Chapter 19 Oligopoly Mc GrawHillIrwin Copyright 2008 by

Main Topics ¢ Oligopoly and game theory ¢ The Bertrand model ¢ Cournot quantity competition ¢ Price competition with differentiated products ¢ Collusion ¢ Market entry and monopolistic competition ¢ Antitrust policy 19 -2

Oligopoly and Game Theory ¢ Economists use game theory to analyze oligopoly competition ¢ Game theory looks for price or quantity choices at which each firm is doing as well as it can given the prices charged or quantities produced by its rivals ¢ In a Nash Equilibrium, each firm is making a profit-maximizing choice given the actions of its rivals ¢ In game theory, a firm’s most profitable choice given the actions of its rivals is called its best response 19 -3

Figure 19. 1: Oligopoly Pricing Game 19 -4

Bertrand Model ¢ The simplest possible oligopoly market is one with two firms (a duopoly) that produce identical (homogeneous) goods ¢ Firms set their prices simultaneously ¢ Buyers observe prices and decide how much to purchase from each firm ¢ Purchase from firm with lower price ¢ This is the Bertrand model of oligopoly ¢ After Joseph Bertrand, published in 1883 ¢ Each firm’s most profitable choice depends on what the other does ¢ With linear demand curve, a price that is closer to the monopoly price results in greater profit ¢ Firms have an incentive to undercut each other’s price in order to win sales ¢ Undercutting behavior drive prices down to marginal cost ¢ Example: two concrete companies, marginal cost = $40 per cubic yard, monopoly price = $70 19 -5

Individual Firm Demand ¢ To identify the Nash equilibrium in the Bertrand game, think about each firm’s demand curve ¢ A firm’s demand curve shows the relationship between the firm’s price and the quantity it sells given the behavior of its rivals ¢ A firm has many demand curves, each one corresponding to a different choice by its rival ¢ Notice that if a firm charges a higher price than his rival, he sells nothing ¢ If he sets the same price as his rival, his sales equal half the market demand at that price ¢ If he charges a lower price than his rival, his sales equal the market demand at his price 19 -6

Figure 19. 2: Market Demand Firm Demand Curve 19 -7

Nash Equilibrium in the Bertrand Duopoly ¢ In the concrete company example, if both firms charge $40 it is a Nash equilibrium ¢ Recall that $40 is their marginal cost ¢ $40 is the best each firm can do given that the other is charging $40 ¢ Bertrand result is the same as the perfectly competitive outcome ¢ Monopoly price would be $70 ¢ To maximize their joint profit each firm would need to charge $70 ¢ Each firm undercuts that price to increase its own profit ¢ Each firm ignores the negative effect of its behavior on its rival’s profit ¢ Implies that welfare losses due to market power are limited to monopoly markets ¢ Overly optimistic ¢ Some of the model’s assumptions may be at odds with reality 19 -8

Figure 19. 3: Nash Equilibrium in the Bertrand Model ¢ Joe can’t do better than charging $40 if his rival is charging $40 ¢ The parallel argument holds from his rival’s perspective ¢ So both firms charging $40 is a Nash equilibrium 19 -9 100 Price ($/cubic yard) ¢ D 40 is Joe’s demand curve when his rival charges $40 ¢ Joe’s profit is zero if he charges $40, negative if he charges less than $40, and zero if he charges more than $40 D D 40 MC 40 2000 4000 3000 6000 8000 Concrete (Cubic Yards per Year) 10000

Sample Problem 1 (19. 1) Suppose Joe, Louie, and Rebecca compete in the Bertrand ready-mix concrete market described in Section 19. 2. Show that in any Nash equilibrium, all sales must occur at a price of $40 (equal to marginal cost). Extend your argument to show that this statement will be true as long as two or more firms are competing in the market. In that example: P = 100 – 0. 01 Q

Cournot Quantity Competition ¢ In many settings a firm can sell only a limited quantity at a time ¢ Bertrand model may overstate firms’ ability to steal business from one another ¢ In some situations quantities rather than prices drive market outcomes ¢ In the Cournot model of oligopoly: ¢ Firms choose quantities simultaneously ¢ Price clears the market given the total quantity produced ¢ Named after French mathematician Augustin Cournot, introduced in 1838 ¢ Assume homogeneous goods ¢ Provides insights when firms make capacity decisions that determine sales capabilities 19 -11

