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501 13.3 Competition and Collusion in the Airline Industry 501 13.4 Wal-Mart Stores’ Preemptive Investment Strategy 509 13.5 DuPont Deters Entry in the Titanium Dioxide Industry 514 13.6 Diaper Wars 515 13.7 Auctioning Legal Services 522 13.8 Internet Auctions 522 487 488 PART 3 • Market Structure and Competitive Strategy • game Situation in which players (participants) make strategic decisions that take into account each other’s actions and responses. • payoff Value associated with a possible outcome. • strategy Rule or plan of action for playing a game. • optimal strategy Strategy that maximizes a player’s expected payoff. • cooperative game Game in which participants can negotiate binding contracts that allow them to plan joint strategies. • noncooperative game Game in which negotiation and enforcement of binding contracts are not possible. for the bidders at the auction, the winner’s payoff is her consumer surplus—i.e., the value she places on the artwork less the amount she must pay. A key objective of game theory is to determine the optimal strategy for each player. A strategy is a rule or plan of action for playing the game. For our pricesetting firms, a strategy might be: “I’ll keep my price high as long as my competitors do the same, but once a competitor lowers his price, I’ll lower mine even more.” For a bidder at an auction, a strategy might be: “I’ll make a first bid of $2000 to convince the other bidders that I’m serious about winning, but I’ll drop out if other bidders push the price above $5000.” The optimal strategy for a player is the one that maximizes the expected payoff. We will focus on games involving players who are rational, in the sense that they think through the consequences of their actions. In essence, we are concerned with the following question: If I believe that my competitors are rational and act to maximize their own payoffs, how should I take their behavior into account when making my decisions? In real life, of course, you may encounter competitors who are irrational, or are less capable than you of thinking through the consequences of their actions. Nonetheless, a good place to start is by assuming that your competitors are just as rational and just as smart as you are.1 As we will see, taking competitors’ behavior into account is
not as simple as it might seem. Determining optimal strategies can be difficult, even under conditions of complete symmetry and perfect information (i.e., my competitors and I have the same cost structure and are fully informed about each others’ costs, about demand, etc.). Moreover, we will be concerned with more complex situations in which firms face different costs, different types of information, and various degrees and forms of competitive “advantage” and “disadvantage.” Noncooperative versus Cooperative Games The economic games that firms play can be either cooperative or noncooperative. In a cooperative game, players can negotiate binding contracts that allow them to plan joint strategies. In a noncooperative game, negotiation and enforcement of binding contracts are not possible. An example of a cooperative game is the bargaining between a buyer and a seller over the price of a rug. If the rug costs $100 to produce and the buyer values the rug at $200, a cooperative solution to the game is possible: An agreement to sell the rug at any price between $101 and $199 will maximize the sum of the buyer’s consumer surplus and the seller’s profit, while making both parties better off. Another cooperative game would involve two firms negotiating a joint investment to develop a new technology (assuming that neither firm would have enough know-how to succeed on its own). If the firms can sign a binding contract to divide the profits from their joint investment, a cooperative outcome that makes both parties better off is possible.2 An example of a noncooperative game is a situation in which two competing firms take each other’s likely behavior into account when independently 1When we asked, 80 percent of our students told us that they were smarter and more capable than most of their classmates. We hope that you don’t find it too much of a strain to imagine competing against people who are as smart and capable as you are. 2Bargaining over a rug is called a constant sum game because no matter what the selling price, the sum of consumer surplus and profit will be the same. Negotiating over a joint venture is a nonconstant sum game: The total profit that results from the venture will depend on the outcome of the negotiations (e.g., the resources that each firm devotes to the venture). CHAPTER 13 • Game Theory and Competitive Strategy 489 setting their prices. Each firm knows that by undercutting its competitor, it can capture more market share. But it also knows that in
doing so, it risks setting off a price war. Another noncooperative game is the auction mentioned above: Each bidder must take the likely behavior of the other bidders into account when determining an optimal bidding strategy. Note that the fundamental difference between cooperative and noncooperative games lies in the contracting possibilities. In cooperative games, binding contracts are possible; in noncooperative games, they are not. We will be concerned mostly with noncooperative games. Whatever the game, however, keep in mind the following key point about strategic decision making: It is essential to understand your opponent’s point of view and to deduce his or her likely responses to your actions. This point may seem obvious—of course, one must understand an opponent’s point of view. Yet even in simple gaming situations, people often ignore or misjudge opponents’ positions and the rational responses that those positions imply. HOW TO BUY A DOLLAR BILL Consider the following game devised by Martin Shubik.3 A dollar bill is auctioned, but in an unusual way. The highest bidder receives the dollar in return for the amount bid. However, the secondhighest bidder must also hand over the amount that he or she bid—and get nothing in return. If you were playing this game, how much would you bid for the dollar bill? Classroom experience shows that students often end up bidding more than a dollar for the dollar. In a typical scenario, one player bids 20 cents and another 30 cents. The lower bidder now stands to lose 20 cents but figures he can earn a dollar by raising his bid, and so bids 40 cents. The escalation continues until two players carry the bidding to a dollar against 90 cents. Now the 90-cent bidder has to choose between bidding $1.10 for the dollar or paying 90 cents to get nothing. Most often, he raises his bid, and the bidding escalates further. In some experiments, the “winning” bidder has ended up paying more than $3 for the dollar! How could intelligent students put themselves in this position? By failing to think through the likely response of the other players and the sequence of events it implies. In the rest of this chapter, we will examine simple games that involve pricing, advertising, and investment decisions. The games are simple in that, given some behavioral assumptions, we can determine the best strategy for each firm. But even for these simple games, we will find that the correct behavioral assumptions are not always easy to make. Often they
will depend on how the game is played (e.g., how long the firms stay in business, their reputations, etc.). Therefore, when reading this chapter, you should try to understand the basic issues involved in making strategic decisions. You should also keep in mind the importance of carefully assessing your opponent’s position and rational response to your actions, as Example 13.1 illustrates. 3Martin Shubik, Game Theory in the Social Sciences (Cambridge, MA: MIT Press, 1982). 490 PART 3 • Market Structure and Competitive Strategy E XAM PLE 13.1 ACQUIRING A COMPANY You represent Company A (the acquirer), which is considering acquiring Company T (the target).4 You plan to offer cash for all of Company T’s shares, but you are unsure what price to offer. The complication is this: The value of Company T—indeed, its viability—depends on the outcome of a major oil exploration project. If the project fails, Company T under current management will be worth nothing. But if it succeeds, Company T’s value under current management could be as high as $100/share. All share values between $0 and $100 are considered equally likely. It is well known, however, that Company T will be worth much more under the progressive management of Company A than under current management. In fact, whatever the ultimate value under current management, Company T will be worth 50 percent more under the management of Company A. If the project fails, Company T is worth $0/share under either management. If the exploration project generates a $50/share value under current management, the value under Company A will be $75/ share. Similarly, a $100/share value under Company T implies a $150/share value under Company A, and so on. You must determine what price Company A should offer for Company T’s shares. This offer must be made now—before the outcome of the exploration project is known. From all indications, Company T would be happy to be acquired by Company A— for the right price. You expect Company T to delay a decision on your bid until the exploration results are in and then accept or reject your offer before news of the drilling results reaches the press. Thus, you (Company A) will not know the results of the exploration project when submitting your price offer, but Company T will know the results when deciding whether to accept your offer. Also, Company T will accept any offer by
Company A that is greater than the (per share) value of the company under current management. As the representative of Company A, you are considering price offers in the range $0/share (i.e., making no offer at all) to $150/share. What price per share should you offer for Company T’s stock? Note: The typical response—to offer between $50 and $75 per share—is wrong. The correct answer to this problem appears at the end of this chapter, but we urge you to try to answer it on your own. 13.2 Dominant Strategies How can we decide on the best strategy for playing a game? How can we determine a game’s likely outcome? We need something to help us determine how the rational behavior of each player will lead to an equilibrium solution. Some strategies may be successful if competitors make certain choices but fail if they make other choices. Other strategies, however, may be successful regardless of what competitors do. We begin with the concept of a dominant strategy—one that is optimal no matter what an opponent does. The following example illustrates this in a duopoly setting. Suppose Firms A and B sell competing products and are deciding whether to undertake advertising campaigns. Each firm will be affected by its competitor’s decision. The possible outcomes of the game are illustrated by the payoff matrix in Table 13.1. (Recall that the payoff matrix summarizes the possible outcomes of the game; the first number in each cell is the payoff to A and the second is the payoff to B.) Observe that if both firms advertise, Firm A will earn a profit of 10 and Firm B a profit of 5. If Firm A advertises and Firm B does not, Firm A will earn 15 and Firm B zero. The table also shows the outcomes for the other two possibilities. 4This is a revised version of an example designed by Max Bazerman for a course at MIT. • dominant strategy Strategy that is optimal no matter what an opponent does. In §12.4, we explain that a payoff matrix is a table showing the payoffs to each player given her decision and the decision of her competitor. CHAPTER 13 • Game Theory and Competitive Strategy 491 TABLE 13.1 PAYOFF MATRIX FOR ADVERTISING GAME Firm B Advertise Don’t advertise Firm A Advertise Don’t advertise 10, 5 6, 8 15, 0 10, 2 • equilibrium in dominant strategies Outcome of a game in which each firm
is doing the best it can regardless of what its competitors are doing. What strategy should each firm choose? First consider Firm A. It should clearly advertise because no matter what firm B does, Firm A does best by advertising. If Firm B advertises, A earns a profit of 10 if it advertises but only 6 if it doesn’t. If B does not advertise, A earns 15 if it advertises but only 10 if it doesn’t. Thus advertising is a dominant strategy for Firm A. The same is true for Firm B: No matter what firm A does, Firm B does best by advertising. Therefore, assuming that both firms are rational, we know that the outcome for this game is that both firms will advertise. This outcome is easy to determine because both firms have dominant strategies. When every player has a dominant strategy, we call the outcome of the game an equilibrium in dominant strategies. Such games are straightforward to analyze because each player’s optimal strategy can be determined without worrying about the actions of the other players. Unfortunately, not every game has a dominant strategy for each player. To see this, let’s change our advertising example slightly. The payoff matrix in Table 13.2 is the same as in Table 13.1 except for the bottom right-hand corner—if neither firm advertises, Firm B will again earn a profit of 2, but Firm A will earn a profit of 20. (Perhaps Firm A’s ads are expensive and largely designed to refute Firm B’s claims, so by not advertising, Firm A can reduce its expenses considerably.) Now Firm A has no dominant strategy. Its optimal decision depends on what Firm B does. If Firm B advertises, Firm A does best by advertising; but if Firm B does not advertise, Firm A also does best by not advertising. Now suppose both firms must make their decisions at the same time. What should Firm A do? To answer this, Firm A must put itself in Firm B’s shoes. What decision is best from Firm B’s point of view, and what is Firm B likely to do? The answer is clear: Firm B has a dominant strategy—advertise, no matter what Firm A does. (If Firm A advertises, B earns 5 by advertising and 0 by not advertising; if A doesn’t advertise, B earns 8 if it advertises and 2 if it doesn’t.) Therefore, Firm A can conclude that Firm B will advertise. This means that
Firm A should advertise (and thereby earn 10 instead of 6). The logical outcome of the game is that both firms will advertise because Firm A is doing the best it can given Firm B’s decision; and Firm B is doing the best it can given Firm A’s decision. TABLE 13.2 MODIFIED ADVERTISING GAME Firm B Advertise Don’t advertise Firm A Advertise Don’t advertise 10, 5 6, 8 15, 0 20, 2 492 PART 3 • Market Structure and Competitive Strategy In §12.2, we explain that the Cournot equilibrium is a Nash equilibrium in which each firm correctly assumes how much its competitor will produce. 13.3 The Nash Equilibrium Revisited To determine the likely outcome of a game, we have been seeking “self-enforcing,” or “stable” strategies. Dominant strategies are stable, but in many games, one or more players do not have a dominant strategy. We therefore need a more general equilibrium concept. In Chapter 12, we introduced the concept of a Nash equilibrium and saw that it is widely applicable and intuitively appealing.5 Recall that a Nash equilibrium is a set of strategies (or actions) such that each player is doing the best it can given the actions of its opponents. Because each player has no incentive to deviate from its Nash strategy, the strategies are stable. In the example shown in Table 13.2, the Nash equilibrium is that both firms advertise: Given the decision of its competitor, each firm is satisfied that it has made the best decision possible, and so has no incentive to change its decision. In Chapter 12, we used the Nash equilibrium to study output and pricing by oligopolistic firms. In the Cournot model, for example, each firm sets its own output while taking the outputs of its competitors as fixed. We saw that in a Cournot equilibrium, no firm has an incentive to change its output unilaterally because each firm is doing the best it can given the decisions of its competitors. Thus a Cournot equilibrium is a Nash equilibrium.6 We also examined models in which firms choose price, taking the prices of their competitors as fixed. Again, in the Nash equilibrium, each firm is earning the largest profit it can given the prices of its competitors, and thus has no incentive to change its price. It is helpful to compare the concept of a Nash equilibrium with that of an equilibrium in dominant strategies: Dominant Strategies: Nash Equilibrium: I’m doing
the best I can no matter what you do. You’re doing the best you can no matter what I do. I’m doing the best I can given what you are doing. You’re doing the best you can given what I am doing. Note that a dominant strategy equilibrium is a special case of a Nash equilibrium. In the advertising game of Table 13.2, there is a single Nash equilibrium—both firms advertise. In general, a game need not have a single Nash equilibrium. Sometimes there is no Nash equilibrium, and sometimes there are several (i.e., several sets of strategies are stable and self-enforcing). A few more examples will help to clarify this. THE PRODUCT CHOICE PROBLEM Consider the following “product choice” problem. Two breakfast cereal companies face a market in which two new variations of cereal can be successfully introduced—provided that each variation is introduced by only one firm. There is a market for a new “crispy” cereal and a 5Our discussion of the Nash equilibrium, and of game theory in general, is at an introductory level. For a more in-depth discussion of game theory and its applications, see James W. Friedman, Game Theory with Applications to Economics (New York: Oxford University Press, 1990); Drew Fudenberg and Jean Tirole, Game Theory (Cambridge, MA: MIT Press, 1991); and Avinash Dixit, David Reiley, Jr., and Susan Skeath, Games of Strategy, 3rd ed. (New York: Norton, 2009). 6A Stackelberg equilibrium is also a Nash equilibrium. In the Stackelberg model, however, the rules of the game are different: One firm makes its output decision before its competitor does. Under these rules, each firm is doing the best it can given the decision of its competitor. CHAPTER 13 • Game Theory and Competitive Strategy 493 TABLE 13.3 PRODUCT CHOICE PROBLEM Firm 1 Crispy Sweet Firm 2 Sweet 10, 10 5, 5 Crispy 5, 5 10, 10 market for a new “sweet” cereal, but each firm has the resources to introduce only one new product. The payoff matrix for the two firms might look like the one in Table 13.3. In this game, each firm is indifferent about which product it produces—so long as it does not introduce the same product as its competitor. If coordination were possible, the firms would probably agree to
divide the market. But what if the firms must behave noncooperatively? Suppose that somehow—perhaps through a news release—Firm 1 indicates that it is about to introduce the sweet cereal, and that Firm 2 (after hearing this) announces its plan to introduce the crispy one. Given the action that it believes its opponent to be taking, neither firm has an incentive to deviate from its proposed action. If it takes the proposed action, its payoff is 10, but if it deviates—and its opponent’s action remains unchanged—its payoff will be - 5. Therefore, the strategy set given by the bottom left-hand corner of the payoff matrix is stable and constitutes a Nash equilibrium: Given the strategy of its opponent, each firm is doing the best it can and has no incentive to deviate. Note that the upper right-hand corner of the payoff matrix is also a Nash equilibrium, which might occur if Firm 1 indicated that it was about to produce the crispy cereal. Each Nash equilibrium is stable because once the strategies are chosen, no player will unilaterally deviate from them. However, without more information, we have no way of knowing which equilibrium (crispy/sweet vs. sweet/crispy) is likely to result—or if either will result. Of course, both firms have a strong incentive to reach one of the two Nash equilibria—if they both introduce the same type of cereal, they will both lose money. The fact that the two firms are not allowed to collude does not mean that they will not reach a Nash equilibrium. As an industry develops, understandings often evolve as firms “signal” each other about the paths the industry is to take. THE BEACH LOCATION GAME Suppose that you (Y) and a competitor (C) plan to sell soft drinks on a beach this summer. The beach is 200 yards long, and sunbathers are spread evenly across its length. You and your competitor sell the same soft drinks at the same prices, so customers will walk to the closest vendor. Where on the beach will you locate, and where do you think your competitor will locate? If you think about this for a minute, you will see that the only Nash equilibrium calls for both you and your competitor to locate at the same spot in the center of the beach (see Figure 13.1). To see why, suppose your competitor located at some other point (A), which is three quarters of the way to the end of the beach. In
that case, you would no longer want to locate in the center; you would locate near your competitor, just to the left. You would thus capture nearly three-fourths of all sales, while your competitor got only the remaining fourth. This outcome is not an equilibrium because your competitor would then want to move to the center of the beach, and you would do the same. 494 PART 3 • Market Structure and Competitive Strategy 0 Ocean Y C Beach A 200 yards Figure 13.1 BEACH LOCATION GAME You (Y) and a competitor (C) plan to sell soft drinks on a beach. If sunbathers are spread evenly across the beach and will walk to the closest vendor, the two of you will locate next to each other at the center of the beach. This is the only Nash equilibrium. If your competitor located at point A, you would want to move until you were just to the left, where you could capture three-fourths of all sales. But your competitor would then want to move back to the center, and you would do the same. The “beach location game” can help us understand a variety of phenomena. Have you ever noticed how, along a two- or three-mile stretch of road, two or three gas stations or several car dealerships will be located close to each other? Likewise, as a U.S. presidential election approaches, the Democratic and Republican candidates typically move close to the center as they define their political positions. Maximin Strategies The concept of a Nash equilibrium relies heavily on individual rationality. Each player’s choice of strategy depends not only on its own rationality, but also on the rationality of its opponent. This can be a limitation, as the example in Table 13.4 shows. In this game, two firms compete in selling file-encryption software. Because both firms use the same encryption standard, files encrypted by one firm’s software can be read by the other’s—an advantage for consumers. Nonetheless, Firm 1 has a much larger market share. (It entered the market earlier and its software has a better user interface.) Both firms are now considering an investment in a new encryption standard. Note that investing is a dominant strategy for Firm 2 because by doing so it will do better regardless of what Firm 1 does. Thus Firm 1 should expect Firm 2 to invest. In this case, Firm 1 would also do better by investing (and earning TABLE 13.4 MAXIMIN STRATEGY Firm 1 Don’t
invest Invest Firm 2 Don’t invest 0, 0 100, 0 Invest 10, 10 20, 10 CHAPTER 13 • Game Theory and Competitive Strategy 495 $20 million) than by not investing (and losing $10 million). Clearly the outcome (invest, invest) is a Nash equilibrium for this game, and you can verify that it is the only Nash equilibrium. But note that Firm 1’s managers had better be sure that Firm 2’s managers understand the game and are rational. If Firm 2 should happen to make a mistake and fail to invest, it would be extremely costly to Firm 1. (Consumer confusion over incompatible standards would arise, and Firm 1, with its dominant market share, would lose $100 million.) If you were Firm 1, what would you do? If you tend to be cautious—and if you are concerned that the managers of Firm 2 might not be fully informed or rational—you might choose to play “don’t invest.” In that case, the worst that can happen is that you will lose $10 million; you no longer have a chance of losing $100 million. This strategy is called a maximin strategy because it maximizes the minimum gain that can be earned. If both firms used maximin strategies, the outcome would be that Firm 1 does not invest and Firm 2 does. A maximin strategy is conservative, but it is not profit-maximizing. (Firm 1, for example, loses $10 million rather than earning $20 million.) Note that if Firm 1 knew for certain that Firm 2 was using a maximin strategy, it would prefer to invest (and earn $20 million) instead of following its own maximin strategy of not investing. MAXIMIZING THE EXPECTED PAYOFF If Firm 1 is unsure about what Firm 2 will do but can assign probabilities to each feasible action for Firm 2, it could instead use a strategy that maximizes its expected payoff. Suppose, for example, that Firm 1 thinks that there is only a 10-percent chance that Firm 2 will not invest. In that case, Firm 1’s expected payoff from investing is (.1)(100) + (.9)(20) = $8 million. Its expected payoff if it doesn’t invest is (.1)(0) + (.9)(10) = $9 million. In this case, Firm 1 should invest. On the other hand, suppose Firm 1 thinks that the probability that Firm 2 will not invest is 30
percent. Then Firm 1’s expected payoff from investing is (.3) (100) + (.7)(20) = $16 million, while its expected payoff from not investing is (.3)(0) + (.7)(10) = $7 million. Thus Firm 1 will choose not to invest. You can see that Firm 1’s strategy depends critically on its assessment of the probabilities of different actions by Firm 2. Determining these probabilities may seem like a tall order. However, firms often face uncertainty (over market conditions, future costs, and the behavior of competitors), and must make the best decisions they can based on probability assessments and expected values. THE PRISONERS’ DILEMMA What is the Nash equilibrium for the prisoners’ dilemma discussed in Chapter 12? Table 13.5 shows the payoff matrix for the prisoners’ dilemma. Recall that the ideal outcome is one in which neither prisoner confesses, so that both get two years in prison. Confessing, however, is a dominant strategy for each prisoner—it yields a higher payoff regardless of the strategy of the other prisoner. Dominant strategies are also maximin strategies. TABLE 13.5 PRISONERS’ DILEMMA Prisoner A Confess Don’t confess Prisoner B Confess 5, 5 10, 1 Don’t confess 1, 10 2, 2 • maximin strategy Strategy that maximizes the minimum gain that can be earned. For a review of expected value, see §5.1, where it is defined as a weighted average of the payoffs associated with all possible outcomes, with the probabilities of each outcome used as weights. 496 PART 3 • Market Structure and Competitive Strategy • pure strategy Strategy in which a player makes a specific choice or takes a specific action. • mixed strategy Strategy in which a player makes a random choice among two or more possible actions, based on a set of chosen probabilities. Therefore, the outcome in which both prisoners confess is both a Nash equilibrium and a maximin solution. Thus, in a very strong sense, it is rational for each prisoner to confess. *Mixed Strategies In all of the games that we have examined so far, we have considered strategies in which players make a specific choice or take a specific action: advertise or don’t advertise, set a price of $4 or a price of $6, and so on. Strategies of this kind are called pure strategies. There are games, however, in which a pure strategy is
