run an organic tomato farm. Suppose that the market price of organic tomatoes is $18 per bushel and that Jennifer and Jason can sell as many as they would like at that price. Then we can use the data in Table 53.1 to find their profit-maximizing level of output. The first column shows the quantity of output in bushels, and the second column shows Jennifer and Jason’s total revenue from their output: the market value of their output. Total revenue, TR, is equal to the market price multiplied by the quantity of output: (53-1) TR = P × Q In this example, total revenue is equal to $18 per bushel times the quantity of output in bushels. The third column of Table 53.1 shows Jennifer and Jason’s total cost, TC. The fourth column shows their profit, equal to total revenue minus total cost: (53-2) Profit = TR − TC As indicated by the numbers in the table, profit is maximized at an output of five bushels, where profit is equal to $18. But we can gain more insight into the profitmaximizing choice of output by viewing it as a problem of marginal analysis, a task we’ll dive into next. 536 53.1 Profit for Jennifer and Jason’s Farm When Market Price Is $18 Quantity of tomatoes Q (bushels) Total revenue TR 0 1 2 3 4 5 6 7 $0 18 36 54 72 90 108 126 Total cost TC $14 30 36 44 56 72 92 116 Profit TR − TC −$14 −12 0 10 16 18 16 10 Using Marginal Analysis to Choose the Profit-Maximizing Quantity of Output The principle of marginal analysis provides a clear message about when to stop doing anything: proceed until marginal benefit equals marginal cost. To apply this principle, consider the effect on a producer’s profit of increasing output by one unit. The marginal benefit of that unit is the additional revenue generated by selling it; this
measure has a name—it is called the marginal revenue of that output. The general formula for marginal revenue is: (53-3) Marginal revenue = Change in total revenue generated by one additional unit of output = Change in total revenue Change in quantity of output or MR = ΔTR/ΔQ In this equation, the Greek uppercase delta (the triangular symbol) represents the change in a variable. The application of the principle of marginal analysis to the producer’s decision of how much to produce is called the optimal output rule, which states that profit is maximized by producing the quantity at which the marginal revenue of the last unit produced is equal to its marginal cost. As this rule suggests, we will see that Jennifer and Jason maximize their profit by equating marginal revenue and marginal cost. Note that there may not be any particular quantity at which marginal revenue exactly equals marginal cost. In this case the producer should produce until one more unit would cause marginal benefit to fall below marginal cost. As a common simplification, we can think of marginal cost as rising steadily, rather than jumping from one level at one quantity to a different level at the next quantity. This ensures that marginal cost will equal marginal revenue at some quantity. We employ this simplified approach in what follows. Consider Table 53.2 on the next page, which provides cost and revenue data for Jennifer and Jason’s farm. The second column contains the farm’s total cost of output. According to the principle of marginal analysis, every activity should continue until marginal benefit equals marginal cost. Marginal revenue is the change in total revenue generated by an additional unit of output. The optimal output rule says that profit is maximized by producing the quantity of output at which the marginal revenue of the last unit produced is equal to its marginal cost 537 t a b l e 53.2 Short -Run Costs for Jennifer and Jason’s Farm Quantity of tomatoes Q (bushels) 0 1 2 3 4 5 6 7 Total cost TC $14 30 36 44 56 72 92 116 Marginal cost of bushel MC = ΔTC/ΔQ Marginal revenue of bushel MR Net gain of bushel = MR − MC $16 6 8 12 16 20 24 $18 18 18 18 18 18 18 $2 12 10 6 2 −2 −6 The third column shows their marginal cost. Notice that, in this example, marginal cost initially falls as output rises but then begins to increase, so that the marginal cost curve has a “sw
oosh” shape. (Later it will become clear that this shape has important implications for short-run production decisions.) The fourth column contains the farm’s marginal revenue, which has an important feature: Jennifer and Jason’s marginal revenue is assumed to be constant at $18 for every output level. The assumption holds true for a particular type of market—perfectly competitive markets—which we will study in Modules 58–60, but for now it is just to make the calculations easier. The fifth and final column shows the calculation of the net gain per bushel of tomatoes, which is equal to marginal revenue minus marginal cost. As you can see, it is positive for the first through fifth bushels; producing each of these bushels raises Jennifer and Jason’s profit. For the sixth and seventh bushels, however, net gain is negative: producing them would decrease, not increase, profit. (You can verify this by reexamining Table 53.1.) So five bushels are Jennifer and Jason’s profitmaximizing output; it is the level of output at which marginal cost is equal to the market price, $18. Figure 53.1 shows that Jennifer and Jason’s profit-maximizing quantity of output is, indeed, the number of bushels at which the marginal cost of production is equal to marginal revenue (which is equivalent to price in perfectly competitive markets). The figure shows the marginal cost curve, MC, drawn from the data in the third column of Table 53.2. We plot the marginal cost of increasing output from one to two bushels halfway between one and two, and so on. The horizontal line at $18 is Jennifer and Jason’s marginal revenue curve. Note that marginal revenue stays the same regardless of how much Jennifer and Jason sell because we have assumed marginal revenue is constant. Does this mean that the firm’s production decision can be entirely summed up as “produce up to the point where the marginal cost of production is equal to the price”? No, not quite. Before applying the principle of marginal analysis to determine how much to produce, a potential producer must, as a first step, answer an “either–or” question: Should I produce at all? If the answer to that question is yes, the producer then proceeds to the second step—a “how much” decision: maximizing profit by choosing the quantity of output at which marginal cost is
equal to price. The marginal cost curve shows how the cost of producing one more unit depends on the quantity that has already been produced. The marginal revenue curve shows how marginal revenue varies as output varies. 538 53.1 The Firm’s ProfitMaximizing Quantity of Output At the profit-maximizing quantity of output, marginal revenue is equal to marginal cost. It is located at the point where the marginal cost curve crosses the marginal revenue curve, which is a horizontal line at the market price. Here, the profit-maximizing point is at an output of 5 bushels of tomatoes, the output quantity at point E. Price, cost of bushel Market price $24 20 18 16 12 8 6 0 Optimal point MC E MR = P 1 2 3 4 5 6 Proﬁt-maximizing quantity 7 Quantity of tomatoes (bushels To understand why the first step in the production decision involves an “either–or” question, we need to ask how we determine whether it is profitable or unprofitable to produce at all. When Is Production Profitable? Recall that a firm’s decision whether or not to stay in a given business depends on its economic profit—a measure based on the opportunity cost of resources used in the business. To put it a slightly different way: in the calculation of economic profit, a firm’s total cost incorporates the implicit cost—the benefits forgone in the next best use of the firm’s resources—as well as the explicit cost in the form of actual cash outlays. In contrast, accounting profit is profit calculated using only the explicit costs incurred by the firm. This means that economic profit incorporates the opportunity cost of resources owned by the firm and used in the production of output, while accounting profit does not. As in the example of Babette’s Cajun Café, a firm may make positive accounting profit while making zero or even negative economic profit. It’s important to understand clearly that a firm’s decision to produce or not, to stay in business or to close down permanently, should be based on economic profit, not accounting profit. So we will assume, as we always do, that the cost numbers given in Tables 53.1 and 53.2 include all costs, implicit as well as explicit, and that the profit numbers in Table 53.1 are economic profit. What determines whether Jennifer and Jason’s farm earns a profit or generates a loss? The answer is