not the best way to play. MATCHING PENNIES An example is the game of “Matching Pennies.” In this game, each player chooses heads or tails and the two players reveal their coins at the same time. If the coins match (i.e., both are heads or both are tails), Player A wins and receives a dollar from Player B. If the coins do not match, Player B wins and receives a dollar from Player A. The payoff matrix is shown in Table 13.6. Note that there is no Nash equilibrium in pure strategies for this game. Suppose, for example, that Player A chose the strategy of playing heads. Then Player B would want to play tails. But if Player B plays tails, Player A would also want to play tails. No combination of heads or tails leaves both players satisfied—one player or the other will always want to change strategies. Although there is no Nash equilibrium in pure strategies, there is a Nash equilibrium in mixed strategies: strategies in which players make random choices among two or more possible actions, based on sets of chosen probabilities. In this game, for example, Player A might simply flip the coin, thereby playing heads with probability 1/2 and playing tails with probability 1/2. In fact, if Player A follows this strategy and Player B does the same, we will have a Nash equilibrium: Both players will be doing the best they can given what the opponent is doing. Note that although the outcome is random, the expected payoff is 0 for each player. It may seem strange to play a game by choosing actions randomly. But put yourself in the position of Player A and think what would happen if you followed a strategy other than just flipping the coin. Suppose you decided to play heads. If Player B knows this, she would play tails and you would lose. Even if Player B didn’t know your strategy, if the game were played repeatedly, she could eventually discern your pattern of play and choose a strategy that countered it. Of course, you would then want to change your strategy—which is why this would not be a Nash equilibrium. Only if you and your opponent both choose heads or tails randomly with probability 1/2 would neither of you have any incentive to change strategies. (You can check that the use of different probabilities, say 3/4 for heads and 1/4 for tails, does not generate a Nash equilibrium.) TABLE 13.6 MATCHING PENNIES Player A Heads Tails Player B Heads 1, 1
1, 1 Tails 1, 1 1, 1 CHAPTER 13 • Game Theory and Competitive Strategy 497 TABLE 13.7 THE BATTLE OF THE SEXES Jim Wrestling Opera Joan Wrestling Opera 2, 1 0, 0 0, 0 1, 2 One reason to consider mixed strategies is that some games (such as “Matching Pennies”) do not have any Nash equilibria in pure strategies. It can be shown, however, that once we allow for mixed strategies, every game has at least one Nash equilibrium.7 Mixed strategies, therefore, provide solutions to games when pure strategies fail. Of course, whether solutions involving mixed strategies are reasonable will depend on the particular game and players. Mixed strategies are likely to be very reasonable for “Matching Pennies,” poker, and other such games. A firm, on the other hand, might not find it reasonable to believe that its competitor will set its price randomly. THE BATTLE OF THE SEXES Some games have Nash equilibria both in pure strategies and in mixed strategies. An example is “The Battle of the Sexes,” a game that you might find familiar. It goes like this. Jim and Joan would like to spend Saturday night together but have different tastes in entertainment. Jim would like to go to the opera, but Joan prefers mud wrestling. As the payoff matrix in Table 13.7 shows, Jim would most prefer to go to the opera with Joan, but prefers watching mud wrestling with Joan to going to the opera alone, and similarly for Joan. First, note that there are two Nash equilibria in pure strategies for this game— the one in which Jim and Joan both watch mud wrestling, and the one in which they both go to the opera. Joan, of course, would prefer the first of these outcomes and Jim the second, but both outcomes are equilibria—neither Jim nor Joan would want to change his or her decision, given the decision of the other. This game also has an equilibrium in mixed strategies: Joan chooses wrestling with probability 2/3 and opera with probability 1/3, and Jim chooses wrestling with probability 1/3 and opera with probability 2/3. You can check that if Joan uses this strategy, Joan cannot do better with any other strategy, and vice versa.8 The outcome is random, and Jim and Joan will each have an expected payoff of 2/3. Should we expect Jim and Joan to use these mixed strategies? Unless they’re very
risk loving or in some other way a strange couple, probably not. By agreeing to either form of entertainment, each will have a payoff of at least 1, which exceeds the expected payoff of 2/3 from randomizing. In this game 7More precisely, every game with a finite number of players and a finite number of actions has at least one Nash equilibrium. For a proof, see David M. Kreps, A Course in Microeconomic Theory (Princeton, NJ: Princeton University Press, 1990), p. 409. 8Suppose Joan randomizes, letting p be the probability of wrestling and (1 - p) the probability of opera. Because Jim is using probabilities of 1/3 for wrestling and 2/3 for opera, the probability that both will choose wrestling is (1/3)p, and the probability that both will choose opera is (2/3)(1 - p). Thus, Joan’s expected payoff is 2(1/3)p + 1(2/3)(1 - p) = (2/3)p + 2/3 - (2/3)p = 2/3. This payoff is independent of p, so Joan cannot do better in terms of expected payoff no matter what she chooses. 498 PART 3 • Market Structure and Competitive Strategy • repeated game Game in which actions are taken and payoffs received over and over again. as in many others, mixed strategies provide another solution, but not a very realistic one. Hence, for the remainder of this chapter we will focus on pure strategies. 13.4 Repeated Games We saw in Chapter 12 that in oligopolistic markets, firms often find themselves in a prisoners’ dilemma when making output or pricing decisions. Can firms find a way out of this dilemma, so that oligopolistic coordination and cooperation (whether explicit or implicit) could prevail? To answer this question, we must recognize that the prisoners’ dilemma, as we have described it so far, is limited: Although some prisoners may have only one opportunity in life to confess or not, most firms set output and price over and over again. In real life, firms play repeated games: Actions are taken and payoffs received over and over again. In repeated games, strategies can become more complex. For example, with each repetition of the prisoners’ dilemma, each firm can develop a reputation about its own behavior and can study the behavior of its competitors. How does repetition change the likely outcome of the game? Suppose you are Firm 1 in the
prisoners’ dilemma illustrated by the payoff matrix in Table 13.8. If you and your competitor both charge a high price, you will both make a higher profit than if you both charged a low price. However, you are afraid to charge a high price because if your competitor charges a low price, you will lose money and, to add insult to injury, your competitor will get rich. But suppose this game is repeated over and over again—for example, you and your competitor simultaneously announce your prices on the first day of every month. Should you then play the game differently, perhaps changing your price over time in response to your competitor’s behavior? In an interesting study, Robert Axelrod asked game theorists to come up with the best strategy they could think of to play this game in a repeated manner.9 (A possible strategy might be: “I’ll start off with a high price, then lower my price. But then if my competitor lowers his price, I’ll raise mine for a while before lowering it again, etc.”) Then, in a computer simulation, Axelrod played these strategies off against one another to see which worked best. TIT-FOR-TAT STRATEGY As you would expect, any given strategy would work better against some strategies than it would against others. The objective, however, was to find the strategy that was most robust—that would TABLE 13.8 PRICING PROBLEM Firm 2 Low price High price Firm 1 Low price High price 10, 10 50, 100 100, 50 50, 50 9See Robert Axelrod, The Evolution of Cooperation (New York: Basic Books, 1984). CHAPTER 13 • Game Theory and Competitive Strategy 499 • tit-for-tat strategy Repeated-game strategy in which a player responds in kind to an opponent’s previous play, cooperating with cooperative opponents and retaliating against uncooperative ones. work best on average against all, or almost all, other strategies. The result was surprising. The strategy that worked best was an extremely simple tit-for-tat strategy: I start out with a high price, which I maintain so long as you continue to “cooperate” and also charge a high price. As soon as you lower your price, however, I follow suit and lower mine. If you later decide to cooperate and raise your price again, I’ll immediately raise my price as well. Why does this tit-for-tat strategy work best
? In particular, can I expect that using the tit-for-tat strategy will induce my competitor to behave cooperatively (and charge a high price)? INFINITELY REPEATED GAME Suppose the game is infinitely repeated. In other words, my competitor and I repeatedly set prices month after month, forever. Cooperative behavior (i.e., charging a high price) is then the rational response to a tit-for-tat strategy. (This assumes that my competitor knows, or can figure out, that I am using a tit-for-tat strategy.) To see why, suppose that in one month my competitor sets a low price and undercuts me. In that month he will make a large profit. But my competitor knows that the following month I will set a low price, so that his profit will fall and will remain low as long as we both continue to charge a low price. Because the game is infinitely repeated, the cumulative loss of profits that results must outweigh any short-term gain that accrued during the first month of undercutting. Thus, it is not rational to undercut. In fact, with an infinitely repeated game, my competitor need not even be sure that I am playing tit-for-tat to make cooperation its own rational strategy. Even if my competitor believes there is only some chance that I am playing tit-for-tat, he will still find it rational to start by charging a high price and maintain it as long as I do. Why? With infinite repetition of the game, the expected gains from cooperation will outweigh those from undercutting. This will be true even if the probability that I am playing tit-for-tat (and so will continue cooperating) is small. FINITE NUMBER OF REPETITIONS Now suppose the game is repeated a finite number of times—say, N months. (N can be large as long as it is finite.) If my competitor (Firm 2) is rational and believes that I am rational, he will reason as follows: “Because Firm 1 is playing tit-for-tat, I (Firm 2) cannot undercut—that is, until the last month. I should undercut the last month because then I can make a large profit that month, and afterward the game is over, so Firm 1 cannot retaliate. Therefore, I will charge a high price until the last month, and then I will charge a low price.” However, since I (Firm 1) have also figured this
out, I also plan to charge a low price in the last month. Of course, Firm 2 can figure this out as well, and therefore knows that I will charge a low price in the last month. But then what about the next-to-last month? Because there will be no cooperation in the last month, anyway, Firm 2 figures that it should undercut and charge a low price in the next-to-last month. But, of course, I have figured this out too, so I also plan to charge a low price in the next-to-last month. And because the same reasoning applies to each preceding month, the game unravels: The only rational outcome is for both of us to charge a low price every month. TIT-FOR-TAT IN PRACTICE Since most of us do not expect to live forever, the unravelling argument would seem to make the tit-for-tat strategy of little 500 PART 3 • Market Structure and Competitive Strategy value, leaving us stuck in the prisoners’ dilemma. In practice, however, tit- for-tat can sometimes work and cooperation can prevail. There are two primary reasons. First, most managers don’t know how long they will be competing with their rivals, and this also serves to make cooperative behavior a good strategy. If the end point of the repeated game is unknown, the unraveling argument that begins with a clear expectation of undercutting in the last month no longer applies. As with an infinitely repeated game, it will be rational to play tit-for-tat. Second, my competitor might have some doubt about the extent of my rationality. Suppose my competitor thinks (and he need not be certain) that I am playing tit-for-tat. He also thinks that perhaps I am playing titfor-tat “blindly,” or with limited rationality, in the sense that I have failed to work out the logical implications of a finite time horizon as discussed above. My competitor thinks, for example, that perhaps I have not figured out that he will undercut me in the last month, so that I should also charge a low price in the last month, and so on. “Perhaps,” thinks my competitor, “Firm 1 will play tit-for-tat blindly, charging a high price as long as I charge a high price.” Then (if the time horizon is long enough), it is rational for my competitor to maintain a high price until the last
month (when he will undercut me). Note that we have stressed the word perhaps. My competitor need not be sure that I am playing tit-for-tat “blindly,” or even that I am playing tit-for-tat at all. Just the possibility can make cooperative behavior a good strategy (until near the end) if the time horizon is long enough. Although my competitor’s conjecture about how I am playing the game might be wrong, cooperative behavior is profitable in expected value terms. With a long time horizon, the sum of current and future profits, weighted by the probability that the conjecture is correct, can exceed the sum of profits from price competition, even if my competitor is the first to undercut. After all, if I am wrong and my competitor charges a low price, I can shift my strategy at the cost of only one period’s profit—a minor cost in light of the substantial profit that I can make if we both choose to set a high price. Thus, in a repeated game, the prisoners’ dilemma can have a cooperative outcome. In most markets, the game is in fact repeated over a long and uncertain length of time, and managers have doubts about how “perfectly rationally” they and their competitors operate. As a result, in some industries, particularly those in which only a few firms compete over a long period under stable demand and cost conditions, cooperation prevails, even though no contractual arrangements are made. (The water meter industry, discussed below, is an example.) In many other industries, however, there is little or no cooperative behavior. Sometimes cooperation breaks down or never begins because there are too many firms. More often, failure to cooperate is the result of rapidly shifting demand or cost conditions. Uncertainties about demand or costs make it difficult for the firms to reach an implicit understanding of what cooperation should entail. (Remember that an explicit understanding, arrived at through meetings and discussions, could lead to an antitrust violation.) Suppose, for example, that cost differences or different beliefs about demand lead one firm to conclude that cooperation means charging $50 while a second firm thinks it means $40. If the second firm charges $40, the first firm might view that as a grab for market share and respond in tit-for-tat fashion with a $35 price. A price war could then develop. CHAPTER 13 • Game Theory and Competitive Strategy 501 EXAM PLE 13.2 OLIGOPOLISTIC COOPERATION IN THE
WATER METER INDUSTRY For some four decades, almost all the water meters sold in the United States have been produced by four American companies: Rockwell International, Badger Meter, Neptune Water Meter Company, and Hersey Products.10 Most buyers of water meters are municipal water utilities, who install the meters in residential and commercial establishments in order to measure water consumption and bill consumers accordingly. Because the cost of meters is a small part of the total cost of providing water, utilities are concerned mainly that the meters be accurate and reliable. Price is not a primary issue, and demand is very inelastic. Demand is also very stable; because every residence or business must have a water meter, demand grows slowly along with the population. In addition, utilities tend to have long-standing relationships with suppliers and are reluctant to shift from one to another. Because any new entrant will find it difficult to lure customers from existing firms, this creates a barrier to entry. Substantial economies of scale create a second barrier to entry: To capture a significant share of the market, a new entrant must invest in a large factory. This requirement virtually precludes entry by new firms. With inelastic and stable demand and little threat of entry by new firms, the existing four firms could earn substantial monopoly profits if they set prices cooperatively. If, on the other hand, they compete aggressively, with each firm cutting price to increase its own share of the market, profits would fall to nearly competitive levels. The firms thus face a prisoners’ dilemma. Can cooperation prevail? It can and has prevailed. Remember that the same four firms have been playing a repeated game for decades. Demand has been stable and predictable, and over the years, the firms have been able to assess their own and each other’s costs. In this situation, titfor-tat strategies work well: It pays each firm to cooperate as long as its competitors are cooperating. As a result, the four firms operate as though they were members of a country club. There is rarely an attempt to undercut price, and each firm appears satisfied with its share of the market. While the business may appear dull, it is certainly profitable. All four firms have been earning returns on their investments that far exceed those in more competitive industries. EXAM PLE 13.3 COMPETITION AND COLLUSION IN THE AIRLINE INDUSTRY In March 1983, American Airlines proposed that all airlines adopt a uniform fare schedule based on mileage. The rate per mile would depend on the
length of the trip, with the lowest rate of 15 cents per mile for trips over 2500 miles, higher rates for shorter trips, and the highest rate, 53 cents per mile, for trips under 250 miles. For example, a one-way coach ticket from Boston to Chicago, a distance of 932 miles, would cost 10This example is based in part on Nancy Taubenslag, “Rockwell International,” Harvard Business School Case No. 9-383-019, July 1983. In the late 1980s, Rockwell split up and sold its water meter division to British Tyre & Rubber, which later became part of Invensys, a multinational company that markets water meters in the United States under the Foxboro brand. Hersey became a subsidiary of Mueller Products in 1999, but still sells meters under the Hersey name. Badger and Neptune continue to operate as stand-alone companies. 502 PART 3 • Market Structure and Competitive Strategy $233 (based on a rate of 25 cents per mile for trips between 751 and 1000 miles). This proposal would have done away with the many different fares (some heavily discounted) then available. The cost of a ticket from one city to another would depend only on the number of miles between those cities. As a senior vice-president of American Airlines said, “The new streamlined fare structure will help reduce fare confusion.” Most other major airlines reacted favorably to the plan and began to adopt it. A vice-president of TWA said, “It’s a good move. It’s very businesslike.” United Airlines quickly announced that it would adopt the plan on routes where it competes with American, which included most of its system, and TWA and Continental said that they would adopt it for all their routes.11 Why did American propose this plan, and what made it so attractive to the other airlines? Was it really to “help reduce fare confusion”? No, the aim was to reduce price competition and achieve a collusive pricing arrangement. Prices had been driven down by competitive undercutting, as airlines competed for market share. And as Robert Crandall had learned less than a year earlier, fixing prices over the telephone is illegal. Instead, the companies would implicitly fix prices by agreeing to use the same fare-setting formula. The plan failed, a victim of the prisoners’ dilemma. Only two weeks after the plan was announced and adopted by most airlines, Pan Am, which was dissatisfied with its
small share of the U.S. market, dropped its fares. American, United, and TWA, afraid of losing their own shares of the market, quickly dropped their fares to match Pan Am. The price-cutting continued, and fortunately for consumers, the plan was soon dead. American Airlines introduced another simplified, four-tier fare structure in April 1992, which was quickly adopted by most major carriers. But it, too, soon fell victim to competitive discounts. In May 1992, Northwest Airlines announced a “kids fly free” program, and American responded with a summer half-price sale, which other carriers matched. As a result, the airline industry lost billions. Why is airline pricing so intensively competitive? Airlines plan route capacities two or more years into the future, but they make pricing decisions over short horizons—month by month or even week by week. In the short run, the marginal cost of adding passengers to a flight is very low—essentially the cost of a soft drink and a bag of peanuts. Each airline, therefore, has an incentive to lower fares in order to capture passengers from its competitors. In addition, the demand for air travel often fluctuates unpredictably. Such factors as these stand in the way of implicit price cooperation. Thus, aggressive competition has continued to be the rule in the airline industry. In fact, pricing has become even more competitive in recent years. First, discount airlines—such as Southwest and JetBlue—have attracted millions of priceconscious consumers and forced the major carriers to cut fares. Second, during periods of sluggish demand, airlines are compelled to reduce prices in order to attract consumers. Finally, Internet services such as Expedia, Orbitz, and Travelocity have promoted “fare shopping” by online consumers and encouraged more competitive pricing. These developments have forced several major airlines into bankruptcy and resulted in record losses for the industry. 13.5 Sequential Games • sequential game Game in which players move in turn, responding to each other’s actions and reactions. In most of the games we have discussed so far, both players move at the same time. In the Cournot model of duopoly, for example, both firms set output at the same time. In sequential games, players move in turn. The Stackelberg model discussed in Chapter 12 is an example of a sequential game; one firm sets output before the other does. There are many other examples: an advertising decision 11“American to Base Fares on Mileage,” New York
Times, March 15, 1983; “Most Big Airlines Back American’s Fare Plan,” New York Times, March 17, 1983. CHAPTER 13 • Game Theory and Competitive Strategy 503 by one firm and the response by its competitor; entry-deterring investment by an incumbent firm and the decision whether to enter the market by a potential competitor; or a new government regulatory policy and the investment and output response of the regulated firms. We will look at a variety of sequential games in the remainder of this chapter. As we will see, they are often easier to analyze than games in which the players move at the same time. In a sequential game, the key is to think through the possible actions and rational reactions of each player. As a simple example, let’s return to the product choice problem first discussed in Section 13.3. This problem involves two companies facing a market in which two new variations of breakfast cereal can be successfully introduced as long as each firm introduces only one variation. This time, let’s change the payoff matrix slightly. As Table 13.9 shows, the new sweet cereal will inevitably be a better seller than the new crispy cereal, earning a profit of 20 rather than 10 (perhaps because consumers prefer sweet things to crispy things). Both new cereals will still be profitable, however, as long as each is introduced by only one firm. (Compare Table 13.9 with Table 13.3—page 493.) Suppose that both firms, in ignorance of each other’s intentions, must announce their decisions independently and simultaneously. In that case, both will probably introduce the sweet cereal—and both will lose money. Now suppose that Firm 1 can gear up its production faster and introduce its new cereal first. We now have a sequential game: Firm 1 introduces a new cereal, and then Firm 2 introduces one. What will be the outcome of this game? When making its decision, Firm 1 must consider the rational response of its competitor. It knows that whichever cereal it introduces, Firm 2 will introduce the other kind. Thus it will introduce the sweet cereal, knowing that Firm 2 will respond by introducing the crispy one. The Extensive Form of a Game Although this outcome can be deduced from the payoff matrix in Table 13.9, sequential games are sometimes easier to visualize if we represent the possible moves in the form of a decision tree. This representation is called the extensive form of a game and is shown in Figure 13.2. The figure shows the possible choices of Firm 1
(introduce a crispy or a sweet cereal) and the possible responses of Firm 2 to each of those choices. The resulting payoffs are given at the end of each branch. For example, if Firm 1 produces a crispy cereal and Firm 2 responds by also producing a crispy cereal, each firm will have a payoff of - 5. To find the solution to the extensive form game, work backward from the end. For Firm 1, the best sequence of moves is the one in which it earns 20 and Firm 2 earns 10. Thus it can deduce that it should produce the sweet cereal because Firm 2’s best response is then to produce the crispy cereal. TABLE 13.9 MODIFIED PRODUCT CHOICE PROBLEM Firm 1 Crispy Sweet Firm 2 Crispy −5, −5 20, 10 Sweet 10, 20 −5, −5 • extensive form of a game Representation of possible moves in a game in the form of a decision tree. 504 PART 3 • Market Structure and Competitive Strategy FIGURE 13.2 PRODUCT CHOICE GAME IN EXTENSIVE FORM Firm 1 Crispy Firm 2 Sweet Firm 2 Crispy Sweet Crispy Sweet 5, 5 10, 20 20, 10 5, 5 In §12.2, we explain that the Stackelberg model is an oligopoly model in which one firm sets its output before other firms do. Recall that in §12.2, we explain that in the Cournot model each firm treats the output of its competitors as fixed, and that all firms simultaneously decide how much to produce. The Advantage of Moving First In this product-choice game, there is a clear advantage to moving first: By introducing the sweet cereal, Firm 1 leaves Firm 2 little choice but to introduce the crispy one. This is much like the first-mover advantage that we saw in the Stackelberg model in Chapter 12. In that model, the firm that moves first can choose a large level of output, thereby giving its competitor little choice but to choose a small level. To clarify the nature of this first-mover advantage, it will be useful to review the Stackelberg model and compare it to the Cournot model in which both firms choose their outputs simultaneously. As in Chapter 12, we will use the example in which two duopolists face the market demand curve P = 30 - Q where Q is the total production, i.e., Q = Q1 + Q2. As before, we will also assume that both firms have zero marginal cost.
Recall that the Cournot equilibrium is then Q1 = Q2 = 10, so that P = 10 and each firm earns a profit of 100. Recall also that if the two firms colluded, they would set Q1 = Q2 = 7.5, so that P = 15 and each firm earns a profit of 112.50. Finally, recall from Section 12.3 that in the Stackelberg model, in which Firm 1 moves first, the outcome is Q1 = 15 and Q2 = 7.5, so that P = 7.50 and the firms’ profits are 112.50 and 56.25, respectively. These and a few other possible outcomes are summarized in the payoff matrix in Table 13.10. If both firms move simultaneously, the only solution to the game is that both produce 10 and earn 100. In this Cournot equilibrium each firm is doing the best it can given what its competitor is doing. If Firm 1 moves first, however, it knows that its decision will constrain Firm 2’s choice. Observe from the payoff matrix that if Firm 1 sets Q1 = 7.5, Firm 2’s best response will be TABLE 13.10 CHOOSING OUTPUT 7.5 Firm 2 10 15 7.5 112.50, 112.50 93.75, 125 56.25, 112.50 Firm 1 10 15 125, 93.75 100, 100 112.50, 56.25 75, 50 50, 75 0, 0 CHAPTER 13 • Game Theory and Competitive Strategy 505 to set Q2 = 10. This will give Firm 1 a profit of 93.75 and Firm 2 a profit of 125. If Firm 1 sets Q1 = 10, Firm 2 will set Q2 = 10, and both firms will earn 100. But if Firm 1 sets Q1 = 15, Firm 2 will set Q2 = 7.5, so that Firm 1 earns 112.50, and Firm 2 earns 56.25. Therefore, the most that Firm 1 can earn is 112.50, and it does so by setting Q1 = 15. Compared to the Cournot outcome, when Firm 1 moves first, it does better—and Firm 2 does much worse. 13.6 Threats, Commitments, and Credibility The product choice problem and the Stackelberg model are two examples of how a firm that moves first can create a fait accompli that gives it an advantage over its competitor. In
this section, we’ll take a broader look at the advantage that a firm can have by moving first. We’ll also consider what determines which firm goes first. We will focus on the following question: What actions can a firm take to gain advantage in the marketplace? For example, how might a firm deter entry by potential competitors, or induce existing competitors to raise prices, reduce output, or leave the market altogether? Recall that in the Stackelberg model, the firm that moved first gained an advantage by committing itself to a large output. Making a commitment— constraining its future behavior—is crucial. To see why, suppose that the first mover (Firm 1) could later change its mind in response to what Firm 2 does. What would happen? Clearly, Firm 2 would produce a large output. Why? Because it knows that Firm 1 will respond by reducing the output that it first announced. The only way that Firm 1 can gain a first-mover advantage is by committing itself. In effect, Firm 1 constrains Firm 2’s behavior by constraining its own behavior. The idea of constraining your own behavior to gain an advantage may seem paradoxical, but we’ll soon see that it is not. Let’s consider a few examples. First, let’s return once more to the product-choice problem shown in Table 13.9. The firm that introduces its new breakfast cereal first will do best. But which firm will introduce its cereal first? Even if both firms require the same amount of time to gear up production, each has an incentive to commit itself first to the sweet cereal. The key word is commit. If Firm 1 simply announces it will produce the sweet cereal, Firm 2 will have little reason to believe it. After all, Firm 2, knowing the incentives, can make the same announcement louder and more vociferously. Firm 1 must constrain its own behavior in some way that convinces Firm 2 that Firm 1 has no choice but to produce the sweet cereal. Firm 1 might launch an expensive advertising campaign describing the new sweet cereal well before its introduction, thereby putting its reputation on the line. Firm 1 might also sign a contract for the forward delivery of a large quantity of sugar (and make the contract public, or at least send a copy to Firm 2). The idea is for Firm 1 to commit itself to produce the sweet cereal. Commitment is a strategic move that will induce Firm 2 to make the decision that Firm 1 wants it
to make—namely, to produce the crispy cereal. Why can’t Firm 1 simply threaten Firm 2, vowing to produce the sweet cereal even if Firm 2 does the same? Because Firm 2 has little reason to believe the threat—and can make the same threat itself. A threat is useful only if it is credible. The following example should help make this clear. 506 PART 3 • Market Structure and Competitive Strategy TABLE 13.11 PRICING OF COMPUTERS AND WORD PROCESSORS Firm 2 High price Low price Firm 1 High price Low price 100, 80 20, 0 80, 100 10, 20 Empty Threats Suppose Firm 1 produces personal computers that can be used both as word processors and to do other tasks. Firm 2 produces only dedicated word processors. As the payoff matrix in Table 13.11 shows, as long as Firm 1 charges a high price for its computers, both firms can make a good deal of money. Even if Firm 2 charges a low price for its word processors, many people will still buy Firm 1’s computers (because they can do so many other things), although some buyers will be induced by the price differential to buy the dedicated word processor instead. However, if Firm 1 charges a low price, Firm 2 will also have to charge a low price (or else make zero profit), and the profit of both firms will be significantly reduced. Firm 1 would prefer the outcome in the upper left-hand corner of the matrix. For Firm 2, however, charging a low price is clearly a dominant strategy. Thus the outcome in the upper right-hand corner will prevail (no matter which firm sets its price first). Firm 1 would probably be viewed as the “dominant” firm in this industry because its pricing actions will have the greatest impact on overall industry profits. Can Firm 1 induce Firm 2 to charge a high price by threatening to charge a low price if Firm 2 charges a low price? No, as the payoff matrix in Table 13.11 makes clear: Whatever Firm 2 does, Firm 1 will be much worse off if it charges a low price. As a result, its threat is not credible. Commitment and Credibility Sometimes firms can make threats credible. To see how, consider the following example. Race Car Motors, Inc., produces cars, and Far Out Engines, Ltd., produces specialty car engines. Far Out Engines sells most of its engines to Race Car Motors, and a few to a limited outside market. Nonetheless, it depends heavily on
Race Car Motors and makes its production decisions in response to Race Car’s production plans. We thus have a sequential game in which Race Car is the “leader.” It will decide what kind of cars to build, and Far Out Engines will then decide what kind of engines to produce. The payoff matrix in Table 13.12(a) shows the possible outcomes of this game. (Profits are in millions of dollars.) Observe that Race Car will do best by deciding to produce small cars. It knows that in response to this decision, Far Out will produce small engines, most of which Race Car will then buy. As a result, Far Out will make $3 million and Race Car $6 million. Far Out, however, would much prefer the outcome in the lower right-hand corner of the payoff matrix. If it could produce big engines, and if Race Car produced big cars and thus bought the big engines, it would make $8 million. (Race Car, however, would make only $3 million.) Can Far Out induce Race Car to produce big cars instead of small ones? CHAPTER 13 • Game Theory and Competitive Strategy 507 TABLE 13.12(a) PRODUCTION CHOICE PROBLEM Race Car Motors Small cars Big cars Far Out Engines Small engines Big engines 3, 6 1, 1 3, 0 8, 3 Suppose Far Out threatens to produce big engines no matter what Race Car does; suppose, too, that no other engine producer can easily satisfy the needs of Race Car. If Race Car believed Far Out’s threat, it would produce big cars: Otherwise, it would have trouble finding engines for its small cars and would earn only $1 million instead of $3 million. But the threat is not credible: Once Race Car responded by announcing its intentions to produce small cars, Far Out would have no incentive to carry out its threat. Far Out can make its threat credible by visibly and irreversibly reducing some of its own payoffs in the matrix, thereby constraining its own choices. In particular, Far Out must reduce its profits from small engines (the payoffs in the top row of the matrix). It might do this by shutting down or destroying some of its small engine production capacity. This would result in the payoff matrix shown in Table 13.12(b). Now Race Car knows that whatever kind of car it produces, Far Out will produce big engines. If Race Car produces the small cars, Far Out will sell the big engines as best it
can to other car producers and settle for making only $1 million. But this is better than making no profits by producing small engines. Because Race Car will have to look elsewhere for engines, its profit will also be lower ($1 million). Now it is clearly in Race Car’s interest to produce large cars. By taking an action that seemingly puts itself at a disadvantage, Far Out has improved its outcome in the game. Although strategic commitments of this kind can be effective, they are risky and depend heavily on having accurate knowledge of the payoff matrix and the industry. Suppose, for example, that Far Out commits itself to producing big engines but is surprised to find that another firm can produce small engines at a low cost. The commitment may then lead Far Out to bankruptcy rather than continued high profits. THE ROLE OF REPUTATION Developing the right kind of reputation can also give one a strategic advantage. Again, consider Far Out Engines’ desire to produce big engines for Race Car Motors’ big cars. Suppose that the managers of Far Out Engines develop a reputation for being irrational—perhaps downright crazy. They threaten to produce big engines no matter what Race Car Motors TABLE 13.12(b) MODIFIED PRODUCTION CHOICE PROBLEM Race Car Motors Small cars Big cars Far Out Engines Small engines Big engines 0, 6 1, 1 0, 0 8, 3 508 PART 3 • Market Structure and Competitive Strategy does (refer to Table 13.12a). Now the threat might be credible without any further action; after all, you can’t be sure that an irrational manager will always make a profit-maximizing decision. In gaming situations, the party that is known (or thought) to be a little crazy can have a significant advantage. Developing a reputation can be an especially important strategy in a repeated game. A firm might find it advantageous to behave irrationally for several plays of the game. This might give it a reputation that will allow it to increase its longrun profits substantially. Bargaining Strategy Our discussion of commitment and credibility also applies to bargaining problems. The outcome of a bargaining situation can depend on the ability of either side to take an action that alters its relative bargaining position. For example, consider two firms that are each planning to introduce one of two products which are complementary goods. As the payoff matrix in Table 13.13 shows, Firm 1 has a cost advantage over Firm 2 in producing A. Therefore, if both firms produce A, Firm 1 can maint
ain a lower price and earn a higher profit. Similarly, Firm 2 has a cost advantage over Firm 1 in producing product B. If the two firms could agree about who will produce what, the rational outcome would be the one in the upper right-hand corner: Firm 1 produces A, Firm 2 produces B, and both firms make profits of 50. Indeed, even without cooperation, this outcome will result whether Firm 1 or Firm 2 moves first or both firms move simultaneously. Why? Because producing B is a dominant strategy for Firm 2, so (A, B) is the only Nash equilibrium. Firm 1, of course, would prefer the outcome in the lower left-hand corner of the payoff matrix. But in the context of this limited set of decisions, it cannot achieve that outcome. Suppose, however, that Firms 1 and 2 are also bargaining over a second issue—whether to join a research consortium that a third firm is trying to form. Table 13.14 shows the payoff matrix for this decision problem. Clearly, the dominant strategy is for both firms to enter the consortium, thereby increasing profits to 40. Now suppose that Firm 1 links the two bargaining problems by announcing that it will join the consortium only if Firm 2 agrees to produce product A. In this case, it is indeed in Firm 2’s interest to produce A (with Firm 1 producing B) in return for Firm 1’s participation in the consortium. This example illustrates how combining issues in a bargaining agenda can sometimes benefit one side at the other’s expense. As another example, consider bargaining over the price of a house. Suppose I, as a potential buyer, do not want to pay more than $200,000 for a house that is actually worth $250,000 to me. The seller is willing to part with the house at any price above $180,000 but would like to receive the highest price she can. If I am the only bidder for the house, how can I make the seller think that I will walk away rather than pay more than $200,000? TABLE 13.13 PRODUCTION DECISION Firm 2 Produce A Produce B Firm 1 Produce A Produce B 40, 5 60, 40 50, 50 5, 45 CHAPTER 13 • Game Theory and Competitive Strategy 509 TABLE 13.14 DECISION TO JOIN CONSORTIUM Firm 2 Work alone Enter consortium Firm 1 Work alone Enter consortium 10, 10 20, 10 10, 20 40, 40 I might declare that I will never, ever
pay more than $200,000 for the house. But is such a promise credible? It may be if the seller knows that I have a reputation for toughness and that I have never reneged on a promise of this sort. But suppose I have no such reputation. Then the seller knows that I have every incentive to make the promise (making it costs nothing) but little incentive to keep it. (This will probably be our only business transaction together.) As a result, this promise by itself is not likely to improve my bargaining position. The promise can work, however, if it is combined with an action that gives it credibility. Such an action must reduce my flexibility—limit my options—so that I have no choice but to keep the promise. One possibility would be to make an enforceable bet with a third party—for example, “If I pay more than $200,000 for that house, I’ll pay you $60,000.” Alternatively, if I am buying the house on behalf of my company, the company might insist on authorization by the Board of Directors for a price above $200,000, and announce that the board will not meet again for several months. In both cases, my promise becomes credible because I have destroyed my ability to break it. The result is less flexibility—and more bargaining power. EXAM PLE 13.4 WAL-MART STORES’ PREEMPTIVE INVESTMENT STRATEGY Wal-Mart Stores, Inc., is an enormously successful chain of discount retail stores started by Sam Walton in 1969.12 Its success was unusual in the industry. During the 1960s and 1970s, rapid expansion by existing firms and the entry and expansion of new firms made discount retailing increasingly competitive. During the 1970s and 1980s, industry-wide profits fell, and large discount chains—including such giants as King’s, Korvette’s, Mammoth Mart, W. T. Grant, and Woolco—went bankrupt. Wal-Mart Stores, however, kept on growing and became even more profitable. By the end of 1985, Sam Walton was one of the richest people in the United States. How did Wal-Mart Stores succeed where others failed? The key was Wal-Mart’s expansion strategy. To charge less than ordinary department stores and small retail stores, discount stores rely on size, no frills, and high inventory turnover. Through the 1960s, the conventional wisdom held that a discount store could succeed
only in a city with a population of 100,000 or more. Sam Walton disagreed and decided to open his stores in small Southwestern towns; by 1970, there were 30 Wal-Mart stores in small towns in Arkansas, Missouri, 12This example is based in part on information in Pankaj Ghemawat, “Wal-Mart Stores’ Discount Operations,” Harvard Business School, 1986. 510 PART 3 • Market Structure and Competitive Strategy and Oklahoma. The stores succeeded because WalMart had created 30 “local monopolies.” Discount stores that had opened in larger towns and cities were competing with other discount stores, which drove down prices and profit margins. These small towns, however, had room for only one discount operation. Wal-Mart could undercut the nondiscount retailers and never had to worry that another discount store would open and compete with it. By the mid-1970s, other discount chains realized that Wal-Mart had a profitable strategy: Open a store in a small town that could support only one discount store and enjoy a local monopoly. There are a lot of small towns in the United States, so the issue became who would get to each town first. Wal-Mart now found itself in a preemption game of the sort illustrated by the payoff matrix in Table 13.15. As the matrix shows, if Wal-Mart enters a town but Company X does not, Wal-Mart will make 20 and Company X will make 0. Similarly, if Wal-Mart doesn’t enter but Company X does, Wal-Mart makes 0 and Company X makes 20. But if Wal-Mart and Company X both enter, they both lose 10. This game has two Nash equilibria—the lower left-hand corner and the upper right-hand corner. Which equilibrium results depends on who moves first. If Wal-Mart moves first, it can enter, knowing that the rational response of Company X will be not to enter, so that Wal-Mart will be assured of earning 20. The trick, therefore, is to preempt—to set up stores in other small towns quickly, before Company X (or Company Y or Z) can do so. That is exactly what Wal-Mart did. By 1986, it had 1009 stores in operation and was earning an annual profit of $450 million. And while other discount chains were going under, Wal-Mart continued to grow. By 1999, WalMart had become the world’s largest retailer, with 2454 stores in the United
States and another 729 stores in the rest of the world, and had annual sales of $138 billion. In recent years, Wal-Mart has continued to preempt other retailers by opening new discount stores, warehouse stores (such as Sam’s Club), and combination discount and grocery stores (WalMart Supercenters) all over the world. Wal-Mart has been especially aggressive in applying its preemption strategy in other countries. As of 2010, WalMart had about 4413 stores in the United States and about 4557 stores throughout Europe, Latin America, and Asia. Wal-Mart had also become the world’s largest private employer, with more than 2.1 million employees worldwide. TABLE 13.15 THE DISCOUNT STORE PREEMPTION GAME Wal-Mart Enter Don’t enter Company X Enter 10, 10 0, 20 Don’t enter 20, 0 0, 0 13.7 Entry Deterrence Barriers to entry, which are an important source of monopoly power and profits, sometimes arise naturally. For example, economies of scale, patents and licenses, or access to critical inputs can create entry barriers. However, firms themselves can sometimes deter entry by potential competitors. To deter entry, the incumbent firm must convince any potential competitor that entry will be unprofitable. To see how this might be done, put yourself in the position of an incumbent monopolist facing a prospective entrant, Firm X. Suppose that to enter the industry, Firm X will have to pay a (sunk) cost of $80 million to build a plant. You, of course, would like to induce Firm X to stay out of the CHAPTER 13 • Game Theory and Competitive Strategy 511 In §7.1, we explain that a sunk cost is an expenditure that has been made and cannot be recovered. TABLE 13.16(a) ENTRY POSSIBILITIES Incumbent High price (accommodation) Low price (warfare) Potential Entrant Enter Stay out 100, 20 70, 10 200, 0 130, 0 industry. If X stays out, you can continue to charge a high price and enjoy monopoly profits. As shown in the upper right-hand corner of the payoff matrix in Table 13.16(a), you would earn $200 million in profits. If Firm X does enter the market, you must make a decision. You can be “accommodating,” maintaining a high price in the hope that X will do the same. In that case,
you will earn only $100 million in profit because you will have to share the market. New entrant X will earn a net profit of $20 million: $100 million minus the $80 million cost of constructing a plant. (This outcome is shown in the upper left-hand corner of the payoff matrix.) Alternatively, you can increase your production capacity, produce more, and lower your price. The lower price will give you a greater market share and a $20 million increase in revenues. Increasing production capacity, however, will cost $50 million, reducing your net profit to $70 million. Because warfare will also reduce the entrant’s revenue by $30 million, it will have a net loss of $10 million. (This outcome is shown in the lower left-hand corner of the payoff matrix.) Finally, if Firm X stays out but you expand capacity and lower price nonetheless, your net profit will fall by $70 million (from $200 million to $130 million): the $50 million cost of the extra capacity and a $20 million reduction in revenue from the lower price with no gain in market share. Clearly this choice, shown in the lower right-hand corner of the matrix, would make no sense. If Firm X thinks you will be accommodating and maintain a high price after it has entered, it will find it profitable to enter and will do so. Suppose you threaten to expand output and wage a price war in order to keep X out. If X takes the threat seriously, it will not enter the market because it can expect to lose $10 million. The threat, however, is not credible. As Table 13.16(a) shows (and as the potential competitor knows), once entry has occurred, it will be in your best interest to accommodate and maintain a high price. Firm X’s rational move is to enter the market; the outcome will be the upper left-hand corner of the matrix. But what if you can make an irrevocable commitment that will alter your incentives once entry occurs—a commitment that will give you little choice but to charge a low price if entry occurs? In particular, suppose you invest the $50 million now, rather than later, in the extra capacity needed to increase output and engage in competitive warfare should entry occur. Of course, if you later maintain a high price (whether or not X enters), this added cost will reduce your payoff. We now have a new payoff matrix, as shown in Table 13.16(b). As a result of
your decision to invest in additional capacity, your threat to engage in competitive warfare is completely credible. Because you already have the additional capacity with which to wage war, you will do better in competitive warfare than you would by maintaining a high price. Because the potential competitor now knows that entry will result in warfare, it is rational for it to stay out of the market. Meanwhile, having deterred entry, you can maintain a high price and earn a profit of $150 million. 512 PART 3 • Market Structure and Competitive Strategy TABLE 13.16(b) ENTRY DETERRENCE High price (accommodation) Incumbent Low price (warfare) Potential Entrant Enter 50, 20 70, 10 Stay out 150, 0 130, 0 Can an incumbent monopolist deter entry without making the costly move of installing additional production capacity? Earlier we saw that a reputation for irrationality can bestow a strategic advantage. Suppose the incumbent firm has such a reputation. Suppose also that by means of vicious price-cutting, this firm has eventually driven out every entrant in the past, even though it incurred losses in doing so. Its threat might then be credible: The incumbent’s irrationality suggests to the potential competitor that it might be better off staying away. Of course, if the game described above were to be indefinitely repeated, then the incumbent might have a rational incentive to engage in warfare whenever entry actually occurs. Why? Because short-term losses from warfare might be outweighed by longer-term gains from preventing entry. Understanding this, the potential competitor might find the incumbent’s threat of warfare credible and decide to stay out. Now the incumbent relies on its reputation for being rational—and far-sighted—to provide the credibility needed to deter entry. The success of this strategy depends on the time horizon and the relative gains and losses associated with accommodation and warfare. We have seen that the attractiveness of entry depends largely on the way incumbents can be expected to react. In general, once entry has occurred, incumbents cannot be expected to maintain output at their pre-entry levels. Eventually, they may back off and reduce output, raising price to a new joint profit- maximizing level. Because potential entrants know this, incumbent firms must create a credible threat of warfare to deter entry. A reputation for irrationality can help. Indeed, this seems to be the basis for much of the entry-preventing behavior that goes on in actual markets. The potential entrant must consider that rational industry discipline can break down after entry
occurs. By fostering an image of irrationality and belligerence, an incumbent firm might convince potential entrants that the risk of warfare is too high.13 Strategic Trade Policy and International Competition We have seen how a preemptive investment can give a firm an advantage by creating a credible threat to potential competitors. In some situations, a preemptive investment—subsidized or otherwise encouraged by the government—can 13There is an analogy here to nuclear deterrence. Consider the use of a nuclear threat to deter the former Soviet Union from invading Western Europe during the Cold War. If it invaded, would the United States actually react with nuclear weapons, knowing that the Soviets would then respond in kind? Because it is not rational for the United States to react this way, a nuclear threat might not seem credible. But this assumes that everyone is rational; there is a reason to fear an irrational response by the United States. Even if an irrational response is viewed as very improbable, it can be a deterrent, given the costliness of an error. The United States can thus gain by promoting the idea that it might act irrationally, or that events might get out of control once an invasion occurs. This is the “rationality of irrationality.” See Thomas Schelling, The Strategy of Conflict (Harvard Univ. Press, 1980). CHAPTER 13 • Game Theory and Competitive Strategy 513 give a country an advantage in international markets and so be an important instrument of trade policy. Does this conflict with what you have learned about the benefits of free trade? In Chapter 9, for example, we saw how trade restrictions such as tariffs or quotas lead to deadweight losses. In Chapter 16 we go further and show how, in a general way, free trade between people (or between countries) is mutually beneficial. Given the virtues of free trade, how can government intervention in an international market ever be warranted? In certain situations, a country can benefit by adopting policies that give its domestic industries a competitive advantage. To see how this might occur, consider an industry with substantial economies of scale—one in which a few large firms can produce much more efficiently than many small ones. Suppose that by granting subsidies or tax breaks, the government can encourage domestic firms to expand faster than they would otherwise. This might prevent firms in other countries from entering the world market, so that the domestic industry can enjoy higher prices and greater sales. Such a policy works by creating a credible threat to potential entrants. Large domestic firms, taking advantage of scale economies, would be able to satisfy world