that whether or not it is profitable depends on the market price of tomatoes—specifically, whether selling the firm’s optimal quantity of output at the market price results in at least a normal profit. In the next modules, we look in detail at the two components used to calculate profit; firm revenue (which is determined by the level of production) and firm cost 539 M o d u l e 53 AP R e v i e w Solutions appear at the back of the book. Check Your Understanding 1. Suppose a firm can sell as many units of output as it wants for a price of $15 per unit and faces total costs as indicated in the table below. Use the optimal output rule to determine the profit-maximizing level of output for the firm. Q 0 1 2 3 4 5 TC $2 10 20 33 50 71 Tackle the Test: Multiple-Choice Questions Use the data in the table provided to answer questions 1–3. Quantity Q 0 1 2 3 4 5 6 7 Total Revenue TR $0 18 36 54 72 90 108 126 Total Cost TC $14 30 36 44 56 72 92 116 1. What is the marginal revenue of the third unit of output? a. $8 b. $14 c. $18 d. $44 e. $54 2. What is the marginal cost of the first unit of output? a. $0 b. $14 c. $16 2. Use the data from Question 1 to graph the firm’s MC and MR curves and show the profit-maximizing level of output. d. $18 e. $30 3. At what level of output is profit maximized? a. 0 b. 1 c. 3 d. 5 e. 7 4. A firm should continue to produce as long as its a. total revenue is less than its total costs. b. total revenue is greater than its total explicit costs. c. accounting profit is greater than its economic profit. d. accounting profit is not negative. e. economic profit is at least zero. 5. A firm earns a normal profit when its a. accounting profit equals 0. b. economic profit is positive. c. total revenue equals its total costs. d. accounting profit equals its economic profit. e. economic profit equals its total explicit and implicit costs. 540. Use a graph to illustrate the typical shape of the two curves used to find a firm’s profit-maximizing level of output on the basis of the optimal output rule. Assume
all units of output can be sold for $5. Indicate the profit-maximizing level of output with a “Q*” on the appropriate axis. (You don’t have enough information to provide a specific numerical answer.) Tackle the Test: Free-Response Questions 1. Use the data in the table provided. Quantity Q 0 1 2 3 4 5 6 7 Total Revenue TR $0 18 36 54 72 90 108 126 Total Cost TC $7 23 29 37 49 65 87 112 a. What is the marginal revenue of the fourth unit? b. Calculate profit at a quantity of two. Explain how you calculated the profit. c. What is the profit-maximizing level of output? Explain how to use the optimal output rule to determine the profit-maximizing level of output. Answer (5 points) 1 point: $18 1 point: $7 1 point: $36 − $29 or TR − TC 1 point: 5 units 1 point: The optimal output rule states that profit is maximized when MC = MR. Here, MC never exactly equals MR. When this occurs, the firm should produce the largest quantity at which MR exceeds MC. At a quantity of 5, MC = $16 and MR = $18. For the sixth unit, MC = $22 and MR = $18, and because MC > MR, the sixth unit would add more to total cost than it would to total revenue, and it therefore should not be produced 541 What you will learn in this Module: • The importance of the firm’s production function, the relationship between the quantity of inputs and the quantity of output • Why production is often subject to diminishing returns to inputs Module 54 The Production Function The Production Function A firm produces goods or services for sale. To do this, it must transform inputs into output. The quantity of output a firm produces depends on the quantity of inputs; this relationship is known as the firm’s production function. As we’ll see, a firm’s production function underlies its cost curves. As a first step, let’s look at the characteristics of a hypothetical production function. Inputs and Output To understand the concept of a production function, let’s consider a farm that we assume, for the sake of simplicity, produces only one output, wheat, and uses only two inputs, land and labor. This particular farm is owned by a couple named George and Martha. They hire workers to do the actual physical labor
on the farm. Moreover, we will assume that all potential workers are of the same quality—they are all equally knowledgeable and capable of performing farmwork. George and Martha’s farm sits on 10 acres of land; no more acres are available to them, and they are currently unable to either increase or decrease the size of their farm by selling, buying, or leasing acreage. Land here is what economists call a fixed input— an input whose quantity is fixed for a period of time and cannot be varied. George and Martha are, however, free to decide how many workers to hire. The labor provided by these workers is called a variable input—an input whose quantity the firm can vary at any time. In reality, whether or not the quantity of an input is really fixed depends on the time horizon. In the long run—that is, given that a long enough period of time has elapsed— firms can adjust the quantity of any input. So there are no fixed inputs in the long run. In contrast, the short run is defined as the time period during which at least one input is fixed. Later, we’ll look more carefully at the distinction between the short run and the long run. But for now, we will restrict our attention to the short run and assume that at least one input (land) is fixed. A production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces. A fixed input is an input whose quantity is fixed for a period of time and cannot be varied. A variable input is an input whose quantity the firm can vary at any time. The long run is the time period in which all inputs can be varied. The short run is the time period in which at least one input is fixed. 542 The total product curve shows how the quantity of output depends on the quantity of the variable input, for a given quantity of the fixed input. The marginal product of an input is the additional quantity of output produced by using one more unit of that input. George and Martha know that the quantity of wheat they produce depends on the number of workers they hire. Using modern farming techniques, one worker can cultivate the 10-acre farm, albeit not very intensively. When an additional worker is added, the land is divided equally among all the workers: each worker has 5 acres to cultivate when 2 workers are employed, each cultivates 31⁄3 acres when 3 are employed, and so on. So as additional workers are employed, the 10 acres of