demand at a low price; if other firms entered, price would be driven below the point at which they could make a profit. THE COMMERCIAL AIRCRAFT MARKET As an example, consider the international market for commercial aircraft. The development and production of a new line of aircraft are subject to substantial economies of scale; it would not pay to develop a new aircraft unless a firm expected to sell many of them. Suppose that Boeing and Airbus (a European consortium that includes France, Germany, Britain, and Spain) are each considering developing a new aircraft. The ultimate payoff to each firm depends in part on what the other firm does. Suppose it is only economical for one firm to produce the new aircraft. Then the payoffs might look like those in Table 13.17(a).14 If Boeing has a head start in the development process, the outcome of the game is the upper right-hand corner of the payoff matrix. Boeing will produce a new aircraft, and Airbus, realizing that it will lose money if it does the same, will not. Boeing will then earn a profit of 100. European governments, of course, would prefer that Airbus produce the new aircraft. Can they change the outcome of this game? Suppose they commit to subsidizing Airbus and make this commitment before Boeing has committed itself to produce. If the European governments commit to a subsidy of 20 to Airbus if it produces the plane regardless of what Boeing does, the payoff matrix would change to the one in Table 13.17(b). TABLE 13.17(a) DEVELOPMENT OF A NEW AIRCRAFT Airbus Produce Don’t produce Boeing Produce Don’t produce 10, 10 0, 100 100, 0 0, 0 14This example is drawn from Paul R. Krugman, “Is Free Trade Passé?” Journal of Economic Perspectives 1 (Fall 1987): 131–44. 514 PART 3 • Market Structure and Competitive Strategy TABLE 13.17(b) DEVELOPMENT OF AIRCRAFT AFTER EUROPEAN SUBSIDY Airbus Produce Don’t produce Boeing Produce Don’t produce −10, 10 0, 120 100, 0 0, 0 Now Airbus will make money from a new aircraft whether or not Boeing produces one. Boeing knows that even if it commits to producing, Airbus will produce as well, and Boeing will lose money. Thus Boeing will decide not to produce, and the outcome will be the one in the lower left-hand corner of Table 13.17(
b). A subsidy of 20, then, changes the outcome from one in which Airbus does not produce and earns 0, to one in which it does produce and earns 120. Of this, 100 is a transfer of profit from the United States to Europe. From the European point of view, subsidizing Airbus yields a high return. European governments did commit to subsidizing Airbus, and during the 1980s, Airbus successfully introduced several new airplanes. The result, however, was not quite the one reflected in our simplified example. Boeing also introduced new airplanes (the 757 and 767 models) that were quite profitable. As commercial air travel grew, it became clear that both companies could profitably develop and sell new airplanes. Nonetheless, Boeing’s market share would have been much larger without the European subsidies to Airbus. One study estimated that those subsidies totalled $25.9 billion during the 1980s and found that Airbus would not have entered the market without them.15 This example shows how strategic trade policy can transfer profits from one country to another. Bear in mind, however, that a country that uses such a policy may provoke retaliation from its trading partners. If a trade war results, all countries can end up much worse off. The possibility of such an outcome must be considered before a nation adopts a strategic trade policy. E XAM PLE 13.5 DUPONT DETERS ENTRY IN THE TITANIUM DIOXIDE INDUSTRY Titanium dioxide is a whitener used in paints, paper, and other products. In the early 1970s, DuPont and National Lead each accounted for about a third of U.S. titanium dioxide sales; another seven firms produced the remainder. In 1972, DuPont was considering whether to expand capacity. The industry was changing, and with the right strategy, those changes might enable DuPont to capture more of the market and dominate the industry.16 Three factors had to be considered. First, although future demand for titanium dioxide was uncertain, it was expected to grow substantially. 15“Aid to Airbus Called Unfair in U.S. Study,” New York Times, September 8, 1990. 16This example is based on Pankaj Ghemawat, “Capacity Expansion in the Titanium Dioxide Industry,” Journal of Industrial Economics 33 (December 1984): 145–63; and P. Ghemawat, “DuPont in Titanium Dioxide,” Harvard Business School, Case No. 9–385–140, June 1986
. CHAPTER 13 • Game Theory and Competitive Strategy 515 Second, the government had announced that new environmental regulations would be imposed. Third, the prices of raw materials used to make titanium dioxide were rising. The new regulations and the higher input prices would have a major effect on production cost and give DuPont a cost advantage, both because its production technology was less sensitive to the change in input prices and because its plants were in areas that made disposal of corrosive wastes much less difficult than for other producers. Because of these cost changes, DuPont anticipated that National Lead and some other producers would have to shut down part of their capacity. DuPont’s competitors would in effect have to “reenter” the market by building new plants. Could DuPont deter them from taking this step? DuPont considered the following strategy: invest nearly $400 million in increased production capacity to try to capture 64 percent of the market by 1985. The production capacity that would be put on line would be much more than what was actually needed. The idea was to deter competitors from investing. Scale economies and movement down the learning curve would give DuPont a cost advantage. This would not only make it hard for other firms to compete, but would make credible the implicit threat that in the future, DuPont would fight rather than accommodate. The strategy was sensible and seemed to work for a few years. By 1975, however, things began to go awry. First, because demand grew by much less than expected, there was excess capacity industrywide. Second, because the environmental regulations were only weakly enforced, competitors did not have to shut down capacity as expected. Finally, DuPont’s strategy led to antitrust action by the Federal Trade Commission in 1978. The FTC claimed that DuPont was attempting to monopolize the market. DuPont won the case, but the decline in demand made its victory moot. EXAM PLE 13.6 DIAPER WARS For more than two decades, the disposable diaper industry in the United States has been dominated by two firms: Procter & Gamble, with an approximately 50-percent market share, and Kimberly-Clark, with another 30–40 percent.17 How do these firms compete? And why haven’t other firms been able to enter and take a significant share of this $5-billion-per-year market? Even though there are only two major firms, competition is intense. The competition occurs mostly in the form of cost-reducing innovation. The key to success is to
perfect the manufacturing process so that a plant can manufacture diapers in high volume and at low cost. This is not as simple as it might seem. Packing cellulose fluff for absorbency, adding an elastic gatherer, and binding, folding, and packaging the diapers—at a rate of about 3000 diapers per minute and at a cost of about 10 cents per diaper—requires an innovative, carefully designed, and finely tuned process. Furthermore, small technological improvements in the manufacturing process can result in a significant competitive advantage. If a firm can shave its production cost even slightly, it can reduce price and capture market share. As a result, both firms are forced to spend heavily on research and development (R&D) in a race to reduce cost. The payoff matrix in Table 13.18 illustrates this. If both firms spend aggressively on R&D, they can expect to maintain their current market shares. P&G will earn a profit of 40, and Kimberly-Clark (with a smaller market share) will earn 20. If neither firm spends money on R&D, their costs and prices will 17Procter & Gamble makes Pampers, Ultra Pampers, and Luvs. Kimberly-Clark has only one major brand, Huggies. 516 PART 3 • Market Structure and Competitive Strategy TABLE 13.18 COMPETING THROUGH R&D P&G R&D No R&D Kimberly-Clark R&D No R&D 40, 20 20, 60 80, 20 60, 40 remain constant and the money saved will become part of profits. P&G’s profit will increase to 60 and Kimberly-Clark’s to 40. However, if one firm continues to do R&D and the other doesn’t, the innovating firm will eventually capture most of its competitor’s market share. For example, if Kimberly-Clark does R&D and P&G does not, P&G can expect to lose 20 while Kimberly-Clark’s profit increases to 60. The two firms are therefore in a prisoners’ dilemma: Spending money on R&D is a dominant strategy for each firm. Why hasn’t cooperative behavior evolved? After all, the two firms have been competing in this market for years, and the demand for diapers is fairly stable. For several reasons, a prisoners’ dilemma involving R&D is particularly hard to resolve. First, it is difficult for a firm to monitor its competitor’s R
&D activities the way it can monitor price. Second, it can take several years to complete an R&D program that leads to a major product improvement. As a result, tit-for-tat strategies, in which both firms cooperate until one of them “cheats,” are less likely to work. A firm may not find out that its competitor has been secretly doing R&D until the competitor announces a new and improved product. By then it may be too late to gear up an R&D program of its own. The ongoing R&D expenditures by P&G and Kimberly-Clark also serve to deter entry. In addition to brand name recognition, these two firms have accumulated so much technological knowhow and manufacturing proficiency that they would have a considerable cost advantage over any firm just entering the market. Besides building new factories, an entrant would have to make a large investment in R&D to capture even a small share of the market. After it began producing, a new firm would have to continue to spend heavily on R&D to reduce its costs over time. Entry would be profitable only if P&G and Kimberly-Clark stop doing R&D, so that the entrant could catch up and eventually gain a cost advantage. But as we have seen, no rational firm would expect this to happen.18 • auction market Market in which products are bought and sold through formal bidding processes. *13.8 Auctions In this section, we examine auction markets—markets in which products are bought and sold through formal bidding processes.19 Auctions come in all sizes and shapes. They are often used for differentiated products, especially unique items such as art, antiques, and the rights to extract oil from a piece of land. In recent years, for example, the U.S. Treasury has relied on auctions to sell Treasury bills, the Federal Communications Commission has used auctions for the sale of portions of the electromagnetic spectrum for cellular telephone services, the International Olympic Committee has auctioned television rights, and the Department of Defense has used auctions to procure military equipment. Auctions like these have important advantages: They are likely to be less time-consuming than one-on-one bargaining, and they encourage competition among buyers in a way that increases the seller’s revenue. Why have auctions become so popular and so successful? The low cost of transacting is only part of the answer. Unlike sales in retail stores, auctions are 18Example 15.4 in Chapter 15 examines in more detail the profitability of
capital investment by a new entrant in the diaper market. 19There is a vast literature on auctions; for example, see Paul Milgrom, “Auctions and Bidding: A Primer,” Journal of Economic Perspectives (Summer 1989): 3–22; Avinash Dixit and Susan Skeath, Games of Strategy, 2nd ed. (New York: Norton, 2004); and Preston McAfee, Competitive Solutions: The Strategist’s Toolkit, Princeton University Press (2002): ch. 12. CHAPTER 13 • Game Theory and Competitive Strategy 517 inherently interactive, with many buyers competing to obtain an item of interest. This interaction can be particularly valuable for the sale of items such as artwork or sports memorabilia that are unique, and therefore do not have established market values. It can also be helpful for the sale of items that are not unique but whose value fluctuates over time. An example is the daily auctioning of fresh tuna at a Tokyo fish market.20 Each tuna is unique in size, shape, and quality, and consequently in value. If each transaction were carried out through rounds of bargaining and negotiation with potential buyers, it would be extremely time-consuming. Instead, sales occur every morning by means of an auction in which each tuna is sold to the highest bidder. This format creates large savings in transaction costs and thereby increases the efficiency of the market. The design of an auction, which involves choosing the rules under which it operates, greatly affects its outcome. A seller will usually want an auction format that maximizes the revenue from the sale of the product. On the other hand, a buyer collecting bids from a group of potential sellers will want an auction that minimizes the expected cost of the product. Auction Formats We will see that the choice of auction format can affect the seller’s auction revenue. Several different kinds of auction formats are widely used: 1. English (or oral) auction: The seller actively solicits progressively higher bids from a group of potential buyers. At each point, all participants are aware of the current high bid. The auction stops when no bidder is willing to surpass the current high bid; the item is then sold to the highest bidder at a price equal to the amount of the high bid. 2. Dutch auction The seller begins by offering the item at a relatively high price. If no potential buyer agrees to that price, the seller reduces the price by fixed amounts. The first buyer who accepts an offered price can buy the item
at that price. 3. Sealed-bid auction All bids are made simultaneously in sealed envelopes, and the winning bidder is the individual who has submitted the highest bid. The price paid by the winning bidder will vary, however, depending on the rules of the auction. In a first-price auction, the sales price is equal to the highest bid. In a second-price auction, the sales price is equal to the second-highest bid. Valuation and Information Suppose you want to sell a distinctive and valuable product such as a painting or a rare coin. Which type of auction is best for you? The answer depends on the preferences of the bidders and the information available to them. We consider two cases: 1. In private-value auctions each bidder knows his or her individual valuation or reservation price, and valuations differ from bidder to bidder. In addition, each bidder is uncertain about the value that other bidders place on the product. For example, I might value a signed Barry Bonds home run baseball very highly but not know that you value it less highly. 20John McMillan, Reinventing the Bazaar: A Natural History of Markets (New York, Norton, 2002). • English (or oral) auction Auction in which a seller actively solicits progressively higher bids from a group of potential buyers. • Dutch auction Auction in which a seller begins by offering an item at a relatively high price, then reduces it by fixed amounts until the item is sold. • sealed-bid auction Auction in which all bids are made simultaneously in sealed envelopes, the winning bidder being the individual who has submitted the highest bid. • first-price auction Auction in which the sales price is equal to the highest bid. • second-price auction Auction in which the sales price is equal to the second- highest bid. • private-value auction Auction in which each bidder knows his or her individual valuation of the object up for bid, with valuations differing from bidder to bidder. Recall from §11.2 that the reservation price is the maximum amount of money that an individual will pay for a product. 518 PART 3 • Market Structure and Competitive Strategy • common-value auction Auction in which the item has the same value to all bidders, but bidders do not know that value precisely and their estimates of it vary. 2. In common-value auctions, the item to be auctioned has approximately the same value to all bidders. Bidders, however, do not know precisely what that
value is—they can only estimate it, and bidders’ estimates will vary. For example, in an auction of an offshore oil reserve, the value of the reserve is the price of oil minus the extraction cost, times the amount of oil in the reserve. As a result, the value should be about the same for all bidders. However, bidders will not know the amount of oil or the extraction cost—they can only estimate these numbers. Because their estimates will differ, they might bid very different amounts to get the reserve. In reality, auctions can have both private-value and common-value elements. In the oil reserve auction, for example, there may be some private-value elements because different oil reserves may entail different extraction costs. However, to simplify matters we will separate the two. We begin our discussion with private-value auctions and then move on to common-value auctions. Private-Value Auctions In private-value auctions, bidders have different reservation prices for the offered item. We might suppose, for example, that in an auction for a signed Barry Bonds baseball, individuals’ reservation prices range from $1 (someone who doesn’t like baseball but is bidding just for fun) to $600 (a San Francisco Giants fan). Of course, if you are bidding for the baseball, you don’t know how many people will bid against you or what their bids will be. Whatever the auction format, each bidder must choose his or her bidding strategy. For an open English auction, this strategy is a choice of a price at which to stop bidding. For a Dutch auction, the strategy is the price at which the individual expects to make his or her only bid. For a sealed-bid auction, the strategy is the choice of bid to place in a sealed envelope. What are the payoffs in this bidding game? The payoff for winning is the difference between the winner’s reservation price and the price paid; the payoff for losing is zero. Given these payoffs, let’s examine bidding strategies and outcomes for different auction formats. We will begin by showing that English oral auctions and second-price sealed-bid auctions generate nearly identical outcomes. Let’s begin with the second-price sealed-bid auction. In this auction, bidding truthfully is a dominant strategy—there is no advantage to bidding below your reservation price. Why? Because the price you pay is based on the valuation of the second highest bidder, not on your own valuation
. Suppose that your reservation price is $100. If you bid below your reservation price—say, $80—you risk losing to the secondhighest bidder, who bids $85, when winning (at, say, $87) would have given you a positive payoff. If you bid above your reservation price—say $105—you risk winning but receiving a negative payoff. Similarly, in an English auction the dominant strategy is to continue bidding until the second person is unwilling to make a bid. Then the winning bid will be approximately equal to the reservation price of the second person. In any case, you should stop bidding when the bidding reaches your reservation price. Why? Because if you stop bidding at a point below your reservation price, you risk losing a positive payoff; if you continue beyond your reservation price, you will be guaranteed a negative payoff. How high will the bidding go? It will continue until the winning bid is approximately equal to the reservation price of the second-highest bidder. Likewise, in the sealed-bid auction the winning bid will equal the reservation price of the second-highest bidder. Thus, both auction CHAPTER 13 • Game Theory and Competitive Strategy 519 formats generate nearly identical outcomes. (The outcomes should differ in theory only by a dollar or two.) To illustrate, suppose that there are three bidders whose valuations are $50, $40, and $30, respectively, and furthermore the auctioneer and the bidders have complete information about these valuations. In an English auction, if your valuation was $50 you would offer a winning bid of $40.01 in order to win the bidding from the individual whose reservation price was $40.00. You would make the identical bid in a sealed-bid auction. Even in a world of incomplete information, we would expect similar results. Indeed, you know that as a seller, you should be indifferent between an oral English auction and a second-price sealed-bid auction, because bidders in each case have private values. Suppose that you plan to sell an item using a sealed-bid auction. Which should you choose, a first-price or a secondprice auction? You might think that the first-price auction is better because the payment is given by the highest rather than the second-highest bid. Bidders, however, are aware of this reasoning and will alter their bidding strategies accordingly: They will bid less in anticipation of paying the winning bid if they are successful. The second-price sealed-bid auction generates revenue equal
to the secondhighest reservation price. However, the revenue implications of a first-price sealed-bid auction for the seller are more complicated because the optimal strategy of bidders is more complex. The best strategy is to choose a bid that you believe will be equal to or slightly above the reservation price of the individual with the second-highest reservation price.21 Why? Because the winner must pay his or her bid, and it is never worth paying more than the second-highest reservation price. Thus, we see that the first-price and second-price sealed-bid auctions generate the same expected revenue. Common-Value Auctions Suppose that you and four other people participate in an oral auction to purchase a large jar of pennies, which will go to the winning bidder at a price equal to the highest bid. Each bidder can examine the jar but cannot open it and count the pennies. Once you have estimated the number of pennies in the jar, what is your optimal bidding strategy? This is a classic common-value auction, because the jar of pennies has the same value for all bidders. The problem for you and other bidders is the fact that the value is unknown. You might be tempted to do what many novices would do in this situation— bid up to your own estimate of the number of pennies in the jar, and no higher. This, however, is not the best way to bid. Remember that neither you nor the other bidders knows the number of pennies for certain. All of you have independently made estimates of the number, and those estimates are subject to error—some will be too high and some too low. Who, then, will be the winning bidder? If each bidder bids up to his or her estimate, the winning bidder is likely to be the person with the largest positive error—i.e., the person with the largest overestimate of the number of pennies. THE WINNER’S CURSE To appreciate this possibility, suppose that there are actually 620 pennies in the jar. Let’s say the bidders’ estimates are 540, 590, 615, 650, and 690. Finally, suppose that you are the bidder whose estimate is 21To be more exact, the best strategy is to choose a bid that you believe will be equal to or slightly above the second-highest expected reservation price conditional on your value being the highest. 520 PART 3 • Market Structure and Competitive Strategy • winner’
s curse Situation in which the winner of a commonvalue auction is worse off as a consequence of overestimating the value of the item and thereby overbidding. 690 and that you win the auction with a bid of $6.80. Should you be happy about winning? No—you will have paid $6.80 for $6.20 worth of pennies. You will have fallen prey to the winner’s curse: The winner of a common-value auction is often worse off than those who did not win because the winner was overly optimistic and, as a consequence, bid more for the item than it was actually worth. The winner’s curse can arise in any common-value auction, and bidders often fail to take it into account. Suppose, for example, that your house needs to be painted. You ask five companies to give you cost estimates for the job, telling each that you will accept the lowest estimate. Who will win the job? It will probably be the painter who has most seriously underestimated the amount of work involved. At first, that painter might be happy to have won the job, only later to realize that much more work is required than was anticipated. The same problem can arise for oil companies bidding for offshore oil reserves when the size of the reserve and cost of extraction are uncertain (so that the value of the reserve is uncertain). Unless the companies take the winner’s curse into account, the winning bidder is likely to win by overestimating the value of the reserve and will thus pay more than the reserve is worth. How should you take the winner’s curse into account when bidding for an item in a common-value auction? You must not only estimate the value of the item that you are bidding for, but also account for the fact that your estimate— and the estimates of the other bidders—are subject to error. To avoid the winner’s curse, you must reduce your maximum bid below your value estimate by an amount equal to the expected error of the winning bidder. The more precise your estimate, the less you need to reduce your bid. If you can’t assess the precision of your estimate directly, you can estimate the variation in the estimates of the other bidders. If there is a lot of disagreement among these bidders, it is likely that your estimate will be similarly imprecise. To measure the variation in bids, you can use the standard deviation of the estimates, which can be calculated using statistical methods.
Oil companies have been bidding for oil reserves for years, and thus are able to estimate this standard deviation quite well. They can thereby take the winner’s curse into account by reducing their maximum bids below their value estimates by an amount equal to the expected error of the winning bidder. As a result, oil companies rarely feel they have made a mistake after winning an auction. House painters, on the other hand, are often less sophisticated in their bidding decisions and suffer from the winner’s curse. The winner’s curse is more likely to be a problem in a sealed-bid auction than in a traditional English auction. In a traditional auction, if you are the only bidder who is overly optimistic, you can still win the bidding by offering only slightly more than the second-highest bidder. Therefore, for the winner’s curse to be a problem, at least two bidders must be overly optimistic. By contrast, in a sealed-bid auction, your optimism could encourage you to outbid everyone else by a substantial margin. Maximizing Auction Revenue Now let’s return to the question of auction design from the viewpoint of the seller. Here are some useful tips for choosing the best auction format. 1. In a private-value auction, you should encourage as many bidders as possible: Additional bidders increase the expected bid of the winner and the expected valuation of the second-highest bidder as well. CHAPTER 13 • Game Theory and Competitive Strategy 521 2. In a common-value auction, you should (a) use an open rather than a sealedbid auction because, as a general rule, an English (open) common-value auction will generate greater expected revenue than a sealed-bid auction; and (b) reveal information about the true value of the object being auctioned, thereby reducing concern about the winner’s curse and, consequently, encouraging more bidding. 3. In a private-value auction, set a minimum bid equal to or even somewhat higher than the value to you of keeping the good for future sale. This will protect against a loss if there are relatively few bidders who do not value the good very highly. Moreover, it could increase the size of the bids by signaling to buyers that the object is valuable. Having the opportunity to try again to sell the good if there is no minimum bid is obviously an advantage; however, it can be a disadvantage if failure to sell the good the first time is seen as a signal of low quality to bidd
ers in future auctions. Why use an open auction? Recall that in order to avoid the winner’s curse, each bidder in a common value auction will bid below his individual valuation. The greater the uncertainty about the true value of the object, the greater the likelihood of an overbid, and therefore the greater the incentive for the bidder to reduce his bid. (If the bidder is risk-averse, this effect will be magnified.) However, the bidder faces less uncertainty in an English auction than in a sealed-bid auction because he can observe the prices at which other bidders drop out of the competition—an advantage that provides information about their valuations. In short, when you provide more information to bidders, riskaverse bidders will be encouraged to bid more because they will be more confident that they can account for the possibility of a winner’s curse. Bidding and Collusion We have seen that sellers at auctions can obtain a significant share of the gains from trade by encouraging competition among buyers. It follows, therefore, that buyers can increase their bargaining power by reducing the number of bidders or the frequency of bidding. In some cases this can be accomplished legally through the formation of buying groups, but it may also be accomplished illegally through collusive agreements that violate the antitrust laws. Collusion among buyers is not easy, because even if an “agreement” is reached, individual buyers will have an incentive to cheat by increasing their bids at the last minute in order to obtain the desired item. However, repeated auctions allow for participants to penalize those that break from the agreement by outbidding the “cheater” again and again. Buyer collusion is more of a problem in open-bid auctions than in the case of sealed bids because open auctions offer the best opportunity for colluding bidders to detect and punish cheating. A well-known case of buyer collusion was the agreement in the mid-1980s among baseball owners to limit their bidding for free-agent players. The fact that such bidding was repeated and open made it possible for owners to retaliate against those that bid too often and too aggressively. Collusion, however, is not limited to buyers. In 2001, two of the world’s most successful auction houses, Sotheby’s and Christie’s, were found guilty of agreeing to fix the price of commissions offered to sellers of auctioned items. Former Sotheby’s chairman Alfred Taubman was sentenced to
a year in jail for his involvement in the scheme. 522 PART 3 • Market Structure and Competitive Strategy E XAM PLE 13.7 AUCTIONING LEGAL SERVICES In the United States, plaintiff attorneys often bring cases in which they represent classes of individuals who were allegedly harmed by defendants’ actions that adversely affect human health or well-being. The attorneys are typically paid on a contingent fee basis, which means they are paid nothing if they lose the case, but if they win the case, they receive a percentage of the amount recovered, typically around 30%. In a number of instances, class action cases have followed successful investigations and prosecutions by government agencies. For example, after the U.S. government successfully sued Microsoft and found that it had monopolized the market for PC operating systems, attorneys representing consumers who had purchased PCs filed suit to recover damages for excess payments. Because of the government suit, the lawyers for the class action plaintiffs had a head start that greatly simplified their work. Many of the critical documents had already been uncovered, and they did not have to prove that Microsoft was a monopoly in the PC operating systems market. As a result of cases such as this one, the percentage fee awards have been seen as unreasonably large relative to the efforts made by the attorneys. What could be done about this? A number of federal judges had a solution: hold auctions in which attorneys bid for the right to represent the class of potential plaintiffs. In a typical such auction, attorneys would offer a percentage fee as part of a sealedbid process. In one unusual auction following on a criminal verdict against auction houses Sotheby’s and Christie’s, Judge Lewis Kaplan of the Southern District of New York allowed law firms to offer a broader range of payment terms as part of their bids. It turned out that the winning bidder was the law firm of Boies, Schiller, & Flexner, which bid a payment of 25 percent of the award on an amount recovered that is greater than $425 million. Months after taking the case, David Boies settled with defendants for $512 million, earning the attorneys a $26.75 million fee (25 percent of the $107 million excess over the minimum of $425 million) and generating just over $475 million for members of the class. EXAMPLE 13.8 INTERNET AUCTIONS The popularity of auctions has skyrocketed in recent years with the growth of the Internet. Indeed, the Internet has lowered transaction costs by so much that individuals anywhere in the
world can now trade relatively low-value items without leaving the comfort of home. Many Internet sites are now devoted to auctions at which participants can buy and sell a wide variety of items. Let’s see how these Internet auctions work.22 The most popular Internet auction site in the United States is www.ebay.com. It conducts auctions each day for items ranging from 22For more information on Internet auctions, see Patrick Bajari and Ali Hortaçsu, “Economic Insights from Internet Auctions,” Journal of Economic Literature 42 (June 2004): 457–86. CHAPTER 13 • Game Theory and Competitive Strategy 523 In §4.5 we explain how network externalities affect sales of a product. antiques and automobiles to Beanie Babies and rare coins. Founded in 1995 by Pierre Omidyar in an effort to sell a broken laser pointer, eBay dominates the online person-to-person auction industry. It recently listed millions of products for sale, including such unusual items as a Caribbean island, 154 acres in the Catskills, and a ghost town in Nevada. In 2011, eBay accounted for about 85 percent of all U.S. online auction sales, totalling over $60 billion of merchandise sold. On average, over 14 million items are listed for sale at any given time. How has eBay come to dominate the U.S. Internet auction market? Why haven’t other Internet auction sites (such as Yahoo and Amazon) succeeded in taking market share from eBay? The answer is that Internet auctions are subject to very strong network externalities. If you wanted to auction off some rare coins or stamps which auction site would you choose? The one that had the largest number of potential bidders. Likewise, if you wanted to bid for rare coins or stamps, you would choose the auction site with the largest number of sellers. Thus, both sellers and buyers gravitate to the auction site with the largest market share. Because eBay was the first major Internet auction site, it began with a large market share, and its share grew thanks to the network externality. To understand the critical role of network effects, look at what happened when eBay tried to expand internationally. In China it had to compete with Taobao, whose managers knew how important it was to gain an early market share advantage. Thus Taobao decided not to charge sellers any commissions, so that most of its revenue was from advertising. While its revenue was limited by this strategy, Taobao
quickly became the dominant Internet auction site in China, with a market share exceeding 80 percent in 2010.23 And eBay likewise lost out in Japan, this time to Yahoo! Japan Auctions, which aggressively obtained an early market share lead. The strong network effect then made it nearly impossible for eBay (or anyone else) to challenge Yahoo!’s dominance in Japan. Let’s return to the United States and see how eBay auctions operate. For single items, eBay uses an increasing price auction which works roughly as follows: Bids must be increased with minimum increments. The highest bidder at the close of the auction wins and pays the seller a price equal to the second-highest bid plus the minimum increment by which bids are increased (say 25 cents). So, if you bid $20 for a particular DVD and you are the winning bidder, you will pay the second highest paid that was paid – say $19, plus the 25-cent minimum increment. The eBay increasing price auction does not correspond precisely to the auction formats described previously because there is a fixed and known stopping time, which can cause bidders to place bids strategically at the end of the auction. Many Internet auctions are dominated by private-value items. (However, because anyone can put an item up for sale, there are common-value issues— how reliable is the seller, and are there possibilities for resale?) The privatevalue emphasis of these auctions is especially true of unique antiques that may have considerable value to particular bidders. With private-value auctions, you needn’t worry so much about the prior history of bidding: The bids of others 23According to Forbes, May 3, 2011. 524 PART 3 • Market Structure and Competitive Strategy In Section 9.6 we explain that the burden of a tax falls partly on the seller and partly on the buyers, depending on the relative elasticities of demand and supply. tell you about their preferences, but the value that you place on the object is personal to you. Although you want to win the bidding at a price as far below your valuation as possible, the winner’s curse needn’t be a concern: You can’t be disappointed if your value for the object is more than what you paid for it. In the United States, the seller pays the buyer when an item is purchased. EBay’s profit from most auctions comes from the fees paid by the seller. In most auctions, the seller pays a fee when the item is put up for
sale, and an additional fee when and if the item is sold. Of course, the issue of who ultimately bears the burden of these fees is a complex one. To illustrate, suppose that the product being sold on the Internet is a common value item that is widely available elsewhere (e.g., a music CD, a DVD, or a book). Then the fee is like a tax (but collected by eBay, not the government). Like a tax, the burden of the fees will be borne by both buyers and sellers, and as we explained in Section 9.6, will depend on the relative elasticities of demand and supply. Finally, a few caveats are in order when buying items via Internet auctions. Unlike traditional auction houses, low-end auction sites like eBay provide only a forum for buyers and sellers to interact; they provide no quality control functions. Although many sites, including eBay, make available feedback from buyers for each seller, this is usually the only evidence of a seller’s reliability that buyers receive. In recent years, eBay has established a buyer protection program, but the claims process can be lengthy. In addition, the possibility of bid manipulation looms large in Internet auctions. It is always possible that sellers may file spurious bids in order to manipulate the bidding process. Thus, “caveat emptor” (buyer beware) is a sound philosophy when buying items on the Internet. SUMMARY 1. A game is cooperative if the players can communicate and arrange binding contracts; otherwise, it is noncooperative. In either kind of game, the most important aspect of strategy design is understanding your opponent’s position, and (if your opponent is rational) correctly deducing the likely response to your actions. Misjudging an opponent’s position is a common mistake, as Example 13.1 “Acquiring a Company” (page 490) illustrates.24 2. A Nash equilibrium is a set of strategies such that all players are doing their best given the strategies of the other players. An equilibrium in dominant strategies is a special case of a Nash equilibrium; a dominant strategy is optimal no matter what the other players do. A Nash equilibrium relies on the rationality of each player. A maximin strategy is more conservative because it maximizes the minimum possible outcome. 3. Some games have no Nash equilibria in pure strategies but have one or more equilibria in mixed strategies. A mixed strategy is one in which the player makes a random choice among two or more possible actions
, based on a set of chosen probabilities. 4. Strategies that are not optimal for a one-shot game may be optimal for a repeated game. Depending on the number of repetitions, a “tit-for-tat” strategy, in which you play cooperatively as long as your competitor does the same, may be optimal for the repeated prisoners’ dilemma. 24Here is the solution to Company A’s problem: It should offer nothing for Company T’s stock. Remember that Company T will accept an offer only if it is greater than the per-share value under current management. Suppose you offer $50. Thus Company T will accept this offer only if the outcome of the exploration project results in a per-share value under current management of $50 or less. Any values between $0 and $100 are equally likely. Therefore, the expected value of Company T’s stock, given that it accepts the offer—i.e., given that the outcome of the exploration project leads to a value less than $50—is $25. Under the management of Company A, therefore, the value would be (1.5)($25) = $37.5, which is less than $50. In fact, for any price P, if the offer is accepted, Company A can expect a value of only (3/4)P. CHAPTER 13 • Game Theory and Competitive Strategy 525 5. In a sequential game, the players move in turn. In some cases, the player who moves first has an advantage. Players may then have an incentive to try to precommit themselves to particular actions before their competitors can do the same. 6. An empty threat is a threat that one has no incentive to carry out. If one’s competitors are rational, empty threats are of no value. To make a threat credible, it is sometimes necessary to make a strategic move to constrain one’s later behavior, thereby creating an incentive to carry out the threat. 7. Bargaining situations are examples of cooperative games. As in noncooperative games, in bargaining, players can sometimes gain a strategic advantage by limiting their own flexibility. 8. To deter entry, an incumbent firm must convince any potential competitor that entry will be unprofitable. This may be done by investing, and thereby giving credibility to the threat that entry will be met by price warfare. Strategic trade policies by governments sometimes have this objective. 9. Auctions can be conducted in a number of formats
, including English (oral with increasing bids), Dutch (oral with decreasing bids), and sealed bid. The opportunity for a seller to raise revenue and for a buyer to obtain an object at a reasonable price depends on the auction format, and on whether the items being auctioned have the same value to all bidders (as in a common-value auction) or different values to different bidders (as in a private-value auction). QUESTIONS FOR REVIEW 1. What is the difference between a cooperative and a noncooperative game? Give an example of each. 2. What is a dominant strategy? Why is an equilibrium stable in dominant strategies? 3. Explain the meaning of a Nash equilibrium. How does it differ from an equilibrium in dominant strategies? 4. How does a Nash equilibrium differ from a game’s maximin solution? When is a maximin solution a more likely outcome than a Nash equilibrium? 5. What is a “tit-for-tat” strategy? Why is it a rational strategy for the infinitely repeated prisoners’ dilemma? 6. Consider a game in which the prisoners’ dilemma is repeated 10 times and both players are rational and fully informed. Is a tit-for-tat strategy optimal in this case? Under what conditions would such a strategy be optimal? 7. Suppose you and your competitor are playing the pricing game shown in Table 13.8 (page 498). Both of you EXERCISES 1. In many oligopolistic industries, the same firms compete over a long period of time, setting prices and observing each other’s behavior repeatedly. Given the large number of repetitions, why don’t collusive outcomes typically result? 2. Many industries are often plagued by overcapacity: Firms simultaneously invest in capacity expansion, so that total capacity far exceeds demand. This happens not only in industries in which demand is highly volatile and unpredictable, but also in industries in which demand is fairly stable. What factors lead to overcapacity? Explain each briefly. 3. Two computer firms, A and B, are planning to market network systems for office information management. Each firm can develop either a fast, high-quality must announce your prices at the same time. Can you improve your outcome by promising your competitor that you will announce a high price? 8. What is meant by “first-mover advantage”? Give an example of a gaming situation with a first-mover advantage. 9. What is a “
strategic move”? How can the development of a certain kind of reputation be a strategic move? 10. Can the threat of a price war deter entry by potential competitors? What actions might a firm take to make this threat credible? 11. A strategic move limits one’s flexibility and yet gives one an advantage. Why? How might a strategic move give one an advantage in bargaining? 12. Why is the winner’s curse potentially a problem for a bidder in a common-value auction but not in a privatevalue auction? system (High), or a slower, low-quality system (Low). Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix: Firm B High 50, 40 55, 55 Low 60, 45 15, 20 Firm A High Low a. If both firms make their decisions at the same time and follow maximin (low-risk) strategies, what will the outcome be? 526 PART 3 • Market Structure and Competitive Strategy Firm 2 Firm 1 b. Suppose that both firms try to maximize profits, but that Firm A has a head start in planning and can commit first. Now what will be the outcome? What will be the outcome if Firm B has the head start in planning and can commit first? c. Getting a head start costs money. (You have to gear up a large engineering team.) Now consider the two-stage game in which, first, each firm decides how much money to spend to speed up its planning, and, second, it announces which product (H or L) it will produce. Which firm will spend more to speed up its planning? How much will it spend? Should the other firm spend anything to speed up its planning? Explain. 4. Two firms are in the chocolate market. Each can choose to go for the high end of the market (high quality) or the low end (low quality). Resulting profits are given by the following payoff matrix: Firm 1 Low High Low High 20, 30 900, 600 100, 800 50, 50 a. What outcomes, if any, are Nash equilibria? b. If the managers of both firms are conservative and each follows a maximin strategy, what will be the outcome? c. What is the cooperative outcome? d. Which firm benefits most from the cooperative outcome? How much would that firm need to offer the other to persuade it to collude? 5. Two major networks are competing for viewer ratings in the 8:00–9:
00 p.m. and 9:00–10:00 p.m. slots on a given weeknight. Each has two shows to fill these time periods and is juggling its lineup. Each can choose to put its “bigger” show first or to place it second in the 9:00–10:00 p.m. slot. The combination of decisions leads to the following “ratings points” results: Network 2 First 20, 30 First Second 15, 15 Second 18, 18 30, 10 Network 1 a. Find the Nash equilibria for this game, assuming that both networks make their decisions at the same time. b. If each network is risk-averse and uses a maximin strategy, what will be the resulting equilibrium? c. What will be the equilibrium if Network 1 makes its selection first? If Network 2 goes first? d. Suppose the network managers meet to coordinate schedules and Network 1 promises to schedule its big show first. Is this promise credible? What would be the likely outcome? 6. Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below. A 10, 10 10, 0 20, 10 A B C Firm 2 B 0, 10 20, 20 C 10, 20 5, 15 15, 5 30, 30 a. Are there any Nash equilibria in pure strategies? If so, what are they? b. If both firms use maximin strategies, what outcome will result? c. If Firm 1 uses a maximin strategy and Firm 2 knows this, what will Firm 2 do? 7. We can think of U.S. and Japanese trade policies as a prisoners’ dilemma. The two countries are considering policies to open or close their import markets. The payoff matrix is shown below. Japan Open 10, 10 100, 5 Close 5, 5 1, 1 U.S. Open Close a. Assume that each country knows the payoff matrix and believes that the other country will act in its own interest. Does either country have a dominant strategy? What will be the equilibrium policies if each country acts rationally to maximize its welfare? b. Now assume that Japan is not certain that the United States will behave rationally. In particular, Japan is concerned that U.S. politicians may want to penalize Japan even if that does not maximize U.S. welfare
. How might this concern affect Japan’s choice of strategy? How might this change the equilibrium? CHAPTER 13 • Game Theory and Competitive Strategy 527 8. You are a duopolist producer of a homogeneous good. Both you and your competitor have zero marginal costs. The market demand curve is P = 30 - Q where Q = Q1 + Q2. Q1 is your output and Q2 your competitor’s output. Your competitor has also read this book. a. Suppose you will play this game only once. If you and your competitor must announce your outputs at the same time, how much will you choose to produce? What do you expect your profit to be? Explain. b. Suppose you are told that you must announce your output before your competitor does. How much will you produce in this case, and how much do you think your competitor will produce? What do you expect your profit to be? Is announcing first an advantage or a disadvantage? Explain briefly. How much would you pay for the option of announcing either first or second? c. Suppose instead that you are to play the first round of a series of 10 rounds (with the same competitor). In each round, you and your competitor announce your outputs at the same time. You want to maximize the sum of your profits over the 10 rounds. How much will you produce in the first round? How much do you expect to produce in the tenth round? In the ninth round? Explain briefly. d. Once again you will play a series of 10 rounds. This time, however, in each round your competitor will announce its output before you announce yours. How will your answers to (c) change in this case? 9. You play the following bargaining game. Player A moves first and makes Player B an offer for the division of $100. (For example, Player A could suggest that she take $60 and Player B take $40.) Player B can accept or reject the offer. If he rejects it, the amount of money available drops to $90, and he then makes an offer for the division of this amount. If Player A rejects this offer, the amount of money drops to $80 and Player A makes an offer for its division. If Player B rejects this offer, the amount of money drops to 0. Both players are rational, fully informed, and want to maximize their payoffs. Which player will do best in this game? *10. Defendo has decided to introduce a revolutionary video game. As the first firm
in the market, it will have a monopoly position for at least some time. In deciding what type of manufacturing plant to build, it has the choice of two technologies. Technology A is publicly available and will result in annual costs of C A(q) = 10 + 8q Technology B is a proprietary technology developed in Defendo’s research labs. It involves a higher fixed cost of production but lower marginal costs: C B(q) = 60 + 2q Defendo must decide which technology to adopt. Market demand for the new product is P = 20 Q, where Q is total industry output. a. Suppose Defendo were certain that it would maintain its monopoly position in the market for the entire product lifespan (about five years) without threat of entry. Which technology would you advise Defendo to adopt? What would be Defendo’s profit given this choice? b. Suppose Defendo expects its archrival, Offendo, to consider entering the market shortly after Defendo introduces its new product. Offendo will have access only to Technology A. If Offendo does enter the market, the two firms will play a Cournot game (in quantities) and arrive at the Cournot-Nash equilibrium. i. If Defendo adopts Technology A and Offendo enters the market, what will be the profit of each firm? Would Offendo choose to enter the market given these profits? ii. If Defendo adopts Technology B and Offendo enters the market, what will be the profit of each firm? Would Offendo choose to enter the market given these profits? iii. Which technology would you advise Defendo to adopt given the threat of possible entry? What will be Defendo’s profit given this choice? What will be consumer surplus given this choice? c. What happens to social welfare (the sum of consumer surplus and producer profit) as a result of the threat of entry in this market? What happens to equilibrium price? What might this imply about the role of potential competition in limiting market power? 11. Three contestants, A, B, and C, each has a balloon and a pistol. From fixed positions, they fire at each other’s balloons. When a balloon is hit, its owner is out. When only one balloon remains, its owner gets a $1000 prize. At the outset, the players decide by lot the order in which they will fire, and each player can choose any remaining balloon as his target. Everyone knows that A is the best shot and always hits
the target, that B hits 528 PART 3 • Market Structure and Competitive Strategy the target with probability.9, and that C hits the target with probability.8. Which contestant has the highest probability of winning the $1000? Explain why. 12. An antique dealer regularly buys objects at hometown auctions whose bidders are limited to other dealers. Most of her successful bids turn out to be financially worthwhile because she is able to resell the antiques for a profit. On occasion, however, she travels to a nearby town to bid in an auction that is open to the public. She often finds that on the rare occasions in which she does bid successfully, she is disappointed— the antique cannot be sold at a profit. Can you explain the difference in her success between the two sets of circumstances? 13. You are in the market for a new house and have decided to bid for a house at auction. You believe that the value of the house is between $125,000 and $150,000, but you are uncertain as to where in the range it might be. You do know, however, that the seller has reserved the right to withdraw the house from the market if the winning bid is not satisfactory. a. Should you bid in this auction? Why or why not? b. Suppose you are a building contractor. You plan to improve the house and then to resell it at a profit. How does this situation affect your answer to (a)? Does it depend on the extent to which your skills are uniquely suitable to improving this particular house? C H A P T E R 14 Markets for Factor Inputs So far we have concentrated on output markets: markets for goods and services that firms sell and consumers purchase. In this chapter, we discuss factor markets: markets for labor, raw materials, and other inputs to production. Much of our material will be familiar because the same forces that shape supply and demand in output markets also affect factor markets. We have seen that some output markets are perfectly or almost perfectly competitive, while producers in others have market power. The same is true for factor markets. We will examine three different factor market structures: 1. Perfectly competitive factor markets; 2. Markets in which buyers of factors have monopsony power; 3. Markets in which sellers of factors have monopoly power. We will also point out instances in which equilibrium in the factor market depends on the extent of market power in output markets. 14.1 Competitive Factor Markets A competitive factor market is one in which there are a large number of
sellers and buyers of a factor of production, such as labor or raw materials. Because no single seller or buyer can affect the price of a given factor, each is a price taker. For example, if individual firms that buy lumber to construct homes purchase a small share of the total volume of lumber available, their purchasing decision will have no effect on price. Likewise, if each supplier of lumber controls only a small share of the market, no individual supplier’s decision will affect the price of the lumber that he sells. Instead, the price of lumber (and the total quantity produced) will be determined by the aggregate supply and demand for lumber. We begin by analyzing the demands for a factor by individual firms. These demands are added to get market demand. We then shift to the supply side of the market and show how market price and input levels are determined 14.1 Competitive Factor Markets 529 14.2 Equilibrium in a Competitive Factor Market 542 14.3 Factor Markets with Monopsony Power 546 14.4 Factor Markets with Monopoly Power 550 14.1 The Demand for Jet Fuel 536 14.2 Labor Supply for One- and Two-Earner Households 541 14.3 Pay in the Military 545 14.4 Monopsony Power in the Market for Baseball Players 548 14.5 Teenage Labor Markets and the Minimum Wage 549 14.6 The Decline of Private-Sector Unionism 553 14.7 Wage Inequality Revisited 554 529 530 PART 3 • Market Structure and Competitive Strategy • derived demand Demand for an input that depends on, and is derived from, both the firm’s level of output and the cost of inputs. • marginal revenue product Additional revenue resulting from the sale of output created by the use of one additional unit of an input. Recall that in §8.3, marginal revenue is defined to be the increase in revenue resulting from a one-unit increase in output. Demand for a Factor Input When Only One Input Is Variable Like demand curves for the final goods that result from the production process, demand curves for factors of production are downward sloping. Unlike consumers’ demands for goods and services, however, factor demands are derived demands: They depend on, and are derived from, the firm’s level of output and the costs of inputs. For example, the demand of the Microsoft Corporation for computer programmers is a derived demand that depends not only on the current salaries of programmers, but also on how much software Microsoft expects to