land are cultivated more intensively and more bushels of wheat are produced. The relationship between the quantity of labor and the quantity of output, for a given amount of the fixed input, constitutes the farm’s production function. The production function for George and Martha’s farm, where land is the fixed input and labor is the variable input, is shown in the first two columns of the table in Figure 54.1; the diagram there shows the same information graphically. The curve in Figure 54.1 shows how the quantity of output depends on the quantity of the variable input for a given quantity of the fixed input; it is called the farm’s total product curve. The physical quantity of output, bushels of wheat, is measured on the vertical axis; the quantity of the variable input, labor (that is, the number of workers employed), is measured on the horizontal axis. The total product curve here slopes upward, reflecting the fact that more bushels of wheat are produced as more workers are employed. Although the total product curve in Figure 54.1 slopes upward along its entire length, the slope isn’t constant: as you move up the curve to the right, it flattens out. To understand this changing slope, look at the third column of the table in Figure 54.1, which shows the change in the quantity of output generated by adding one more worker. That is, it shows the marginal product of labor, or MPL: the additional quantity of output from using one more unit of labor (one more worker). 54.1 Production Function and Total Product Curve for George and Martha’s Farm Adding a 7th worker leads to an increase in output of only 7 bushels. Total product, TP Adding a 2nd worker leads to an increase in output of 17 bushels. Quantity of wheat (bushels) 100 80 60 40 20 Quantity of labor L (workers) Quantity of wheat Q (bushels) Marginal product of labor MPL = ΔQ/ΔL (bushels per worker 19 36 51 64 75 84 91 96 19 17 15 13 11 Quantity of labor (workers) 7 The table shows the production function, the relationship between the quantity of the variable input (labor, measured in number of workers) and the quantity of output (wheat, measured in bushels) for a given quantity of the fixed input. It also shows the marginal product of labor on George and Martha’s farm. The
total product curve shows the production function graphically. It slopes upward because more wheat is produced as more workers are employed. It also becomes flatter because the marginal product of labor declines as more and more workers are employed 543 In this example, we have data at intervals of 1 worker—that is, we have information on the quantity of output when there are 3 workers, 4 workers, and so on. Sometimes data aren’t available in increments of 1 unit—for example, you might have information on the quantity of output only when there are 40 workers and when there are 50 workers. In this case, you can use the following equation to calculate the marginal product of labor: (54-1) Marginal product of labor = Change in quantity of output produced by one additional unit of labor = Change in quantity of output Change in quantity of labor or MPL = ΔQ ΔL Recall that Δ, the Greek uppercase delta, represents the change in a variable. Now we can explain the significance of the slope of the total product curve: it is equal to the marginal product of labor. The slope of a line is equal to “rise” over “run.” This implies that the slope of the total product curve is the change in the quantity of output (the “rise”) divided by the change in the quantity of labor (the “run”). And this, as we can see from Equation 54-1, is simply the marginal product of labor. So in Figure 54.1, the fact that the marginal product of the first worker is 19 also means that the slope of the total product curve in going from 0 to 1 worker is 19. Similarly, the slope of the total product curve in going from 1 to 2 workers is the same as the marginal product of the second worker, 17, and so on. In this example, the marginal product of labor steadily declines as more workers are hired—that is, each successive worker adds less to output than the previous worker. So as employment increases, the total product curve gets flatter. Figure 54.2 shows how the marginal product of labor depends on the number of workers employed on the farm. The marginal product of labor, MPL, is measured on the vertical axis in units of physical output—bushels of wheat—produced per additional worker, and the number of workers employed is measured on the horizontal axis. You can see from the table in Figure 54.1 that if 5 workers are employed instead
of 4, output rises from 64 to 75 bushels; in this case the marginal product of labor is f i g u r e 54.2 Marginal Product of Labor Curve for George and Martha’s Farm The marginal product of labor curve plots each worker’s marginal product, the increase in the quantity of output generated by each additional worker. The change in the quantity of output is measured on the vertical axis and the number of workers employed on the horizontal axis. The first worker employed generates an increase in output of 19 bushels, the second worker generates an increase of 17 bushels, and so on. The curve slopes downward due to diminishing returns to labor. Marginal product of labor (bushels per worker) 19 17 15 13 11 9 7 5 0 There are diminishing returns to labor. Marginal product of labor, MPL 1 2 3 4 5 8 Quantity of labor (workers) 6 7 544 11 bushels—the same number found in Figure 54.2. To indicate that 11 bushels is the marginal product when employment rises from 4 to 5, we place the point corresponding to that information halfway between 4 and 5 workers. In this example the marginal product of labor falls as the number of workers increases. That is, there are diminishing returns to labor on George and Martha’s farm. In general, there are diminishing returns to an input when an increase in the quantity of that input, holding the quantity of all other inputs fixed, reduces that input’s marginal product. Due to diminishing returns to labor, the MPL curve is negatively sloped. To grasp why diminishing returns can occur, think about what happens as George and Martha add more and more workers without increasing the number of acres. As the number of workers increases, the land is farmed more intensively and the number of bushels increases. But each additional worker is working with a smaller share of the 10 acres—the fixed input—than the previous worker. As a result, the additional worker cannot produce as much output as the previous worker. So it’s not surprising that the marginal product of the additional worker falls. The crucial point to emphasize about diminishing returns is that, like many propositions in economics, it is an “other things equal” proposition: each successive unit of an input will raise production by less than the last if the quantity of all other inputs is held fixed. What would happen if the levels of other inputs were allowed to change? You can see the
answer illustrated in Figure 54.3. Panel (a) shows two total product curves, TP10 and TP20. TP10 is the farm’s total product curve when its total area is 10 acres (the same curve as in Figure 54.1). TP20 is the total product curve when the farm’s area has increased to 20 acres. Except when 0 workers are employed, TP20 lies everywhere above TP10 because with more acres available, any given number of workers produces more output. Panel (b) shows the corresponding marginal product of labor curves There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input. With diminishing marginal returns to labor, as more and more workers are added to a fixed amount of land, each worker adds less to total output than the previous worker 54.3 Total Product, Marginal Product, and the Fixed Input (a) Total Product Curves (b) Marginal Product Curves Quantity of wheat (bushels) 160 140 120 100 80 60 40 20 0 1 2 3 TP20 TP10 5 4 Quantity of labor (workers) 6 7 8 Marginal product of labor (bushels per worker) 30 25 20 15 10 5 0 1 2 3 MPL20 MPL10 5 4 Quantity of labor (workers) 7 6 8 This figure shows how the quantity of output—illustrated by the total product curve—and marginal product depend on the level of the fixed input. Panel (a) shows two total product curves for George and Martha’s farm, TP10 when their farm is 10 acres and TP20 when it is 20 acres. With more land, each worker can produce more wheat. So an increase in the fixed input shifts the total product curve up from TP10 to TP20. This also implies that the marginal product of each worker is higher when the farm is 20 acres than when it is 10 acres. As a result, an increase in acreage also shifts the marginal product of labor curve up from MPL10 to MPL20. Panel (b) shows the marginal product of labor curves. Note that both marginal product of labor curves still slope downward due to diminishing returns to labor 545 fyi Was Malthus Right? In 1798, Thomas Malthus, an English pastor, authored the book An Essay on the Principle of Population, which introduced the principle of diminishing returns to an input. M
althus’s writings were influential in his own time and continue to provoke heated argument to this day. Malthus argued that as a country’s popula- tion grew but its land area remained fixed, it would become increasingly difficult to grow enough food. Though more intensive cultivation of the land could increase yields, as the marginal product of labor declined, each successive farmer would add less to the total than the last. From this argument, Malthus drew a power- ful conclusion—that misery was the normal condition of humankind. In a country with a small population and abundant land (a description of the United States at the time), he argued, families would be large and the population would grow rapidly. Ultimately, the pressure of population on the land would reduce the condi- tion of most people to a level at which starvation and disease held the population in check. (Arguments like this led the historian Thomas Carlyle to dub economics the “dismal science.”) Happily, over the long term, Malthus’s pre- dictions have turned out to be wrong. World population has increased from about 1 billion when Malthus wrote to more than 6.8 billion in 2010, but in most of the world people eat better now than ever before. So was Malthus completely wrong? And do his incorrect predictions refute the idea of diminishing returns? No, on both counts. First, the Malthusian story is a pretty accurate description of 57 of the last 59 centuries: peasants in eighteenth-century France probably did not live much better than Egyptian peasants in the age of the pyramids. Yet diminishing returns does not mean that using more labor to grow food on a given amount of land will lead to a decline in the marginal product of labor—if there is also a radical improvement in farming technology. Fortunately, since the eighteenth century, technological progress has been so rapid that it has alleviated much of the limits imposed by diminishing returns. Diminishing returns implies that the marginal product declines when all other things—including technology— remain the same. So the happy fact that Malthus’s predictions were wrong does not invalidate the concept of diminishing returns. Typically, however, technological progress relaxes the limits imposed by diminishing returns only over the very long term. This was demonstrated in 2008 when bad weather, an ethanoldriven increase in the demand for corn, and a brisk rise in world income led to soaring world grain prices. As farmers scrambled to
plant more acreage, they ran up against limits in the availability of inputs like land and fertilizer. Hopefully, we can prove Malthus wrong again before long. MPL10 is the marginal product of labor curve given 10 acres to cultivate (the same curve as in Figure 54.2), and MPL20 is the marginal product of labor curve given 20 acres. Both curves slope downward because, in each case, the amount of land is fixed, albeit at different levels. But MPL20 lies everywhere above MPL10, reflecting the fact that the marginal product of the same worker is higher when he or she has more of the fixed input to work with. Figure 54.3 demonstrates a general result: the position of the total product curve depends on the quantities of other inputs. If you change the quantities of the other inputs, both the total product curve and the marginal product curve of the remaining input will shift. The importance of the “other things equal” assumption in discussing diminishing returns is illustrated in the FYI above. M o d u l e 54 AP R e v i e w Solutions appear at the back of the book. Check Your Understanding 1. Bernie’s ice-making company produces ice cubes using a 10-ton machine and electricity (along with water, which we will ignore as an input for simplicity). The quantity of output, measured in pounds of ice, is given in the accompanying table. a. What is the fixed input? What is the variable input? b. Construct a table showing the marginal product of the variable input. Does it show diminishing returns? c. Suppose a 50% increase in the size of the fixed input increases output by 100% for any given amount of the variable input. What is the fixed input now? Construct a table showing the quantity of output and the marginal product in this case. 546 Quantity of electricity (kilowatts) 0 1 2 3 4 Quantity of ice (pounds) 0 1,000 1,800 2,400 2,800 Tackle the Test: Multiple-Choice Questions 1. A production function shows the relationship between inputs and a. fixed costs. b. variable costs. c. total revenue. d. output. e. profit. 2. Which of the following defines the short run? less than a year a. b. when all inputs are fixed c. when no inputs are variable d. when only one input is variable e. when at least one input is fixed 3. The slope of the total product curve is also known
as a. marginal product. b. marginal cost. c. average product. d. average revenue. e. profit. Tackle the Test: Free-Response Questions 1. Draw a correctly labeled graph of a production function that exhibits diminishing returns to labor. Assume labor is the variable input and capital is the fixed input. Explain how your graph illustrates diminishing returns to labor. 4. Diminishing returns to an input ensures that as a firm continues to produce, the total product curve will have what kind of slope? a. negative decreasing b. positive decreasing c. negative increasing d. positive increasing e. positive constant 5. Historically, the limits imposed by diminishing returns have investment in capital. increases in the population. been alleviated by a. b. c. discovery of more land. d. Thomas Malthus. e. economic models. 1 point: Graph with vertical axis labeled “Quantity of output” or “Q” and horizontal axis labeled “Quantity of labor” or “L” 1 point: Upward sloping curve labeled “Total product” or “TP” 1 point: The slope of the total product curve is positive and decreasing Answer (4 points) Quantity of output 1 point: Explanation that a positive and decreasing slope illustrates diminishing returns to labor because each additional unit of labor increases total product by less than the previous unit of labor TP 2. Use the data in the table below to graph the production function and the marginal product of labor. Do the data illustrate diminishing returns to labor? Explain. Quantity of labor Quantity of output Q 0 19 36 51 64 75 84 91 96 547 Quantity of labor What you will learn in this Module: • The various types of cost a firm faces, including fixed cost, variable cost, and total cost • How a firm’s costs generate marginal cost curves and average cost curves Module 55 Firm Costs From the Production Function to Cost Curves Now that we have learned about the firm’s production function, we can use that knowledge to develop its cost curves. To see how a firm’s production function is related to its cost curves, let’s turn once again to George and Martha’s farm. Once George and Martha know their production function, they know the relationship between inputs of labor and land and output of wheat. But if they want to maximize their profits, they need to translate this knowledge into information about the relationship between the quantity of output and cost. Let’s see how