sell. To analyze factor demands, we will use the material from Chapter 7 that shows how a firm chooses its production inputs. We will assume that the firm produces its output using two inputs, capital K and labor L, that can be hired at the prices r (the rental cost of capital) and w (the wage rate), respectively.1 We will also assume that the firm has its plant and equipment in place (as in a shortrun analysis) and must only decide how much labor to hire. Suppose that the firm has hired a certain number of workers and wants to know whether it is profitable to hire one additional worker. This will be profitable if the additional revenue from the output of the worker’s labor is greater than its cost. The additional revenue from an incremental unit of labor, the marginal revenue product of labor, is denoted MRPL. The cost of an incremental unit of labor is the wage rate, w. Thus, it is profitable to hire more labor if the MRPL is at least as large as the wage rate w. How do we measure the MRPL? It’s the additional output obtained from the additional unit of this labor, multiplied by the additional revenue from an extra unit of output. The additional output is given by the marginal product of labor MPL and the additional revenue by the marginal revenue MR. Formally, the marginal revenue product is R/L, where L is the number of units of labor input and R is revenue. The additional output per unit of labor, the MPL, is given by Q/L, and marginal revenue, MR, is equal to R/Q. Because R/L = (R)/(Q)(Q/L), it follows that MRPL = (MR)(MPL) (14.1) In §8.2, we explain that because the demand facing each firm in a competitive market is perfectly elastic, each firm will sell its output at a price equal to its average revenue and to its marginal revenue. This important result holds for any competitive factor market, whether or not the output market is competitive. However, to examine the characteristics of the MRPL, let’s begin with the case of a perfectly competitive output (and input) market. In a competitive output market, a firm will sell all its output at the market price P. The marginal revenue from the sale of an additional unit of output is then equal to P. In this case, the marginal revenue product of labor is equal to the marginal product of labor times the
price of the product: MRPL = (MPL)(P) (14.2) In §6.2, we explain the law of diminishing marginal returns—as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease. The higher of the two curves in Figure 14.1 represents the MRPL curve for a firm in a competitive output market. Note that because there are diminishing marginal returns to labor, the marginal product of labor falls as the amount of labor increases. The marginal revenue product curve thus slopes downward, even though the price of the output is constant. 1We implicitly assume that all inputs to production are identical in quality. Differences in workers’ skills and abilities are discussed in Chapter 17. CHAPTER 14 • Markets for Factor Inputs 531 Wage (dollars per hour) Competitive Output Market Monopolistic Output Market MRPL MPL · MR MRPL MPL · P Hours of work FIGURE 14.1 MARGINAL REVENUE PRODUCT In a competitive factor market in which the producer is a price taker, the buyer’s demand for an input is given by the marginal revenue product curve. The MRP curve falls because the marginal product of labor falls as hours of work increase. When the producer of the product has monopoly power, the demand for the input is also given by the MRP curve. In this case, however, the MRP curve falls because both the marginal product of labor and marginal revenue fall. The lower curve in Figure 14.1 is the MRPL curve when the firm has monopoly power in the output market. When firms have monopoly power, they face a downward-sloping demand curve and must therefore lower the price of all units of the product in order to sell more of it. As a result, marginal revenue is always less than price (MR < P). This explains why the monopolistic curve lies below the competitive curve and why marginal revenue falls as output increases. Thus the marginal revenue product curve slopes downward in this case because the marginal revenue curve and the marginal product curve slope downward. Note that the marginal revenue product tells us how much the firm should be willing to pay to hire an additional unit of labor. As long as the MRPL is greater than the wage rate, the firm should hire more labor. If the marginal revenue product is less than the wage rate, the firm should lay off workers. Only when the marginal revenue product is equal to the wage rate will the firm have hired the profit-maximizing
amount of labor. The profit-maximizing condition is therefore MRPL = w (14.3) Figure 14.2 illustrates this condition. The demand for labor curve DL is the MRPL. Note that the quantity of labor demanded increases as the wage rate falls. 532 PART 3 • Market Structure and Competitive Strategy Price of labor w* FIGURE 14.2 HIRING BY A FIRM IN THE LABOR MARKET (WITH FIXED CAPITAL) In a competitive labor market, a firm faces a perfectly elastic supply of labor SL and can hire as many workers as it wants at a wage rate w. The firm’s demand for labor DL is given by its marginal revenue product of labor MRPL. The profit-maximizing firm will hire L units of labor at the point where the marginal revenue product of labor is equal to the wage rate. SL MRPL DL L* Quantity of labor Because the labor market is perfectly competitive, the firm can hire as many workers as it wants at the market wage w* and is not able to affect the market wage. The supply of labor curve facing the firm SL is thus a horizontal line. The profit-maximizing amount of labor that the firm hires, L*, is at the intersection of the supply and demand curves. Figure 14.3 shows how the quantity of labor demanded changes in response to a drop in the market wage rate from w1 to w2. The wage rate might decrease if more people entering the labor force are looking for jobs for the first time (as happened, for example, when the baby boomers came of age). The quantity of labor demanded by the firm is initially L1, at the intersection of MRPL and S1. In §8.3, we explain that a firm maximizes its profit by choosing an output at which marginal revenue equals marginal cost. Price of labor w1 w2 FIGURE 14.3 A SHIFT IN THE SUPPLY OF LABOR When the supply of labor facing the firms is S1, the firm hires L1 units of labor at wage w1. But when the market wage rate decreases and the supply of labor shifts to S2, the firm maximizes its profit by moving along the demand for labor curve until the new wage rate w2 is equal to the marginal revenue product of labor. As a result, L2 units of labor are hired. S1 S2 MRPL = DL L 1 L 2 Quantity of labor CHAPTER 14 • Markets for Factor
Inputs 533 However, when the supply of labor curve shifts from S1 to S2, the wage falls from w1 to w2 and the quantity of labor demanded increases from L1 to L2. Factor markets are similar to output markets in many ways. For example, the factor market profit-maximizing condition that the marginal revenue product of labor be equal to the wage rate is analogous to the output market condition that marginal revenue be equal to marginal cost. To see why this is true, recall that MRPL = (MPL)(MR) and divide both sides of equation (14.3) by the marginal product of labor. Then, MR = w/MPL (14.4) Because MPL measures additional output per unit of input, the right-hand side of equation (14.4) measures the marginal cost of an additional unit of output (the wage rate multiplied by the labor needed to produce one unit of output). Equation (14.4) shows that both the hiring and output choices of the firm follow the same rule: Inputs or outputs are chosen so that marginal revenue (from the sale of output) is equal to marginal cost (from the purchase of inputs). This principle holds in both competitive and noncompetitive markets. Demand for a Factor Input When Several Inputs Are Variable When the firm simultaneously chooses quantities of two or more variable inputs, the hiring problem becomes more difficult because a change in the price of one input will change the demand for others. Suppose, for example, that both labor and assembly-line machinery are variable inputs for producing farm equipment. Let’s say that we wish to determine the firm’s demand for labor curve. As the wage rate falls, more labor will be demanded even if the firm’s investment in machinery is unchanged. But as labor becomes less expensive, the marginal cost of producing the farm equipment falls. Consequently, it is profitable for the firm to increase its output. In that case, the firm is likely to invest in additional machinery to expand production capacity. Expanding the use of machinery causes the marginal revenue product of labor curve to shift to the right; in turn, the quantity of labor demanded increases. Figure 14.4 illustrates this. Suppose that when the wage rate is $20 per hour, the firm hires 100 worker-hours, as shown by point A on the MRPL1 curve. Now consider what happens when the wage rate falls to $15 per hour. Because the marginal revenue product of labor is now greater than the
wage rate, the firm will demand more labor. But the MRPL1 curve describes the demand for labor when the use of machinery is fixed. In fact, a greater amount of labor causes the marginal product of capital to rise, which encourages the firm to rent more machinery as well as hire more labor. Because there is more machinery, the marginal product of labor will increase. (With more machinery, workers can be more productive.) The marginal revenue product curve will therefore shift to the right (to MRPL2). Thus, when the wage rate falls, the firm will use 140 hours of labor. This is shown by a new point on the demand curve, C, rather than 120 hours as given by B. A and C are both on the firm’s demand for labor curve (with machinery variable) DL; B is not. Note that as constructed, the demand for labor curve is more elastic than either of the two marginal product of labor curves (which presume no change in the amount of machinery). Thus, when capital inputs are variable in the long run, there is a greater elasticity of demand because firms can substitute capital for labor in the production process. 534 PART 3 • Market Structure and Competitive Strategy FIGURE 14.4 FIRM’S DEMAND CURVE FOR LABOR (WITH VARIABLE CAPITAL) When two or more inputs are variable, a firm’s demand for one input depends on the marginal revenue product of both inputs. When the wage rate is $20, A represents one point on the firm’s demand for labor curve. When the wage rate falls to $15, the marginal product of capital rises, encouraging the firm to rent more machinery and hire more labor. As a result, the MRP curve shifts from MRPL1 to MRPL2, generating a new point C on the firm’s demand for labor curve. Thus A and C are on the demand for labor curve, but B is not. Wage (dollars per hour) 20 15 10 5 A C B DL MRPL2 MRPL1 40 80 120 160 Hours of work Recall from §4.3 that the market demand curve for a product shows how much of the product consumers are willing to buy as the price of the product changes. The Market Demand Curve When we aggregated the individual demand curves of consumers to obtain the market demand curve for a product, we were concerned with a single industry. However, a factor input such as skilled labor is demanded by firms in
many different industries. Moreover, as we move from industry to industry, we are likely to find that firms’ demands for labor (which are derived in part from the demands for the firms’ output) vary substantially. Therefore, to obtain the total market demand for labor curve, we must first determine each industry’s demand for labor, and then add the industry demand curves horizontally. The second step is straightforward. Adding industry demand curves for labor to obtain a market demand curve for labor is just like adding individual product demand curves to obtain the market demand curve for that product. So let’s concentrate our attention on the more difficult first step. DETERMINING INDUSTRY DEMAND The first step—determining industry demand—takes into account the fact that both the level of output produced by the firm and its product price change as the prices of the inputs to production change. It is easiest to determine market demand when there is a single producer. In that case, the marginal revenue product curve is the industry demand curve for the input. When there are many firms, however, the analysis is more complex because of the possible interaction among the firms. Consider, for instance, the demand for labor when output markets are perfectly competitive. Then, the marginal revenue product of labor is the product of the price of the good and the marginal product of labor (see equation 14.2), as shown by the curve MRPL1 in Figure 14.5 (a). Suppose initially that the wage rate for labor is $15 per hour and that the firm demands 100 worker-hours of labor. Now the wage rate for this firm falls to $10 per hour. If no other firms could hire workers at the lower wage, then our firm would hire 150 worker-hours of labor (by finding the point on the MRPL1 curve that corresponds to the $10-per-hour wage rate). But if the wage rate falls for all firms in an industry, the industry as a whole will hire more labor. This will Wage (dollars per hour) 15 10 5 CHAPTER 14 • Markets for Factor Inputs 535 Wage (dollars per hour) 15 10 5 MRPL1 MRPL2 Horizontal Sum If Product Price Unchanged Industry Demand Curve 50 100 (a) 120 150 Labor (worker-hours) L0 L1 L2 (b) Labor (worker-hours) FIGURE 14.5 THE INDUSTRY DEMAND FOR LABOR The demand curve for labor of a competitive firm
, MRPL1 in (a), takes the product price as given. But as the wage rate falls from $15 to $10 per hour, the product price also falls. Thus the firm’s demand curve shifts downward to MRPL2. As a result, the industry demand curve, shown in (b), is more inelastic than the demand curve that would be obtained if the product price were assumed to be unchanged. lead to more output from the industry, a shift to the right of the industry supply curve, and a lower market price for its product. In Figure 14.5 (a), when the product price falls, the original marginal revenue product curve shifts downward, from MRPL1 to MRPL2. This shift results in a lower quantity of labor demanded by the firm—120 worker-hours rather than 150. Consequently, industry demand for labor will be lower than it would be if only one firm were able to hire workers at the lower wage. Figure 14.5 (b) illustrates this. The lighter line shows the horizontal sum of the individual firms’ demands for labor that would result if product price did not change as the wage falls. The darker line shows the industry demand curve for labor, which takes into account the fact that product price will fall as all firms expand their output in response to the lower wage rate. When the wage rate is $15 per hour, industry demand for labor is L0 worker-hours. When it falls to $10 per hour, industry demand increases to L1. Note that this is a smaller increase than L2, which would occur if the product price were fixed. The aggregation of industry demand curves into the market demand curve for labor is the final step: To complete it, we simply add the labor demanded in all industries. The derivation of the market demand curve for labor (or for any other input) is essentially the same when the output market is noncompetitive. The only difference is that it is more difficult to predict the change in product price in response to a change in the wage rate because each firm in the market is likely to be pricing strategically rather than taking price as given. 536 PART 3 • Market Structure and Competitive Strategy EXAMPLE 14.1 THE DEMAND FOR JET FUEL In §2.4, we define the price elasticity of demand as the percentage change in quantity demanded resulting from a 1-percent change in the price of a good. Jet fuel costs have been highly volatile during the past several decades, generally increasing
and decreasing in line with oil prices. When fuel prices were high, they made up about 30 percent of airline operating costs, and when they were low, they made up 10 to 15 percent of costs. Overall, jet fuel remains the second-highest expense for airlines (after labor) generally. Understanding the demand for jet fuel is important to managers of oil refineries, who must decide how much jet fuel to produce. It is also crucial to managers of airlines, who must project fuel purchases and costs when fuel prices rise and decide whether to invest in more fuel-efficient planes.2 The effect of the increase in fuel costs on the airline industry depends on the ability of airlines either to cut fuel usage by reducing weight (by carrying less excess fuel) and flying more slowly (reducing drag and increasing engine efficiency) or to pass on their higher costs in customer prices. Thus the price elasticity of demand for jet fuel depends both on the ability to conserve fuel and on the elasticities of demand and supply of travel. To measure the short-run elasticity of demand for jet fuel, we use as the quantity of fuel demanded the number of gallons of fuel used by an airline in all markets within its domestic route network. The price of jet fuel is measured in dollars per gallon. A statistical analysis of demand must control for factors other than price that can explain why some firms demand more fuel than others. Some airlines, for example, use more fuel-efficient jet aircraft than others. A second factor is the length of flights: The shorter the flight, the more fuel consumed per mile of travel. Both of these factors were included in a statistical analysis that relates the quantity of fuel demanded to its price. Table 14.1 shows some short-run price elasticities. (They do not account for the introduction of new types of aircraft.) The jet fuel price elasticities for the airlines range in value from −.06 (for American) to −.15 (for Delta). Overall, the results show that the demand for jet fuel as an input to the production of airline flight-miles is very inelastic. This finding is not surprising: In the short run, there is no good substitute for TABLE 14.1 SHORT-RUN PRICE ELASTICITY OF DEMAND FOR JET FUEL AIRLINE American Continental ELASTICITY −.06 −.09 AIRLINE Delta United ELASTICITY −.15 −.10 2This example is drawn in part from Joseph M. Cigliano, “
The Demand for Jet Fuel by the U.S. Domestic Trunk Airlines,” Business Economics (September 1982): 32–36. Price CHAPTER 14 • Markets for Factor Inputs 537 FIGURE 14.6 THE SHORT- AND LONG-RUN DEMAND FOR JET FUEL The short-run demand for jet fuel MRPSR is more inelastic than the long-run demand MRPLR. In the short run, airlines cannot reduce fuel consumption much when fuel prices increase. In the long run, however, they can switch to longer, more fuel-efficient routes and put more fuel-efficient planes into service. MRPLR MRPSR Quantity of jet fuel jet fuel. The long-run elasticity of demand is higher, however, because airlines can eventually introduce more energy-efficient airplanes. Figure 14.6 shows the short- and long-run demands for jet fuel. The shortrun demand curve, MRPSR, is much less elastic than the long-run demand curve because it takes time to substitute newer, more fuel-efficient airplanes when the price of fuel goes up. The Supply of Inputs to a Firm When the market for a factor input is perfectly competitive, a firm can purchase as much of that input as it wants at a fixed market price, which is determined by the intersection of the market demand and supply curves, as shown in Figure 14.7 (a). The input supply curve facing a firm is then perfectly elastic. Thus, in Figure 14.7 (b), a firm is buying fabric at $10 per yard to sew into clothing. Because the firm is only a small part of the fabric market, it can buy all it wants without affecting the price. In Section 10.5 we explained that the supply curve AE facing the firm in Figure 14.7 (b) is its average expenditure curve (just as the demand curve facing a firm is its average revenue curve), because it represents the price per unit that the firm pays for the good. On the other hand, the marginal expenditure curve represents the firm’s expenditure on an additional unit that it buys. (The marginal expenditure curve in a factor market is analogous to the marginal revenue curve in the output market.) The marginal expenditure depends on whether you are a competitive buyer or a buyer with monopsony power. If you are a competitive buyer, the cost of each unit is the same no matter how many units you purchase; it is the market price of the good. The price paid is the average
expenditure per unit, and the marginal expenditure is equal to the average. Consequently, when the factor market is competitive, the average expenditure and marginal expenditure curves are identical horizontal lines, just as the marginal and average revenue curves are identical (and horizontal) for a competitive firm in the output market. • average expenditure curve Supply curve representing the price per unit that a firm pays for a good. • marginal expenditure curve Curve describing the additional cost of purchasing one additional unit of a good. 538 PART 3 • Market Structure and Competitive Strategy Price (dollars per yard) 10 Price (dollars per yard) Market Supply of Fabric S Market Demand for Fabric 10 D 100 (a) Yards of fabric Supply of Fabric Facing Firm ME = AE MRP Yards of fabric (b) Demand for Fabric 50 FIGURE 14.7 A FIRM’S INPUT SUPPLY IN A COMPETITIVE FACTOR MARKET In a competitive factor market, a firm can buy any amount of the input it wants without affecting the price. Therefore, the firm faces a perfectly elastic supply curve for that input. As a result, the quantity of the input purchased by the producer of the product is determined by the intersection of the input demand and supply curves. In (a), the industry quantity demanded and quantity supplied of fabric are equated at a price of $10 per yard. In (b), the firm faces a horizontal marginal expenditure curve at a price of $10 per yard of fabric and chooses to buy 50 yards. How much of the input should a firm facing a competitive factor market purchase? As long as the marginal revenue product curve lies above the marginal expenditure curve, profit can be increased by purchasing more of the input because the benefit of an additional unit (MRP) exceeds the cost (ME). However, when the marginal revenue product curve lies below the marginal expenditure curve, some units yield benefits that are less than cost. Therefore, profit maximization requires that marginal revenue product be equal to marginal expenditure: ME = MRP (14.5) When we considered the special case of a competitive output market, we saw that the firm bought inputs, such as labor, up to the point at which the marginal revenue product was equal to the price of the input v, as in equation (14.3). In the competitive case, therefore, the condition for profit maximization is that the price of the input be equal to marginal expenditure: ME = w (14.6) CHAPTER 14 • Markets for Factor Inputs 539
In our example, the price of the fabric ($10 per yard) is determined in the competitive fabric market shown in Figure 14.7 (a) at the intersection of the demand and supply curves. Figure 14.7 (b) shows the amount of fabric purchased by a firm at the intersection of the marginal expenditure and marginal revenue product curves. When 50 yards of fabric are purchased, the marginal expenditure of $10 is equal to the marginal revenue from the sale of clothing made possible by the increased use of fabric in the production process. If less than 50 yards of fabric were purchased, the firm would be forgoing an opportunity to make additional profit from clothing sales. If more than 50 yards were purchased, the cost of the fabric would be greater than the additional revenue from the sale of the extra clothing. The Market Supply of Inputs The market supply curve for a factor input is usually upward sloping. We saw in Chapter 8 that the market supply for a good sold in a competitive market is usually upward sloping because the marginal cost of producing the good is typically increasing. This is also the case for fabric and other raw material inputs. When the input is labor, however, people rather than firms are making supply decisions. In this case, utility maximization by workers rather than profit maximization by firms determines supply. In the discussion that follows, we use the analysis of income and substitution effects from Chapter 4 to show that although the market supply curve for labor can be upward sloping, it may also, as in Figure 14.8, be backward bending. In other words, a higher wage rate can lead to less labor being supplied. To see why a labor supply curve may be backward bending, divide the day into hours of work and hours of leisure. Leisure is a term that describes enjoyable non-work activities, including sleeping, eating, and household chores. Work benefits the worker only through the income that it generates. We also assume that a worker has the flexibility to choose how many hours per day to work. The wage rate measures the price that the worker places on leisure time, because his or her wage measures the amount of money that the worker gives In §8.6, we explain that the short-run market supply curve shows the amount of output that will be produced by firms in the market for every possible price. In §4.2, we explain that an increase in the price of a good has two effects: The real purchasing power of each consumer decreases (the income effect) and the good becomes relatively expensive (
the substitution effect). Wage (dollars per hour) Supply of Labor Hours of work per day FIGURE 14.8 BACKWARD-BENDING SUPPLY OF LABOR When the wage rate increases, the hours of work supplied increase initially but can eventually decrease as individuals choose to enjoy more leisure and to work less. The backward-bending portion of the labor supply curve arises when the income effect of the higher wage (which encourages more leisure) is greater than the substitution effect (which encourages more work). 540 PART 3 • Market Structure and Competitive Strategy FIGURE 14.9 SUBSTITUTION AND INCOME EFFECTS OF A WAGE INCREASE When the wage rate increases from $10 to $30 per hour, the worker’s budget line shifts from PQ to RQ. In response, the worker moves from A to B while decreasing work hours from 8 to 5. The reduction in hours worked arises because the income effect outweighs the substitution effect. In this case, the supply of labor curve is backward bending. R 720 Income (dollars per day) w $30 P 240 w $10 B C A 12 16 19 24 Hours of leisure Q Substitution Effect Income Effect up to enjoy leisure. As the wage rate increases, therefore, the price of leisure also increases. This price change brings about both a substitution effect (a change in relative price with utility held constant) and an income effect (a change in utility with relative prices unchanged). There is a substitution effect because the higher price of leisure encourages workers to substitute work for leisure. An income effect occurs because the higher wage rate increases the worker’s purchasing power. With higher income, the worker can buy more of many goods, one of which is leisure. If more leisure was chosen, it is because the income effect has encouraged the worker to work fewer hours. Income effects can be large because wages are the primary component of most people’s income. When the income effect outweighs the substitution effect, the result is a backwardbending supply curve. Figure 14.9 illustrates how a backward-bending supply curve for labor can result from the work–leisure decision for a typical weekday. The horizontal axis shows hours of leisure per day, the vertical axis income generated by work. (We assume there are no other sources of income.) Initially the wage rate is $10 per hour, and the budget line is given by PQ. Point P, for example, shows that if an individual worked a 24-hour day he
would earn an income of $240. The worker maximizes utility by choosing point A, thus enjoying 16 hours of leisure per day (with 8 hours of work) and earning $80. When the wage rate increases to $30 per hour, the budget line rotates about the horizontal intercept to line RQ. (Only 24 hours of leisure are possible.) Now the worker maximizes utility at B by choosing 19 hours of leisure per day (with 5 hours of work), while earning $150. If only the substitution effect came into play, the higher wage rate would encourage the worker to work 12 hours (at C) instead of 8. CHAPTER 14 • Markets for Factor Inputs 541 However, the income effect works in the opposite direction. It overcomes the substitution effect and lowers the work day from 8 hours to 5. In real life, a backward-bending labor supply curve might apply to a college student working during the summer to earn living expenses for the school year. As soon as a target level of earnings is reached, the student stops working and allocates more time to leisure. An increase in the wage rate will then lead to fewer hours worked because it enables the student to reach the target level of earnings more quickly. The backward-bending supply curve also applies to taxi drivers. As we saw in Example 5.9, for taxi drivers who have a daily targeted earnings goal, an increase in the hourly wage will reduce the number of hours that the drivers work. E X AM PLE 14.2 LABOR SUPPLY FOR ONE- AND TWO-EARNER HOUSEHOLDS One of the most dramatic changes in the labor market in the twentieth century has been the increase in women’s participation in the labor force. Whereas only 34 percent of women had entered the labor force in 1950, the number had risen to just under 60 percent by 2010. Married women account for a substantial portion of this increase. The increased role of women in the labor market has also had a major impact on housing markets: Where to live and work has increasingly become a joint husbandand-wife decision. The complex nature of the work choice was analyzed in a study that compared the work decisions of 94 unmarried females with the work decisions of heads of households and spouses in 397 families.3 One way to describe the work decisions of the various family groups is to calculate labor supply elasticities. Each elasticity relates the numbers of hours worked not only to the wage earned by the head of the household, but also to the wage of the