they can do this. To translate information about a firm’s production function into information about its cost, we need to know how much the firm must pay for its inputs. We will assume that George and Martha face either an explicit or an implicit cost of $400 for the use of the land. As we learned previously, it is irrelevant whether George and Martha must rent the land for $400 from someone else or whether they own the land themselves and forgo earning $400 from renting it to someone else. Either way, they pay an opportunity cost of $400 by using the land to grow wheat. Moreover, since the land is a fixed input for which George and Martha pay $400 whether they grow one bushel of wheat or one hundred, its cost is a fixed cost, denoted by FC—a cost that does not depend on the quantity of output produced. In business, a fixed cost is often referred to as an “overhead cost.” We also assume that George and Martha must pay each worker $200. Using their production function, George and Martha know that the number of workers they must hire depends on the amount of wheat they intend to produce. So the cost of labor, which is equal to the number of workers multiplied by $200, is a variable cost, denoted by VC—a cost that depends on the quantity of output produced. Adding the fixed cost and the variable cost of a given quantity of output gives the total cost, or TC, of that quantity of output. We can express the relationship among fixed cost, variable cost, and total cost as an equation: (55-1) Total cost = Fixed cost + Variable cost or TC = FC + VC A fixed cost is a cost that does not depend on the quantity of output produced. It is the cost of the fixed input. A variable cost is a cost that depends on the quantity of output produced. It is the cost of the variable input. The total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output. 548 The total cost curve shows how total cost depends on the quantity of output. The table in Figure 55.1 shows how total cost is calculated for George and Martha’s farm. The second column shows the number of workers employed, L. The third column shows the corresponding level of output, Q, taken from the table in Figure 54.1. The fourth column shows the variable cost, VC, equal to the number of workers
multiplied by $200. The fifth column shows the fixed cost, FC, which is $400 regardless of the quantity of wheat produced. The sixth column shows the total cost of output, TC, which is the variable cost plus the fixed cost. The first column labels each row of the table with a letter, from A to I. These labels will be helpful in understanding our next step: drawing the total cost curve, a curve that shows how total cost depends on the quantity of output. George and Martha’s total cost curve is shown in the diagram in Figure 55.1, where the horizontal axis measures the quantity of output in bushels of wheat and the vertical axis measures total cost in dollars. Each point on the curve corresponds to one row of the table in Figure 55.1. For example, point A shows the situation when 0 workers are employed: output is 0, and total cost is equal to fixed cost, $400. Similarly, point B shows the situation when 1 worker is employed: output is 19 bushels, and total cost is $600, equal to the sum of $400 in fixed cost and $200 in variable cost. Like the total product curve, the total cost curve slopes upward: due to the increasing variable cost, the more output produced, the higher the farm’s total cost. f i g u r e 55.1 Total Cost Curve for George and Martha’s Farm The table shows the variable cost, fixed cost, and total cost for various output quantities on George and Martha’s 10-acre farm. The total cost curve shows how total cost (measured on the vertical axis) depends on the quantity of output (measured on the horizontal axis). The labeled points on the curve correspond to the rows of the table. The total cost curve slopes upward because the number of workers employed, and hence total cost, increases as the quantity of output increases. The curve gets steeper as output increases due to diminishing returns to labor. Cost $2,000 1,800 1,600 1,400 1,200 1,000 800 600 400 200 0 A Total cost, TC I H G F E D C B 19 36 51 75 84 64 Quantity of wheat (bushels) 91 96 Quantity of labor L (workers) Quantity of wheat Q (bushels) Variable cost VC Point on graph 19 36 51 64 75 84 91 96 O $ 200 400 600 800 1,000 1,200 1,400 1,600 Fixed cost FC $400
400 400 400 400 400 400 400 400 Total cost TC = FC + VC $ 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 549 But unlike the total product curve, which gets flatter as employment rises, the total cost curve gets steeper. That is, the slope of the total cost curve is greater as the amount of output produced increases. As we will soon see, the steepening of the total cost curve is also due to diminishing returns to the variable input. Before we can see why, we must first look at the relationships among several useful measures of cost. Two Key Concepts: Marginal Cost and Average Cost We’ve just learned how to derive a firm’s total cost curve from its production function. Our next step is to take a deeper look at total cost by deriving two extremely useful measures: marginal cost and average cost. As we’ll see, these two measures of the cost of production have a somewhat surprising relationship to each other. Moreover, they will prove to be vitally important in later modules, where we will use them to analyze the firm’s output decision and the market supply curve. Marginal Cost Module 53 explained that marginal cost is the added cost of doing something one more time. In the context of production, marginal cost is the change in total cost generated by producing one more unit of output. We’ve already seen that marginal product is easiest to calculate if data on output are available in increments of one unit of input. Similarly, marginal cost is easiest to calculate if data on total cost are available in increments of one unit of output because the increase in total cost for each unit is clear. When the data come in less convenient increments, it’s still possible to calculate marginal cost over each interval. But for the sake of simplicity, let’s work with an example in which the data come in convenient one-unit increments. Selena’s Gourmet Salsas produces bottled salsa; Table 55.1 shows how its costs per day depend on the number of cases of salsa it produces per day. The firm has a fixed t a b l e 55.1 Costs at Selena’s Gourmet Salsas Quantity of salsa Q (cases 10 Fixed cost FC $108 108 108 108 108 108 108 108 108 108 108 Variable cost VC $0 12 48 108 192 300 432 588 768 972 1,200 Total cost TC = FC + VC $108 Marginal
cost of case MC = ΔTC /ΔQ 120 156 216 300 408 540 696 876 1,080 $1,308 $12 0036 0060 0084 108 132 156 180 204 228 550 55.2 Total Cost and Marginal Cost Curves for Selena’s Gourmet Salsas (a) Total Cost (b) Marginal Cost Cost $1,400 1,200 1,000 800 600 400 200 2nd case of salsa increases total cost by $36. 0 1 2 3 4 5 8th case of salsa increases total cost by $180. Cost of case TC $250 MC 200 150 100 50 0 1 2 3 4 5 7 6 Quantity of salsa (cases) 10 8 9 7 6 Quantity of salsa (cases) 10 8 9 Panel (a) shows the total cost curve from Table 55.1. Like the total cost curve in Figure 55.1, it slopes upward and gets steeper as we move up it to the right. Panel (b) shows the marginal cost curve. It also slopes upward, reflecting diminishing returns to the variable input. cost of $108 per day, shown in the second column, which is the daily rental cost of its food-preparation equipment. The third column shows the variable cost, and the fourth column shows the total cost. Panel (a) of Figure 55.2 plots the total cost curve. Like the total cost curve for George and Martha’s farm in Figure 55.1, this curve slopes upward, getting steeper as quantity increases. The significance of the slope of the total cost curve is shown by the fifth column of Table 55.1, which indicates marginal cost—the additional cost of each additional unit. The general formula for marginal cost is: (55-2) Marginal cost = Change in total cost generated by one additional unit of output = Change in total cost Change in quantity of output or MC = ΔTC ΔQ As in the case of marginal product, marginal cost is equal to “rise” (the increase in total cost) divided by “run” (the increase in the quantity of output). So just as marginal product is equal to the slope of the total product curve, marginal cost is equal to the slope of the total cost curve. Now we can understand why the total cost curve gets steeper as it increases from left to right: as you can see in Table 55.1, marginal cost at Selena’s Gourmet Salsas rises as