other member of two-earner households. Table 14.2 summarizes the results. When a higher wage rate leads to fewer hours worked, the labor supply curve is backward bending: The income effect, which encourages more leisure, outweighs the substitution effect, which encourages more work. The elasticity of labor supply is then negative. Table 14.2 shows that heads of one-earner families with children and two-earner TABLE 14.2 ELASTICITIES OF LABOR SUPPLY (HOURS WORKED) GROUP Unmarried males, no children Unmarried females, children Unmarried females, no children One-earner family, children One-earner family, no children Two-earner family, children Two-earner family, no children HEAD’S HOURS WITH RESPECT TO HEAD’S WAGE SPOUSE’S HOURS WITH RESPECT TO SPOUSE’S WAGE HEAD’S HOURS WITH RESPECT TO SPOUSE’S WAGE.026.106.011 −.078.007 −.002 −.107 −.086 −.028 −.004 −.059 3See Janet E. Kohlhase, “Labor Supply and Housing Demand for One- and Two-Earner Households,” Review of Economics and Statistics 68 (1986): 48–56; and Ray C. Fair and Diane J. Macunovich, “Explaining the Labor Force Participation of Women 20–24” (unpublished, February 1997). 542 PART 3 • Market Structure and Competitive Strategy families (with or without children) all have backwardbending labor supply curves, with elasticities ranging from −.002 to −.078. Most single-earner heads of households are on the upward-sloping portion of the labor supply curve, with the largest elasticity of.106 associated with single women with children. Married women (listed as spouses of heads of households) are also on the backward-bending portion of the labor supply curve, with elasticities of −.028 and −.086. 14.2 Equilibrium in a Competitive Factor Market A competitive factor market is in equilibrium when the price of the input equates the quantity demanded to the quantity supplied. Figure 14.10 (a) shows such an equilibrium for a labor market. At point A, the equilibrium wage rate is wC and the equilibrium quantity supplied is LC. Because they are well informed, all workers receive the identical
wage and generate the identical marginal revenue product of labor wherever they are employed. If any worker had a wage lower than her marginal product, a firm would find it profitable to offer that worker a higher wage. In §9.2, we explain that in a perfectly competitive market, efficiency is achieved because the sum of aggregate consumer and producer surplus is maximized. If the output market is also perfectly competitive, the demand curve for an input measures the benefit that consumers of the product place on the additional use of the input in the production process. The wage rate also reflects the cost to the firm and to society of using an additional unit of the input. Thus, at A in Figure 14.10 (a), the marginal benefit of an hour of labor (its marginal revenue product MRPL) is equal to its marginal cost (the wage rate w). When output and input markets are both perfectly competitive, resources are used efficiently because the difference between total benefits and total costs is maximized. Efficiency requires that the additional revenue generated by employing an additional unit of labor (the marginal revenue product of labor, MRPL) equal the benefit to consumers of the additional output, which is given by the price of the product times the marginal product of labor, (P)(MPL). When the output market is not perfectly competitive, the condition MRPL = (P)(MPL) no longer holds. Note in Figure 14.10 (b) that the curve representing the product price multiplied by the marginal product of labor [(P)(MPL)] lies above the marginal revenue product curve [(MR)(MPL)]. Point B is the equilibrium wage wM and the equilibrium labor supply LM. But because the price of the product is a measure of the value to consumers of each additional unit of output that they buy, (P)(MPL) is the value that consumers place on additional units of labor. Therefore, when LM laborers are employed, the marginal cost to the firm wM is less than the marginal benefit to consumers vM. Although the firm is maximizing its profit, its output is below the efficient level and it uses less than the efficient level of the input. Economic efficiency would be increased if more laborers were hired and, consequently, more output produced. (The gains to consumers would outweigh the firm’s lost profit.) In §8.7, we explain that economic rent is the amount that firms are willing to pay for an input less the minimum amount necessary to buy it. Economic Rent The concept of economic rent helps explain how factor markets work
. When discussing output markets in the long run in Chapter 8, we defined economic rent as the payments received by a firm over and above the minimum cost CHAPTER 14 • Markets for Factor Inputs 543 Competitive Output Market Monopolistic Output Market Wage wC A Wage vM wM SL B SL P · MPL DL = MRPL DL = MRPL LC (a) Number of workers LM Number of workers (b) FIGURE 14.10 LABOR MARKET EQUILIBRIUM In a competitive labor market in which the output market is competitive, the equilibrium wage wc is given by the intersection of the demand for labor (marginal revenue product) curve and the supply of labor curve. This is point A in part (a) of the figure. Part (b) shows that when the producer has monopoly power, the marginal value of a worker vM is greater than the wage wM. Thus too few workers are employed. (Point B determines the quantity of labor that the firm hires and the wage rate paid.) of producing its output. For a factor market, economic rent is the difference between the payments made to a factor of production and the minimum amount that must be spent to obtain the use of that factor. Figure 14.11 illustrates the concept of economic rent as applied to a competitive labor market. The equilibrium Wage Economic Rent w* B A SL FIGURE 14.11 ECONOMIC RENT DL MRPL The economic rent associated with the employment of labor is the excess of wages paid above the minimum amount needed to hire workers. The equilibrium wage is given by A, at the intersection of the labor supply and labor demand curves. Because the supply curve is upward sloping, some workers would have accepted jobs for a wage less than w. The green-shaded area ABw is the economic rent received by all workers. 0 L* Number of workers 544 PART 3 • Market Structure and Competitive Strategy price of labor is w, and the quantity of labor supplied is L. The supply of labor curve is the upward-sloping curve, and the demand for labor is the downward-sloping marginal revenue product curve. Because the supply curve tells us how much labor will be supplied at each wage rate, the minimum expenditure needed to employ L* units of labor is given by the tan-shaded area AL0B, below the supply curve to the left of the equilibrium labor supply L. In perfectly competitive markets, all workers are paid the wage w*. This wage is required to
get the last “marginal” worker to supply his or her labor, but all other workers earn rents because their wage is greater than the wage that would be needed to get them to work. Because total wage payments are equal to the rectangle 0wAL, the economic rent earned by labor is given by the area ABw*. Note that if the supply curve were perfectly elastic, economic rent would be zero. There are rents only when supply is somewhat inelastic. And when supply is perfectly inelastic, all payments to a factor of production are economic rents because the factor will be supplied no matter what price is paid. As Figure 14.12 shows, one example of an inelastically supplied factor is land. The supply curve is perfectly inelastic because land for housing (or for agriculture) is fixed, at least in the short run. With land inelastically supplied, its price is determined entirely by demand. The demand for land is given by D1, and its price per unit is s1. Total land rent is given by the green-shaded rectangle. But when the demand for land increases to D2, the rental value per unit of land increases to s2; in this case, total land rent includes the blue-shaded area as well. Thus, an increase in the demand for land (a shift to the right in the demand curve) leads both to a higher price per acre and to a higher economic rent. Price (dollars per acre) s 2 s 1 FIGURE 14.12 LAND RENT When the supply of land is perfectly inelastic, the market price of land is determined at the point of intersection with the demand curve. The entire value of the land is then an economic rent. When demand is given by D1, the economic rent per acre is given by s1, and when demand increases to D2, rent per acre increases to s2. Supply of Land D2 D1 Number of acres CHAPTER 14 • Markets for Factor Inputs 545 EXAM PLE 14.3 PAY IN THE MILITARY The U.S. Army had a personnel problem for many years. During the Civil War, roughly 90 percent of the armed forces were unskilled workers involved in ground combat. Since then, the nature of warfare has evolved. Ground combat forces now make up less than 20 percent of the armed forces. Meanwhile, in the latter half of the 20th century, changes in technology led to shortages in skilled technicians, trained pilots
, computer analysts, mechanics, and others needed to operate sophisticated military equipment. How did the military respond to this shortage? Economics provides some answers. The military pays officers primarily based on years of service. Consequently, officers with differing skill levels and abilities were usually paid similar salaries. Moreover, some skilled officers were substantially underpaid relative to salaries they could receive in the private sector. Figure 14.13 shows the inefficiency that resulted from this pay policy. The equilibrium wage rate w* is the wage that equates the demand for labor to the supply. With an inflexible wage structure, the military paid a wage w0, which is below the equilibrium wage. At w0, the quantity of labor demanded is greater than the quantity supplied, and there is a shortage of skilled workers. Over the past decade the military changed its wage structure to maintain an effective fighting force. First, a 2.7 percent pay raise went into effect in 2007, followed by a 3.9-percent raise in 2009 and a 3.4-percent raise in 2010. Even so, military pay remains low: As of 2011, a private first-class earned $20,470, a sergeant $24,736, a captain $43,927, and a major $49,964.4 However, the military went a step further, increasing the number and size of its reenlistment bonuses. Selective reenlistment bonuses were targeted at skilled jobs where there were shortages. The military also took advantage of the sustained high unemployment rates in the United States from 2008 to 2011 by emphasizing the substantial technical training that it provided, along with free or subsidized housing, food, medical care, and education. The result of these policies was to move the market for skilled labor in the military back toward the equilibrium market-clear wage w* depicted in Figure 14.13. Wage w* w0 SL Shortage DL = MRPL Number of skilled workers FIGURE 14.13 THE SHORTAGE OF SKILLED MILITARY PERSONNEL When the wage w* is paid to military personnel, the labor market is in equilibrium. When the wage is kept below w*, at w0, there is a shortage of personnel because the quantity of labor demanded is greater than the quantity supplied. 4http://militarypay.defense.gov/pay 546 PART 3 • Market Structure and Competitive Strategy 14.3 Factor Markets with Monopsony Power In some factor markets, individual buyers have buyer power that allows them to affect the prices they pay
. Often this happens either when one firm is a monopsony buyer or there are only a few buyers, in which case each firm has some monopsony power. For example, we saw in Chapter 10 that automobile companies have monopsony power as buyers of parts and components. GM and Toyota, for example, buy large quantities of brakes, radiators, and other parts and can negotiate lower prices than those charged smaller purchasers. In other cases, there might be only two or three sellers of a factor and a dozen or more buyers, but each buyer nonetheless has bargaining power—it can negotiate low prices because it makes large and infrequent purchases and can play the sellers off against each other when bargaining over price. Throughout this section, we will assume that the output market is perfectly competitive. In addition, because a single buyer is easier to visualize than several buyers who all have some monopsony power, we will restrict our attention at first to pure monopsony. Monopsony Power: Marginal and Average Expenditure When you are deciding how much of a good to purchase, you keep increasing the number of units purchased until the additional value from the last unit purchased—the marginal value—is just equal to the cost of that unit—the marginal expenditure. In perfect competition, the price that you pay for the good—the average expenditure—is equal to the marginal expenditure. However, when you have monopsony power, the marginal expenditure is greater than the average expenditure, as Figure 14.14 shows. In §10.5, we explain that a buyer has monopsony power when his purchasing decision can affect the price of the product. In §10.5, we explain that marginal expenditure is the cost of one more unit, and average expenditure is the average price paid per unit. 20 Price (per unit of input) 15 wC w* 13 10 5 FIGURE 14.14 MARGINAL AND AVERAGE EXPENDITURE When the buyer of an input has monopsony power, the marginal expenditure curve lies above the average expenditure curve because the decision to buy an extra unit raises the price that must be paid for all units, not just for the last one. The number of units of input purchased is given by L, at the intersection of the marginal revenue product and marginal expenditure curves. The corresponding wage rate w is lower than the competitive wage wc. Marginal Expenditure (ME) C SL Average Expenditure (AE) D MRPL MV 1 2 3 4 L
* 5 6 Units of input LC CHAPTER 14 • Markets for Factor Inputs 547 The factor supply curve facing the monopsonist is the market supply curve, which shows how much of the factor suppliers are willing to sell as its price increases. Because the monopsonist pays the same price for each unit, the supply curve is its average expenditure curve. The average expenditure curve is upward sloping because the decision to buy an extra unit raises the price that must be paid for all units, not just the last one. For a profit-maximizing firm, however, the marginal expenditure curve is relevant in deciding how much to buy. The marginal expenditure curve lies above the average expenditure curve: When the firm increases the price of the factor to hire more units, it must pay all units that higher price, not just the last unit hired. Purchasing Decisions with Monopsony Power How much of the input should the firm buy? As we saw earlier, it should buy up to the point where marginal expenditure equals marginal revenue product. Here the benefit from the last unit bought (MRP) is just equal to the cost (ME). Figure 14.14 illustrates this principle for a labor market. Note that the monopsonist hires L* units of labor; at that point, ME = MRPL. The wage rate w* that workers are paid is given by finding the point on the average expenditure or supply curve with L* units of labor. As we showed in Chapter 10, a buyer with monopsony power maximizes net benefit (utility less expenditure) from a purchase by buying up to the point where marginal value (MV) is equal to marginal expenditure: MV = ME For a firm buying a factor input, MV is just the marginal revenue product of the factor MRP. Thus, we have (as in the case of a competitive factor market) ME = MRP (14.7) Note from Figure 14.14 that the monopsonist hires less labor than a firm or group of firms with no monopsony power. In a competitive labor market, LC workers would be hired: At that level, the quantity of labor demanded (given by the marginal revenue product curve) is equal to the quantity of labor supplied (given by the average expenditure curve). Note also that the monopsonistic firm will be paying its workers a wage w* that is less than the wage wC that would be paid in a competitive market. Monopsony power can arise in different ways. One source can be
the specialized nature of a firm’s business. If the firm buys a component that no one else buys, it is likely to be a monopsonist in the market for that component. Another source can be a business’s location—it may be the only major employer within an area. Monopsony power can also arise when the buyers of a factor form a cartel to limit purchases of the factor, in order to buy it at less than the competitive price. (But as we explained in Chapter 10, this is a violation of the antitrust laws.) Few firms in our economy are pure monopsonists. But many firms (or individuals) have some monopsony power because their purchases account for a large portion of the market. The government is a monopsonist when it hires volunteer soldiers or buys missiles, aircraft, and other specialized military equipment. A mining firm or other company that is the only major employer in a community also has monopsony power in the local labor market. Even in these 548 PART 3 • Market Structure and Competitive Strategy cases, however, monopsony power may be limited because the government competes to some extent with other firms that offer similar jobs. Likewise, the mining firm competes to some extent with companies in nearby communities. Bargaining Power In some factor markets, there are a small number of sellers and a small number of buyers. In such cases, an individual buyer and an individual seller will negotiate with each other to determine a price. The resulting price might be high or low, depending on which side has more bargaining power. The amount of bargaining power that a buyer or seller has is determined in part by the number of competing buyers and competing sellers. But it is also determined by the nature of the purchase itself. If each buyer makes large and infrequent purchases, it can sometimes play the sellers off against each other when negotiating a price and thereby amass considerable bargaining power. An example of this kind of bargaining power occurs in the market for commercial aircraft. Airplanes are clearly key factor inputs for airlines, and airlines want to buy planes at the lowest possible prices. There are dozens of airlines, however, and only two major producers of commercial aircraft—Boeing and Airbus. One might think that as a result, Boeing and Airbus would have a considerable advantage when negotiating prices. The opposite is true. It is important to understand why. Airlines do not buy planes every day, and they do not usually buy one plane at a time. A company like American Airlines will typically order new
planes only every three or four years, and each order might be for 20 or 30 planes, at a cost of several billion dollars. As big as Boeing and Airbus are, this is no small purchase, and each seller will do all it can to win the order. American Airlines knows this and can use it to its advantage. If, for example, American is choosing between 20 new Boeing 787s or 20 new Airbus A380s (which are similar airplanes), it can play the two companies off against each other when negotiating a price. Thus if Boeing offers a price of, say, $300 million per plane, American might go to Airbus and ask it to do better. Whatever Airbus offers, American will then go back to Boeing and demand a bigger discount, claiming (truthfully or otherwise) that Airbus is offering large discounts. Then back to Airbus, back to Boeing, and so on, until American has succeeded in obtaining a large discount from one of the two companies. E XAM PLE 14.4 MONOPSONY POWER IN THE MARKET FOR BASEBALL PLAYERS In the United States, major league baseball is exempt from the antitrust laws, the result of a Supreme Court decision and the policy of Congress not to apply those laws to labor markets.5 This exemption allowed baseball team owners (before 1975) to oper- ate a monopsonistic cartel. Like all cartels, this one depended on an agreement among owners. The agreement involved an annual draft of players and a reserve clause that effectively tied each player to one team for life, thereby eliminating 5This example builds on an analysis of the structure of baseball players’ salaries by Roger Noll, who has kindly supplied us with the relevant data. CHAPTER 14 • Markets for Factor Inputs 549 most interteam competition for players. Once a player was drafted by a team, he could not play for another team unless rights were sold to that team. As a result, baseball owners had monopsony power in negotiating new contracts with their players: The only alternative to signing an agreement was to give up the game or play it outside the United States. During the 1960s and early 1970s, baseball players’ salaries were far below the market value of their marginal products (determined in part by the incremental attention that better hitting or pitching might achieve). For example, if the players’ market had been perfectly competitive, those players receiving a salary of about $42,000 in 1969 would have instead received a salary of $300,000 in 1969 dollars (
which is $1.7 million in year 2007 dollars). Fortunately for the players, and unfortunately for the owners, there was a strike in 1972 followed by a lawsuit by one player (Curt Flood of the St. Louis Cardinals) and an arbitrated labor–management agreement. This process eventually led in 1975 to an agreement by which players could become free agents after playing for a team for six years. The reserve clause was no longer in effect, and a highly monopsonistic labor market became much more competitive. The result was an interesting experiment in labor market economics. Between 1975 and 1980, the market for baseball players adjusted to a new post– reserve clause equilibrium. Before 1975, expenditures on players’ contracts made up approximately 25 percent of all team expenditures. By 1980, those expenditures had increased to 40 percent. Moreover, the average player’s salary doubled in real terms. By 1992, the average baseball player was earning $1,014,942—a very large increase from the monopsonistic wages of the 1960s. In 1969, for example, the average baseball salary was approximately $42,000 adjusted for inflation, about $236,000 in year 2007 dollars. Salaries for baseball players continued to grow. Whereas the average salary was just less than $600,000 in 1990, it had risen to $1,998,000 in 2000 and $3,305,393 by 2011, and many players earned much more. The New York Yankees as a team averaged $8,947,937 in 2011. E X AM PLE 14.5 TEENAGE LABOR MARKETS AND THE MINIMUM WAGE Increases in the national minimum wage rate (which was $4.50 in early 1996 and $7.20 in 2011) were controversial, raising the question of whether the cost of any unemployment that might be generated would be outweighed by the benefit of higher incomes to those whose wages have been increased.6 A study of the effects of the minimum wage on employment in fast-food restaurants in New Jersey added to that controversy.7 Some states have minimum wages above the Federal level. In April 1992 the New Jersey minimum wage was increased 6See Example 1.4 (page 15) for an initial discussion of the minimum wage, and Section 9.3 (page 328) for an analysis of its effects on employment. 7David Card and Alan Krueger, “Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania,
” American Economic Review 84 (September 1994). See also David Card and Alan B. Krueger, “A Reanalysis of the Effect of the New Jersey Minimum Wage on the Fast-Food Industry with Representative Payroll Data,” Working Paper No. 6386, Cambridge, MA: National Bureau of Economic Research, 1998; and Madeline Zavodny, “Why Minimum Wage Hikes May Not Reduce Employment,” Federal Reserve Bank of Atlanta, Economic Review, Second Quarter, 1998. 550 PART 3 • Market Structure and Competitive Strategy from $4.25 to $5.05 per hour. Using a survey of 410 fast-food restaurants, David Card and Alan Krueger found that employment had actually increased by 13 percent after the minimum wage went up. What is the explanation for this surprising result? One possibility is that restaurants responded to the higher minimum wage by reducing fringe benefits, which usually take the form of free and reduced-price meals for employees. A related explanation is that employers responded by providing less on-the-job training and by lowering the wages for those with experience who had previously been paid more than the new minimum wage. An alternative explanation for the increased New Jersey employment holds that the labor market for teenage (and other) unskilled workers is not highly competitive. If so, the analysis of Chapter 9 does not apply. If the unskilled fastfood labor market were monopsonistic, for example, we would expect a different effect from the increased minimum wage. Suppose that the wage of $4.25 was the wage that fast-food employers with monopsony power in the labor market would offer their workers even if there were no minimum wage. Suppose also that $5.10 would be the wage enjoyed by workers if the labor market were fully competitive. As Figure 14.14 shows, the increase in the minimum wage would not only raise the wage, but would also increase the employment level (from L* to LC). Does the fast-food study show that employers have monopsony power in this labor market? The evidence suggests no. If firms do have monopsony power but the fast-food market is competitive, then the increase in the minimum wage should have no effect on the price of fast food. Because the market for fast food is so competitive, firms paying the higher minimum wage would be forced to absorb the higher wage cost themselves. The study suggests, however, that prices did increase after the introduction of the higher minimum wage. The Card-Krueger analysis
of the minimum wage remains hotly debated. A number of critics argued that the New Jersey study was atypical. Others questioned the reliability of the data, arguing that a higher minimum wage reduces employment (see our discussion in Chapter 9).8 In response, Card and Krueger repeated their study, using a more comprehensive and accurate data set. They obtained the same results. Where does this leave us? Perhaps a better characterization of low-wage labor markets requires a more sophisticated theory (e.g., the efficiency wage theory discussed in Chapter 17). In any case, new empirical analyses should shed more light on the effects of the minimum wage. In §9.3, we explain that setting a minimum wage in a perfectly competitive market can create unemployment and a deadweight loss. In §10.2, we explain that a seller of a product has some monopoly power if it can profitably charge a price greater than marginal cost. 14.4 Factor Markets with Monopoly Power Just as buyers of inputs can have monopsony power, sellers of inputs can have monopoly power. In the extreme, the seller of an input may be a monopolist, as when a firm has a patent to produce a computer chip that no other firm can duplicate. Because the most important example of monopoly power in factor markets involves labor unions, we will concentrate most of our attention there. In the subsections that follow, we show how a labor union, which is a monopolist in the sale of labor services, might increase the well-being of its members and substantially affect nonunionized workers. 8For example, see Donald Deere, Kevin M. Murply, and Finis Welch, “Employment and the 1990– 1991 Minimum Wage Hike,” American Economic Review, Papers and Proceedings 85 (May 1995): 232–37; and David Neumark and William Wascher, “Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania: Comment,” American Economic Review 90 (2000): 1362–96. Wage per worker w1 w2 w* CHAPTER 14 • Markets for Factor Inputs 551 FIGURE 14.15 MONOPOLY POWER OF SELLERS OF LABOR When a labor union is a monopolist, it chooses among points on the buyer’s demand for labor curve DL. The seller can maximize the number of workers hired, at L, by agreeing that workers will work at wage w. The quantity of labor L1 that maxim
izes the rent earned by employees is determined by the intersection of the marginal revenue and supply of labor curves; union members will receive a wage rate of w1. Finally, if the union wishes to maximize total wages paid to workers, it should allow L2 union members to be employed at a wage rate of w2. At that point, the marginal revenue to the union will be zero. SL A DL MR L 1 L 2 L* Number of workers Monopoly Power over the Wage Rate Figure 14.15 shows a demand for labor curve in a market with no monopsony power: It aggregates the marginal revenue products of firms that compete to buy labor. The labor supply curve describes how union members would supply labor if the union exerted no monopoly power. In that case, the labor market would be competitive, and L* workers would be hired at a wage of w*, where demand DL equals supply SL. Because of its monopoly power, however, the union can choose any wage rate and the corresponding quantity of labor supplied, just as a monopolist seller of output chooses price and the corresponding quantity of output. If the union wanted to maximize the number of workers hired, it would choose the competitive outcome at A. However, if the union wished to obtain a higher-thancompetitive wage, it could restrict its membership to L1 workers. As a result, the firm would pay a wage rate of w1. Although union members who work would be better off, those who cannot find jobs would be worse off. Is a policy of restrictive union membership worthwhile? If the union wishes to maximize the economic rent that its workers receive, the answer is yes. By restricting membership, the union would be acting like a monopolist, which restricts output in order to maximize profit. To a firm, profit is the revenue that it receives less its opportunity costs. To a union, rent represents the wages that its members earn as a group in excess of their opportunity cost. To maximize rent, the union must choose the number of workers hired so that the marginal revenue to the union (the additional wages earned) is equal to the extra cost of inducing workers to work. This cost is a marginal opportunity cost because it is a measure of what an employer has to offer an additional worker to get him or her to work for the firm. However, the wage that is necessary to encourage additional workers to take jobs is given by the supply of labor curve SL. The rent-maximizing combination of wage rate and number of workers is given by the intersection of the MR
and SL curves. We have chosen the wage- employment combination of w1 and L1 with the rent-maximization premise in mind. The shaded area below the demand for labor curve, above the supply of labor curve and to the left of L1, represents the economic rent that all workers receive. In §7.1, we explain that opportunity cost is the cost associated with opportunities that are foregone by not putting a firm’s resources to their best alternative use. 552 PART 3 • Market Structure and Competitive Strategy A rent-maximizing policy might benefit nonunion workers if they can find nonunion jobs. However, if these jobs are not available, rent maximization could create too sharp a distinction between winners and losers. An alternative objective is to maximize the aggregate wages that all union members receive. Look again at the example in Figure 14.15. To achieve this goal, the number of workers hired is increased from L1 until the marginal revenue to the union is equal to zero. Because any further employment decreases total wage payments, aggregate wages are maximized when the wage is equal to w2 and the number of workers is equal to L2. Unionized and Nonunionized Workers When the union uses its monopoly power to increase members’ wages, fewer unionized workers are hired. Because these workers either move to the nonunion sector or choose initially not to join the union, it is important to understand what happens in the nonunionized part of the economy. Assume that the total supply of unionized and nonunionized workers is fixed. In Figure 14.16, the market supply of labor in both sectors is given by SL. The demand for labor by firms in the unionized sector is given by DU, the demand in the nonunionized sector by DNU. Total market demand is the horizontal sum of the demands in the two sectors and is given by DL. Suppose the union chooses to increase the wage rate of its workers above the competitive wage w*, to wU. At that wage rate, the number of workers hired in the unionized sector falls by an amount LU, as shown on the horizontal axis. As these workers find employment in the nonunionized sector, the wage rate in that sector adjusts until the labor market is in equilibrium. At the new wage rate in the nonunionized sector, wNU, the additional number of workers hired in that sector, LNU, is equal to the number of workers who left the unionized sector. Figure 14.