output increases. And because marginal cost equals the slope of the total cost curve, a higher marginal cost means a steeper slope. Panel (b) of Figure 55.2 shows the marginal cost curve corresponding to the data in Table 55.1. Notice that, as in Figure 53.1, we plot the marginal cost for increasing output from 0 to 1 case of salsa halfway between 0 and 1, the marginal cost for increasing output from 1 to 2 cases of salsa halfway between 1 and 2, and so on 551 Average total cost, often referred to simply as average cost, is total cost divided by quantity of output produced. Why does the marginal cost curve slope upward? Because there are diminishing returns to inputs in this example. As output increases, the marginal product of the variable input declines. This implies that more and more of the variable input must be used to produce each additional unit of output as the amount of output already produced rises. And since each unit of the variable input must be paid for, the additional cost per additional unit of output also rises. Recall that the flattening of the total product curve is also due to diminishing returns: if the quantities of other inputs are fixed, the marginal product of an input falls as more of that input is used. The flattening of the total product curve as output increases and the steepening of the total cost curve as output increases are just flip-sides of the same phenomenon. That is, as output increases, the marginal cost of output also increases because the marginal product of the variable input decreases. Our next step is to introduce another measure of cost: average cost. Average Cost In addition to total cost and marginal cost, it’s useful to calculate average total cost, often simply called average cost. The average total cost is total cost divided by the quantity of output produced; that is, it is equal to total cost per unit of output. If we let ATC denote average total cost, the equation looks like this: (55-3) ATC = Total cost Quantity of output = TC Q Average total cost is important because it tells the producer how much the average or typical unit of output costs to produce. Marginal cost, meanwhile, tells the producer how much one more unit of output costs to produce. Although they may look very similar, these two measures of cost typically differ. And confusion between them is a major source of error in economics, both in the classroom and in real life. Table 55.2 uses data from Selena’s Gourmet S
alsas to calculate average total cost. For example, the total cost of producing 4 cases of salsa is $300, consisting of $108 in fixed cost and $192 in variable cost (from Table 55.1). So the average total cost of producing 4 cases of salsa is t a b l e 55.2 Average Costs for Selena’s Gourmet Salsas Quantity of salsa Q (cases 10 Total cost TC $120 156 216 300 408 540 696 876 1,080 1,308 Average total cost of case ATC = TC /Q $120.00 Average fixed cost of case AFC = FC /Q $108.00 78.00 72.00 75.00 81.60 90.00 99.43 109.50 120.00 130.80 54.00 36.00 27.00 21.60 18.00 15.43 13.50 12.00 10.80 Average variable cost of case AVC = VC/Q $12.00 24.00 36.00 48.00 60.00 72.00 84.00 96.00 108.00 120.00 552 300/4 = $75. You can see from Table 55.2 that as the quantity of output increases, average total cost first falls, then rises. Figure 55.3 plots that data to yield the average total cost curve, which shows how average total cost depends on output. As before, cost in dollars is measured on the vertical axis and quantity of output is measured on the horizontal axis. The average total cost curve has a distinctive U shape that corresponds to how average total cost first falls and then rises as output increases. Economists believe that such U-shaped average total cost curves are the norm for firms in many industries. f i g u r e 55.3 Average Total Cost Curve for Selena’s Gourmet Salsas The average total cost curve at Selena’s Gourmet Salsas is U-shaped. At low levels of output, average total cost falls because the “spreading effect” of falling average fixed cost dominates the “diminishing returns effect” of rising average variable cost. At higher levels of output, the opposite is true and average total cost rises. At point M, corresponding to an output of three cases of salsa per day, average total cost is at its minimum level, the minimum average total cost. Cost of case $140 120 100 80 60 40 20 0 Average total cost, ATC Minimum average
total cost 10 Quantity of salsa (cases) Minimum-cost output To help our understanding of why the average total cost curve is U-shaped, Table 55.2 breaks average total cost into its two underlying components, average fixed cost and average variable cost. Average fixed cost, or AFC, is fixed cost divided by the quantity of output, also known as the fixed cost per unit of output. For example, if Selena’s Gourmet Salsas produces 4 cases of salsa, average fixed cost is $108/4 = $27 per case. Average variable cost, or AVC, is variable cost divided by the quantity of output, also known as variable cost per unit of output. At an output of 4 cases, average variable cost is $192/4 = $48 per case. Writing these in the form of equations: (55-4) AFC = Fixed cost Quantity of output = FC Q AVC = Variable cost Quantity of output = VC Q Average total cost is the sum of average fixed cost and average variable cost; it has a U shape because these components move in opposite directions as output rises. Average fixed cost falls as more output is produced because the numerator (the fixed cost) is a fixed number but the denominator (the quantity of output) increases as more is produced. Another way to think about this relationship is that, as more output is produced, the fixed cost is spread over more units of output; the end result is that the A U-shaped average total cost curve falls at low levels of output and then rises at higher levels. Average fixed cost is the fixed cost per unit of output. Average variable cost is the variable cost per unit of output 553 fixed cost per unit of output—the average fixed cost—falls. You can see this effect in the fourth column of Table 55.2: average fixed cost drops continuously as output increases. Average variable cost, however, rises as output increases. As we’ve seen, this reflects diminishing returns to the variable input: each additional unit of output adds more to variable cost than the previous unit because increasing amounts of the variable input are required to make another unit. So increasing output has two opposing effects on average total cost—the “spreading effect” and the “diminishing returns effect”: ■ The spreading effect. The larger the output, the greater the quantity of output over which fixed cost is spread, leading to lower average fixed cost. ■ The diminishing returns effect. The larger the output, the
greater the amount of variable input required to produce additional units, leading to higher average variable cost. At low levels of output, the spreading effect is very powerful because even small increases in output cause large reductions in average fixed cost. So at low levels of output, the spreading effect dominates the diminishing returns effect and causes the average total cost curve to slope downward. But when output is large, average fixed cost is already quite small, so increasing output further has only a very small spreading effect. Diminishing returns, however, usually grow increasingly important as output rises. As a result, when output is large, the diminishing returns effect dominates the spreading effect, causing the average total cost curve to slope upward. At the bottom of the U-shaped average total cost curve, point M in Figure 55.3, the two effects exactly balance each other. At this point average total cost is at its minimum level, the minimum average total cost. Figure 55.4 brings together in a single picture the four other cost curves that we have derived from the total cost curve for Selena’s Gourmet Salsas: the marginal cost curve (MC), the average total cost curve (ATC), the average variable cost curve (AVC), and the average fixed cost curve (AFC). All are based on the information in Tables 55.1 and 55.2. As before, cost is measured on the vertical axis and the quantity of output is measured on the horizontal axis 55.4 Marginal Cost and Average Cost Curves for Selena’s Gourmet Salsas Here we have the family of cost curves for Selena’s Gourmet Salsas: the marginal cost curve (MC), the average total cost curve (ATC ), the average variable cost curve (AVC ), and the average fixed cost curve (AFC ). Note that the average total cost curve is U-shaped and the marginal cost curve crosses the average total cost curve at the bottom of the U, point M, corresponding to the minimum average total cost from Table 55.2 and Figure 55.3. Cost of case $250 200 150 100 50 M MC ATC AVC AFC 10 Quantity of salsa (cases) Minimum-cost output 554 Let’s take a moment to note some features of the various cost curves. First of all, marginal cost slopes upward—the result of diminishing returns that make an additional unit of output more costly to produce than the one before. Average variable cost also slopes upward—again, due to diminishing returns
—but is flatter than the marginal cost curve. This is because the higher cost of an additional unit of output is averaged across all units, not just the additional unit, in the average variable cost measure. Meanwhile, average fixed cost slopes downward because of the spreading effect. Finally, notice that the marginal cost curve intersects the average total cost curve from below, crossing it at its lowest point, point M in Figure 55.4. This last feature is our next subject of study. Minimum Average Total Cost For a U-shaped average total cost curve, average total cost is at its minimum level at the bottom of the U. Economists call the quantity of output that corresponds to the minimum average total cost the minimum-cost output. In the case of Selena’s Gourmet Salsas, the minimum-cost output is three cases of salsa per day. In Figure 55.4, the bottom of the U is at the level of output at which the marginal cost curve crosses the average total cost curve from below. Is this an accident? No—it reflects general principles that are always true about a firm’s marginal cost and average total cost curves: ■ At the minimum-cost output, average total cost is equal to marginal cost. ■ At output less than the minimum-cost output, marginal cost is less than average total cost and average total cost is falling. ■ And at output greater than the minimum-cost output, marginal cost is greater than average total cost and average total cost is rising. To understand these principles, think about how your grade in one course—say, a 3.0 in physics—affects your overall grade point average. If your GPA before receiving that grade was more than 3.0, the new grade lowers your average. Similarly, if marginal cost—the cost of producing one more unit—is less than average total cost, producing that extra unit lowers average total cost. This is shown in Figure 55.5 by the movement from A1 to A2. In this case, the marginal cost of producing The minimum-cost output is the quantity of output at which average total cost is lowest—it corresponds to the bottom of the U-shaped average total cost curve Cost of unit f i g u r e 55.5 The Relationship Between the Average Total Cost and the Marginal Cost Curves To see why the marginal cost curve (MC ) must cut through the average total cost curve at the minimum average total cost (point M ), corresponding to the minimum-cost output,
we look at what happens if marginal cost is different from average total cost. If marginal cost is less than average total cost, an increase in output must reduce average total cost, as in the movement from A1 to A 2. If marginal cost is greater than average total cost, an increase in output must increase average total cost, as in the movement from B1 to B2. If marginal cost is above average total cost, average total cost is rising. MC MCH ATC B2 A1 A2 MCL M B1 If marginal cost is below average total cost, average total cost is falling. Quantity 555 an additional unit of output is low, as indicated by the point MCL on the marginal cost curve. When the cost of producing the next unit of output is less than average total cost, increasing production reduces average total cost. So any quantity of output at which marginal cost is less than average total cost must be on the downward-sloping segment of the U. But if your grade in physics is more than the average of your previous grades, this new grade raises your GPA. Similarly, if marginal cost is greater than average total cost, producing that extra unit raises average total cost. This is illustrated by the movement from B1 to B2 in Figure 55.5, where the marginal cost, MCH, is higher than average total cost. So any quantity of output at which marginal cost is greater than average total cost must be on the upward-sloping segment of the U. Finally, if a new grade is exactly equal to your previous GPA, the additional grade neither raises nor lowers that average—it stays the same. This corresponds to point M in Figure 55.5: when marginal cost equals average total cost, we must be at the bottom of the U because only at that point is average total cost neither falling nor rising. Does the Marginal Cost Curve Always Slope Upward? Up to this point, we have emphasized the importance of diminishing returns, which lead to a marginal product curve that always slopes downward and a marginal cost curve that always slopes upward. In practice, however, economists believe that marginal cost curves often slope downward as a firm increases its production from zero up to some low level, sloping upward only at higher levels of production: marginal cost curves look like the curve labeled MC in Figure 55.6. This initial downward slope occurs because a firm often finds that, when it starts with only a very small number of workers, employing more workers and expanding output allows its workers to specialize in various
tasks. This, in turn, lowers the firm’s marginal cost as it expands output. For example, one individual producing salsa would have to perform all the tasks involved: selecting and preparing the ingredients, mixing the salsa, bottling and labeling it, packing it into cases, and so on. As more workers are employed, they can divide the tasks, with each worker specializing in one or a few aspects of salsa-making. This specialization leads to increasing returns to the hiring of additional workers and results in a marginal cost curve that initially slopes downward. f i g u r e 55.6 More Realistic Cost Curves A realistic marginal cost curve has a “swoosh” shape. Starting from a very low output level, marginal cost often falls as the firm increases output. That’s because hiring additional workers allows greater specialization of their tasks and leads to increasing returns. Once specialization is achieved, however, diminishing returns to additional workers set in and marginal cost rises. The corresponding average variable cost curve is now U-shaped, like the average total cost curve. Cost of unit 2.... but diminishing returns set in once the beneﬁts from specialization are exhausted and marginal cost rises. MC ATC AVC 1. Increasing specialization leads to lower marginal cost,... Quantity 556 But once there are enough workers to have completely exhausted the benefits of further specialization, diminishing returns to labor set in and the marginal cost curve changes direction and slopes upward. So typical marginal cost curves actually have the “swoosh” shape shown by MC in Figure 55.6. For the same reason, average variable cost curves typically look like AVC in Figure 55.6: they are U-shaped rather than strictly upward sloping. However, as Figure 55.6 also shows, the key features we saw from the example of Selena’s Gourmet Salsas remain true: the average total cost curve is U-shaped, and the marginal cost curve passes through the point of minimum average total cost. M o d u l e 55 AP R e v i e w Solutions appear at the back of the book. Check Your Understanding 1. Alicia’s Apple Pies is a roadside business. Alicia must pay $9.00 in rent each day. In addition, it costs her $1.00 to produce the first pie of the day, and each subsequent pie costs 50% more to produce than the one before. For example, the second pie costs $1