16 shows an adverse consequence of a union strategy directed toward raising union wages: Nonunionized wages fall. Unionization can improve working conditions and provide useful information to workers and management. But when the demand for labor is not perfectly inelastic, union workers are helped at the expense of nonunion workers. FIGURE 14.16 WAGE DISCRIMINATION IN UNIONIZED AND NONUNIONIZED SECTORS When a monopolistic union raises the wage in the unionized sector of the economy from w* to wU, employment in that sector falls, as shown by the movement along the demand curve DU. For the total supply of labor, given by SL, to remain unchanged, the wage in the nonunionized sector must fall from w* to wNU, as shown by the movement along the demand curve DNU. Wage per worker wU w* wNU SL DU DNU DL ΔLU ΔLNU Number of workers CHAPTER 14 • Markets for Factor Inputs 553 EXAM PLE 14.6 THE DECLINE OF PRIVATE-SECTOR UNIONISM For several decades, the membership of labor unions has been declining. Figure 14.7 shows the decline in union membership over the past thirty years. The decline has been relatively steady, but as we moved into the 21st century the rate of decline began to diminish and it has stabilized in recent years at about 12 percent. Interestingly, this 12 percent average masks huge differences between the public sector, where unionization was 36.2 percent in 2010, and the private sector, where unionization was only 6.9%. How have unions responded to this important dynamic? We might expect that the decline in union bargaining power might lead to different responses by union negotiators, and this has indeed been the case. Historically, union wages have been higher than the wages of their nonunion counterparts. During the 1970s, the differential between union and nonunion wages decreased substantially as unions focused on employment rather than wages. In the 1980s in response to union demands, the pattern evolved further as employers put into place two-tiered wage provisions in which wages for experienced workers were kept high, but newer union members were paid on a lower wage scale. During the past two decades, a number of economic forces have led to a further narrowing of the union-nonunion wage differential, which has remained constant over the past ten years.9 Why did the wage differential decline over time? For one thing, the demand for unionized employees has
become increasingly elastic over time as firms have found it easier to substitute capital for skilled labor in the production process. For another, globalization has meant that many companies were able Percent 24 22 20 18 16 14 12 10 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 Year FIGURE 14.17 UNION WORKERS AS A PERCENTAGE OF TOTAL The percentage of workers that are unionized has been declining steadily over the past 30 years. Data from U.S. Bureau of Labor Statistics. 9According to the Bureau of Labor Statistics, in 2010, the average union worker in the private sector earned $23.19 per hour in wage and salary income, while the average nonunion worker earned $19.28 per hour. 554 PART 3 • Market Structure and Competitive Strategy to organize their production processes so as to hire nonunion labor, either within or outside the United States. Faced with an elastic demand for its services, unions would have little choice but to give ground on wages in order to maintain employment levels. Under substantial competitive pressure, they have agreed to maintain a two-tier wage and benefits structure. E XAM PLE 14.7 WAGE INEQUALITY REVISITED In Example 2.2, we explained how the rapid growth in the demand for skilled relative to unskilled labor has been partly responsible for the growing inequality in the distribution of income in the United States. As we explained, while the demand for skilled labor has steadily increased, the supply of skilled labor has not grown much. Instead, it has been the supply of unskilled labor that has grown. What are the reasons for these changes in relative demand and supply? Have the decline in private-sector unionism and the failure of the minimum wage to keep up with inflation been important factors? Or is it the increasing importance of education, along with the role that computers now play in the labor market? A recent study provides some answers.10 From 1980 through the present, college graduates’ relative wages have grown. This is not consistent with what one would expect if the decline of unionism and/or changes in the minimum wage was the primary reason for the growing inequality. In 1963 the hourly wage of a typical college graduate was 1.5 times that of a high school graduate. By 2009, that ratio had increased to 1.95. By 2010, the median weekly salary of those with a college degree (but no further education) was $1038, whereas those with a high-school degree earned only $626
. Moving beyond college to a further professional degree led to a median wage of $1610.11 The importance of education is summarized in Figure 14.18, which shows (for 2010) median weekly earnings— as well as unemployment rates— for different levels of education. Education clearly pays. Workers with more education not only receive higher salaries, but they are also much less likely to lose their jobs and become unemployed in an economic downturn. For example, in 2010 the average unemployment rate was 5.4% for those with a bachelor’s degree, and 14.9% for those who had not completed high school. A clue to what happened is given by the dramatic increase in the use of computers by workers. In 1984, 25 percent of all workers used computers; that figure is now close to 60 percent, and it is over 80 percent for managers and professionals.12 Education and computer use have gone hand in hand to increase the demand for skilled workers. A statistical analysis shows that, overall, the spread of computer technology is responsible for nearly half the increase in relative wages. Furthermore, the growth in the demand for skilled workers has occurred primarily within industries where computers have become increasingly useful. These data, along with the numbers shown in Figure 14.18, should motivate you to continue your college and graduate studies—especially your study of microeconomics. 10David Autor, “The Polarization of Job Opportunities in the U.S. Labor Market,” Center for American Progress: The Hamilton Project, April, 2010. See also David H. Autor, Lawrence Katz, and Alan B. Krueger, “Computing Inequality: Have Computers Changed the Labor Market?” Quarterly Journal of Economics 113 (November 1998): 1169–1213. 11Bureau of Labor Statistics, Current Population Survey 2010. 12National Center for Educational Statistics, Digest of Educational Statistics, Table 432. CHAPTER 14 • Markets for Factor Inputs 555 Unemployment rate in 2010 (%) Median weekly earnings in 2010 ($) 1.9 Doctoral degree 2.4 Professional degree 4.0 Master’s degree 5.4 Bachelor’s degree 1,550 1,610 1,272 1,038 7.0 9.2 10.3 14.9 Average: 8.2% Associate degree Some college, no degree High school diploma Less than a high school diploma 767 712 626 444 Average: $782 FIGURE 14.18 EDUCATION, EARNINGS, AND EMPLOY
MENT Median weekly earnings (in 2010) were much higher, and average unemployment rates were much lower, for workers with higher levels of education. Data from U.S. Bureau of Labor Statistics, Current Population Survey. SUMMARY 1. In a competitive input market, the demand for an input is given by the marginal revenue product, the product of the firm’s marginal revenue, and the marginal product of the input. 2. A firm in a competitive labor market will hire workers to the point at which the marginal revenue product of labor is equal to the wage rate. This principle is analogous to the profit-maximizing output condition that production be increased to the point at which marginal revenue is equal to marginal cost. 3. The market demand for an input is the horizontal sum of industry demands for the input. But industry demand is not the horizontal sum of the demands of all the firms in the industry. To determine industry demand, one must remember that the market price of the product will change in response to changes in the price of an input. 4. When factor markets are competitive, the buyer of an input assumes that its purchases will have no effect on its price. As a result, the firm’s marginal expenditure and average expenditure curves are both perfectly elastic. 5. The market supply of a factor such as labor need not be upward sloping. A backward-bending labor supply curve can result if the income effect associated with a higher wage rate (more leisure is demanded because it is a normal good) is greater than the substitution effect (less leisure is demanded because its price has gone up). 6. Economic rent is the difference between the payments to factors of production and the minimum payment that would be needed to employ them. In a labor market, rent is measured by the area below the wage level and above the marginal expenditure curve. 7. When a buyer of an input has monopsony power, the marginal expenditure curve lies above the average expenditure curve, which reflects the fact that the monopsonist must pay a higher price to attract more of the input into employment. 8. When the input seller is a monopolist, such as a labor union, the seller chooses the point on the marginal revenue product curve that best suits its objective. Maximization of employment, economic rent, and wages are three plausible objectives for labor unions. 556 PART 3 • Market Structure and Competitive Strategy QUESTIONS FOR REVIEW 1. Why is a firm’s demand for labor curve more inelastic when the firm has monopoly power in
the output market than when the firm is producing competitively? 2. Why might a labor supply curve be backward bending? 3. How is a computer company’s demand for computer programmers a derived demand? 4. Compare the hiring choices of a monopsonistic and a competitive employer of workers. Which will hire more workers, and which will pay the higher wage? Explain. 5. Rock musicians sometimes earn several million dollars per year. Can you explain such large incomes in terms of economic rent? 6. What happens to the demand for one input when the use of a complementary input increases? 7. For a monopsonist, what is the relationship between the supply of an input and the marginal expenditure on it? 8. Currently the National Football League has a system for drafting college players by which each player is picked by only one team. The player must sign with that team or not play in the league. What would happen to the wages of both newly drafted and more experienced football players if the draft system were repealed and all teams could compete for college players? 9. The government wants to encourage individuals on welfare to become employed. It is considering two possible incentive programs: a. Give firms $2 per hour for every individual on wel- fare who is hired. b. Give each firm that hires one or more welfare workers a payment of $1000 per year, irrespective of the number of hires. To what extent is each of these programs likely to be effective at increasing the employment opportunities for welfare workers? 10. A small specialty cookie company, whose only variable input is labor, finds that the average worker can produce 50 cookies per day, the cost of the average worker is $64 per day, and the price of a cookie is $1. Is the company maximizing its profit? Explain. 11. A firm uses both labor and machines in production. Explain why an increase in the average wage rate causes both a movement along the labor demand curve and a shift of the curve. EXERCISES 1. Suppose that the wage rate is $16 per hour and the price of the product is $2. Values for output and labor are in units per hour. q 0 20 35 47 57 65 70 L 0 1 2 3 4 5 6 a. Find the profit-maximizing quantity of labor. b. Suppose that the price of the product remains at $2 but that the wage rate increases to $21. Find the new profit-maximizing level of L. c. Suppose that the price of the product increases to
$3 and the wage remains at $16 per hour. Find the new profit-maximizing L. d. Suppose that the price of the product remains at $2 and the wage at $16, but that there is a technological breakthrough that increases output by 25 percent for any given level of labor. Find the new profit-maximizing L. 2. Assume that workers whose incomes are less than $10,000 currently pay no federal income taxes. Suppose a new government program guarantees each worker $5000, whether or not he or she earns any income. For all earned income up to $10,000, the worker must pay a 50-percent tax. Draw the budget line facing the worker under this new program. How is the program likely to affect the labor supply curve of workers? 3. Using your knowledge of marginal revenue product, explain the following: a. A famous tennis star is paid $200,000 for appearing in a 30-second television commercial. The actor who plays his doubles partner is paid $500. b. The president of an ailing savings and loan is paid not to stay in his job for the last two years of his contract. c. A jumbo jet carrying 400 passengers is priced higher than a 250-passenger model even though both aircraft cost the same to manufacture. 4. The demands for the factors of production listed below have increased. What can you conclude about changes in the demands for the related consumer goods? If demands for the consumer goods remain unchanged, what other explanation is there for an increase in derived demands for these items? a. Computer memory chips b. Jet fuel for passenger planes c. Paper used for newsprint d. Aluminum used for beverage cans 5. Suppose there are two groups of workers, unionized and nonunionized. Congress passes a law that requires all workers to join the union. What do you expect to happen to the wage rates of formerly nonunionized workers? Of those workers who were originally unionized? What have you assumed about the union’s behavior? 6. Suppose that a firm’s production function is given by Q = 12L − L2, for L = 0 to 6, where L is labor input per day and Q is output per day. Derive and draw the firm’s demand for labor curve if the firm’s output sells for $10 in a competitive market. How many workers will the firm hire when the wage rate is $30 per day? $60 per day? (Hint
: The marginal product of labor is 12 − 2L.) 7. The only legal employer of military soldiers in the United States is the federal government. If the government uses its knowledge of its monopsonistic position, what criteria will it employ when determining how many soldiers to recruit? What happens if a mandatory draft is implemented? CHAPTER 14 • Markets for Factor Inputs 557 8. The demand for labor by an industry is given by the curve L = 1200 − 10w, where L is the labor demanded per day and w is the wage rate. The supply curve is given by L = 20w. What is the equilibrium wage rate and quantity of labor hired? What is the economic rent earned by workers? 9. Using the same information as in Exercise 8, suppose now that the only labor available is controlled by a monopolistic labor union that wishes to maximize the rent earned by union members. What will be the quantity of labor employed and the wage rate? How does your answer compare with your answer to Exercise 8? Discuss. (Hint: The union’s marginal revenue curve is given by MR = 120 − 0.2L.) *10. A firm uses a single input, labor, to produce output q according to the production function q = 8 1L. The commodity sells for $150 per unit and the wage rate is $75 per hour. a. Find the profit-maximizing quantity of L. b. Find the profit-maximizing quantity of q. c. What is the maximum profit? d. Suppose now that the firm is taxed $30 per unit of output and that the wage rate is subsidized at a rate of $15 per hour. Assume that the firm is a price taker, so the price of the product remains at $150. Find the new profit-maximizing levels of L, q, and profit. e. Now suppose that the firm is required to pay a 20 percent tax on its profits. Find the new profit-maximizing levels of L, q, and profit. This page intentionally left blank C H A P T E R 15 Investment, Time, and Capital Markets In Chapter 14, we saw that in competitive markets, firms decide how much to purchase each month by comparing the marginal revenue product of each factor to its cost. The decisions of all firms determine the market demand for each factor, and the market price is the price that equates the quantity demanded with the quantity supplied. For factor inputs such as labor and raw materials, this
picture is reasonably complete, but not so for capital. The reason is that capital is durable: It can last and contribute to production for years after it is purchased. Firms sometimes rent capital in much the same way that they hire workers. For example, a firm might rent office space for a monthly fee, just as it hires a worker for a monthly wage. But more often, capital expenditures involve the purchases of factories and equipment that are expected to last for years. This introduces the element of time. When a firm decides whether to build a factory or purchase machines, it must compare the outlays it would have to make now with the additional profit that the new capital will generate in the future. To make this comparison, it must address the following question: How much are future profits worth today? This problem does not arise when hiring labor or purchasing raw materials. To make those choices, the firm need only compare its current expenditure on the factor—e.g., the wage or the price of steel—with the factor’s current marginal revenue product. In this chapter, we will learn how to calculate the current value of future flows of money. This is the basis for our study of the firm’s investment decisions. Most of these decisions involve comparing an outlay today with profits that will be received in the future; we will see how firms can make this comparison and determine whether the outlay is warranted. Often, the future profits resulting from a capital investment are higher or lower than anticipated. We will see how firms can take this kind of uncertainty into account. Individuals also make decisions involving costs and benefits occurring at different points in time, and the same principles apply. For example, we will see how a consumer choosing a new air conditioner can determine whether it makes economic sense to buy a more energyefficient model that costs more but will result in lower electricity bills in the future. We will also discuss investments in human capital. Does it make economic sense, for example, to go to college or graduate school rather than take a job and start earning an income 15.1 Stocks versus Flows 560 15.2 Present Discounted Value 15.3 The Value of a Bond 15.4 The Net Present Value Criterion for Capital Investment Decisions 15.5 Adjustments for Risk 15.6 Investment Decisions by Consumers 15.7 Investments in Human Capital 561 564 569 573 578 580 *15.8 Intertemporal Production Decisions—Depletable Resources 15.9 How Are Interest Rates Determined
? 584 588 15.1 The Value of Lost Earnings 15.2 The Yields on Corporate Bonds 563 567 15.3 The Value of a New York City Taxi Medallion 573 15.4 Capital Investment in the Disposable Diaper Industry 576 15.5 Choosing an Air Conditioner and a New Car 15.6 Should You Go to Business School? 579 582 15.7 How Depletable Are Depletable Resources? 587 559 560 PART 3 • Market Structure and Competitive Strategy In §14.1, we explain that in a competitive factor market, the demand for each factor is given by its marginal revenue product—i.e., the additional revenue earned from an incremental unit of the factor. We will examine other intertemporal decisions that firms sometimes face. For example, producing a depletable resource, such as natural gas or oil, means that less will be available to produce in the future. How should a producer take this into account? How long should a timber company let trees grow before harvesting them for lumber? The answers to these investment and production decisions depend in part on the interest rate that one pays or receives when borrowing or lending money. We will discuss the factors that determine interest rates and explain why interest rates on government bonds, corporate bonds, and savings accounts differ. Recall from §6.1 that a firm’s production function involves flows of inputs and outputs: It turns certain amounts of labor and capital each year into an amount of output that same year. 15.1 Stocks versus Flows Before proceeding, we must be clear about how to measure capital and other factor inputs that firms purchase. Capital is measured as a stock, i.e., as a quantity of plant and equipment that the firm owns. For example, if a firm owns an electric motor factory worth $10 million, we say that it has a capital stock worth $10 million. Inputs of labor and raw materials, on the other hand, are measured as flows. The output of the firm is also a flow. For example, this same firm might use 20,000 worker-hours of labor and 20,000 pounds of copper per month to produce 8000 electric motors per month. (The choice of monthly units is arbitrary; we could just as well have expressed these quantities in weekly or annual terms—for example, 240,000 worker- hours of labor per year, 240,000 pounds of copper per year, and 96,000 motors per year.) Let
’s look at this producer of electric motors in more detail. Both variable cost and the rate of output are flows. Suppose the wage rate is $15 per hour and the price of copper is $2.00 per pound. Thus the variable cost is (20,000)($15) + (20,000)($2.00) = $340,000 per month. Average variable cost, on the other hand, is a cost per unit: $340,000 per month 8000 units per month = $42.50 per unit Suppose the firm sells its motors for $52.50 each. Then its average profit is $52.50 - $42.50 = $10.00 per unit, and its total profit is $80,000 per month. (Note that total profit is also a flow.) To make and sell these motors, however, the firm needs capital—namely, the factory that it built for $10 million. Thus the firm’s $10 million capital stock allows it to earn a flow of profit of $80,000 per month. Was the $10 million investment in this factory a sound decision? To answer this question, we must translate the $80,000 per month profit flow into a number that we can compare with the factory’s $10 million cost. Suppose the factory is expected to last for 20 years. In that case the problem, simply put, is: What is the value today of $80,000 per month for the next 20 years? If that value is greater than $10 million, the investment was a good one. A profit of $80,000 per month for 20 years comes to ($80,000)(20)(12) = $19.2 million. That would make the factory seem like an excellent investment. But is $80,000 five years—or 20 years—from now worth $80,000 today? No, because money today can be invested—in a bank account, a bond, or other interest-bearing CHAPTER 15 • Investment, Time, and Capital Markets 561 assets—to yield more money in the future. As a result, $19.2 million received over the next 20 years is worth less than $19.2 million today. 15.2 Present Discounted Value We will return to our $10 million electric motor factory in Section 15.4, but first we must address a basic problem: How much is $1 paid in the future worth today? The answer depends on the
interest rate: the rate at which one can borrow or lend money. Suppose the annual interest rate is R. (Don’t worry about which interest rate this actually is; later, we’ll discuss the various types of interest rates.) Then $1 today can be invested to yield (1 + R) dollars a year from now. Therefore, 1 + R dollars is the future value of $1 today. Now, what is the value today, i.e., the present discounted value (PDV), of $1 paid one year from now? The answer is easy: because 1 + R dollars one year from now is worth (1 + R)/(1 + R) = $1 today, $1 a year from now is worth $1/(1 + R) today. This is the amount of money that will yield $1 after one year if invested at the rate R. What is the value today of $1 paid two years from now? If $1 were invested today at the interest rate R, it would be worth 1 + R dollars after one year, and (1 + R)(1 + R) = (1 + R)2 dollars at the end of two years. Because (1 + R)2 dollars two years from now is worth $1 today, $1 two years from now is worth $1/(1 + R)2 today. Similarly, $1 paid three years from now is worth $1/(1 + R)3 today, and $1 paid n years from now is worth $1/(1 + R)n today.1 We can summarize this as follows: • interest rate Rate at which one can borrow or lend money. • present discounted value (PDV) The current value of an expected future cash flow. PDV of $1 paid after 1 year = PDV of $1 paid after 2 years = PDV of $1 paid after 3 years = f PDV of $1 paid after n years = $1 (1 + R) $1 (1 + R)2 $1 (1 + R)3 $1 (1 + R)n Table 15.1 shows, for different interest rates, the present value of $1 paid after 1, 2, 5, 10, 20, and 30 years. Note that for interest rates above 6 or 7 percent, $1 paid 20 or 30 years from now is worth very little today. But this is not the case for low interest rates. For example, if R is 3
percent, the PDV of $1 paid 20 years from now is about 55 cents. In other words, if 55 cents were invested now at the rate of 3 percent, it would yield about $1 after 20 years. 1We are assuming that the annual rate of interest R is constant from year to year. Suppose the annual interest rate were expected to change, so that R1 is the rate in year 1, R2 is the rate in year 2, and so forth. After two years, $1 invested today would be worth (1 + R1)(1 + R2), so that the PDV of $1 received two years from now is $1/(1 + R1)(1 + R2). Similarly, the PDV of $1 paid n years from now is $1/(1 + R1)(1 + R2)(1 + R3)…(1 + Rn). 562 PART 3 • Market Structure and Competitive Strategy TABLE 15.1 PDV OF $1 PAID IN THE FUTURE INTEREST RATE 1 YEAR 2 YEARS 5 YEARS 10 YEARS 20 YEARS 30 YEARS 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.20 $0.990 $0.980 $0.951 $0.905 $0.820 $0.742 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.870 0.833 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.756 0.694 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.497 0.402 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.247 0.162 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.061 0.026 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.015 0.

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