.00 × 1.5 = $1.50 to produce, and so on. a. Calculate Alicia’s marginal cost, variable cost, average fixed cost, average variable cost, and average total cost as her daily pie output rises from 0 to 6. (Hint: The variable cost of two pies is just the marginal cost of the first pie, plus the marginal cost of the second, and so on.) Tackle the Test: Multiple-Choice Questions 1. When a firm is producing zero output, total cost equals a. zero. b. variable cost. fixed cost. c. d. average total cost. e. marginal cost. 2. Which of the following statements is true? I. Marginal cost is the change in total cost generated by one additional unit of output. II. Marginal cost is the change in variable cost generated by one additional unit of output. III. The marginal cost curve must cross the minimum of the average total cost curve. a. I only b. II only III only c. d. I and II only I, II, and III e. 3. Which of the following is correct? a. AVC is the change in total cost generated by one additional unit of output. b. MC = TC/Q c. The average cost curve crosses at the minimum of the marginal cost curve. b. Indicate the range of pies for which the spreading effect dominates and the range for which the diminishing returns effect dominates. c. What is Alicia’s minimum-cost output? Explain why making one more pie lowers Alicia’s average total cost when output is lower than the minimum-cost output. Similarly, explain why making one more pie raises Alicia’s average total cost when output is greater than the minimum-cost output. d. The AFC curve slopes upward. e. AVC = ATC − AFC 4. The slope of the total cost curve equals a. variable cost. b. average variable cost. c. average total cost. d. average fixed cost. e. marginal cost. 5. Q 0 1 2 3 4 5 VC $0 20 50 90 140 200 TC $40 60 90 130 180 240 On the basis of the data in the table above, what is the marginal cost of the third unit of output? a. 40 b. 50 c. 60 d. 90 e. 130 557 2. Draw a correctly labeled graph showing a firm with an upward sloping MC curve and typically shaped ATC, AVC, and
AFC curves. Tackle the Test: Free-Response Questions 1. Use the information in the table below to answer the following questions. VC Q $0 0 20 1 50 2 90 3 140 4 200 5 a. What is the firm’s level of fixed cost? Explain how you TC $40 60 90 130 180 240 know. b. Draw one correctly labeled graph showing the firm’s marginal and average total cost curves. Answer (6 points) Cost of unit 60 50 40 30 20 0 MC ATC 1 2 3 4 5 Quantity 1 point: FC = $40 1 point: We can identify the fixed cost as $40 because when the firm is not producing, it still incurs a cost of $40. This could only be the result of a fixed cost because variable cost is zero when output is zero. 1 point: Graph with correct labels (“Cost of unit” on vertical axis; “Quantity” on horizontal axis) 1 point: Upward sloping MC curve plotted according to data, labeled “MC” 1 point: U-shaped ATC curve plotted according to the provided data, labeled“ATC” 1 point: MC curve crossing at minimum of ATC curve (Note: We have simplified this graph by drawing smooth lines between discrete points. If we had drawn the MC curve as a step function instead, the MC curve would have crossed the ATC curve exactly at its minimum point.) 558 What you will learn in this Module: • Why a firm’s costs may differ between the short run and the long run • How a firm can enjoy economies of scale Module 56 Long-Run Costs and Economies of Scale Up to this point, we have treated fixed cost as completely outside the control of a firm because we have focused on the short run. But all inputs are variable in the long run: this means that in the long run, even “fixed cost” may change. In the long run, in other words, a firm’s fixed cost becomes a variable it can choose. For example, given time, Selena’s Gourmet Salsas can acquire additional food-preparation equipment or dispose of some of its existing equipment. In this module, we will examine how a firm’s costs behave in the short run and in the long run. We will also see that the firm will choose its fixed cost in the long run based on the level of output it expects to produce. Short-Run
versus Long-Run Costs Let’s begin by supposing that Selena’s Gourmet Salsas is considering whether to acquire additional food-preparation equipment. Acquiring additional machinery will affect its total cost in two ways. First, the firm will have to either rent or buy the additional equipment; either way, that will mean a higher fixed cost in the short run. Second, if the workers have more equipment, they will be more productive: fewer workers will be needed to produce any given output, so variable cost for any given output level will be reduced. The table in Figure 56.1 on the next page shows how acquiring an additional machine affects costs. In our original example, we assumed that Selena’s Gourmet Salsas had a fixed cost of $108. The left half of the table shows variable cost as well as total cost and average total cost assuming a fixed cost of $108. The average total cost curve for this level of fixed cost is given by ATC1 in Figure 56.1. Let’s compare that to a situation in which the firm buys additional food-preparation equipment, doubling its fixed cost to $216 but reducing its variable cost at any given level of output. The right half of the table shows the firm’s variable cost, total cost, and average total cost with this higher level of fixed cost. The average total cost curve corresponding to $216 in fixed cost is given by ATC2 in Figure 56.1 559 f i g u r e 56.1 Choosing the Level of Fixed Cost for Selena’s Gourmet Salsas There is a trade-off between higher fixed cost and lower variable cost for any given output level, and vice versa. ATC 1 is the average total cost curve corresponding to a fixed cost of $108; it leads to lower fixed cost and higher variable cost. ATC 2 is the average total cost curve corresponding to a higher fixed cost of $216 but lower variable cost. At low output levels, at 4 or fewer cases of salsa per day, ATC 1 lies below ATC 2: average total cost is lower with only $108 in fixed cost. But as output goes up, average total cost is lower with the higher amount of fixed cost, $216: at more than 4 cases of salsa per day, ATC 2 lies below ATC 1. Cost of case At low output levels, low ﬁxed cost yields lower average total cost.
At high output levels, high ﬁxed cost yields lower average total cost. $250 200 150 100 50 0 1 2 3 4 5 6 7 Low ﬁxed cost ATC1 ATC2 High ﬁxed cost 8 9 Quantity of salsa (cases) 10 Low ﬁxed cost (FC = $108) High ﬁxed cost (FC = $216) Quantity of salsa (cases) High variable cost 1 2 3 4 5 6 7 8 9 10 $ 12 48 108 192 300 432 588 768 972 1,200 Average total cost of case ATC1 $120.00 78.00 72.00 75.00 81.60 90.00 99.43 109.50 120.00 130.80 Low variable cost $ 6 24 54 96 150 216 294 384 486 600 Total cost $222 240 270 312 366 432 510 600 702 816 Average total cost of case ATC2 $222.00 120.00 90.00 78.00 73.20 72.00 72.86 75.00 78.00 81.60 Total cost $ 120 156 216 300 408 540 696 876 1,080 1,308 From the figure you can see that when output is small, 4 cases of salsa per day or fewer, average total cost is smaller when Selena forgoes the additional equipment and maintains the lower fixed cost of $108: ATC1 lies below ATC2. For example, at 3 cases per day, average total cost is $72 without the additional machinery and $90 with the additional machinery. But as output increases beyond 4 cases per day, the firm’s average total cost is lower if it acquires the additional equipment, raising its fixed cost to $216. For example, at 9 cases of salsa per day, average total cost is $120 when fixed cost is $108 but only $78 when fixed cost is $216. Why does average total cost change like this when fixed cost increases? When output is low, the increase in fixed cost from the additional equipment outweighs the reduction in variable cost from higher worker productivity—that is, there are too few units of output over which to spread the additional fixed cost. So if Selena plans to produce 4 or fewer cases per day, she would be better off choosing the lower level of fixed cost, $108, to achieve a lower average total cost of production. When planned output is high, however, she should acquire the additional machinery.

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