Figure 19. 4: Price Determination in the Cournot Model ¢ Given the output of the two firms: ¢ The price clears the market ¢ Amount demanded equals amount supplied ¢ Here, total output is 4, 000 ¢ Price = $60/cubic yard 19 -12

Nash Equilibrium in a Cournot Market ¢ Important difference from equilibrium in Bertrand market: equilibrium price is always above marginal cost ¢ P=MC will yield profit of zero ¢ Firm could do better by reducing output ¢ This would raise market-clearing price above marginal cost ¢ Profit would be positive ¢ In a Nash equilibrium each firm’s output choice maximizes its profit given its rival’s output choice ¢ Need to find each firm’s best response for each possible output level for its rival ¢ First step is to derive one firm’s demand curve for each possible output level for its competitor ¢ For the cement example, the firm’s demand curve is shifted leftward from the market demand curve by an amount equal to its rival’s output at every price 19 -13

Best Responses ¢ A firm’s best response is the quantity that equates his marginal revenue with his marginal cost ¢ The marginal revenue curve is derived from the firm’s demand curve ¢ By graphing the firm’s best response at each of its competitor’s possible output levels we obtain its best response curve: ¢ Shows its best choice in response to each possible action by its rival ¢ Nash equilibrium occurs where the two firms’ best response curves cross 19 -14

Figure 19. 6: Best Responses in the Cournot Model 19 -15

Figure 19. 7: Best Response Curves in the Cournot Model 19 -16

¢ The Nash equilibrium is the point where the best response curves cross ¢ Each firm produces 2, 000 cubic yards ¢ Can also find these equilibrium output choices using algebra Joe’s Output (Cubic yards per year) Figure 19. 8: Nash Equilibrium in the Cournot Model 6000 5000 4000 3000 BRRebecca Nash equilibrium 2000 BRJoe 1000 2000 3000 4000 5000 6000 Rebecca’s Output (Cubic yds per year) 19 -17

Figure 19. 9: Deadweight Loss from Duopoly vs. Monopoly ¢ Deadweight loss with oligopoly: ¢ Equals area of the light red triangle ¢ $20, 000 per year ¢ Deadweight loss of monopoly ¢ Equals total of dark and light red areas ¢ $45, 000 per year ¢ Larger than oligopoly because monopoly price is further above marginal cost 19 -18

Sample Problem 2 (19. 3) Repeat worked out problem 19. 1 (page 712), but assume instead that Joe and Rebecca both have a marginal cost of $55 per cubic yard. What is the deadweight loss in this market? In this problem: Qd = 10, 000 – 100 P

Oligopoly and Perfect Competition ¢ When the number of competitors in a market grows very large, expect firms to begin acting like price takers ¢ In a Cournot market, as the number of firms grows larger, the market outcome approaches competitive equilibrium ¢ Expand the cement example to include additional firms ¢ Joes doesn’t care who is producing the rest of the output in the market, the effect on the price he receives is the same ¢ Only their total output matters in determining his best response ¢ His best response function will take the same form as before but consider the total output of his rivals rather than just Rebecca’s output ¢ As the number of firms increases the price falls and the quantity produced increases 19 -20

Markups in a Cournot Model ¢ In Cournot oligopoly, size of the markup is related to the elasticity of market demand: ¢ Here, N denotes the number of identical Cournot competitors ¢ For a given number of firms, the less elastic the demand the greater the markup ¢ The less elastic the demand, the greater the increase in price that results from a given reduction in a firm’s output ¢ The more attractive the idea of restricting output ¢ For a given demand elasticity, the larger the number of firms, the lower the markup ¢ Confirms that as N grows larger, the markup falls to zero, so the market price approaches the marginal cost 19 -21

Price Competition with Differentiated Products ¢ Often, the products that firms in an oligopoly market sell are not homogeneous ¢Coke and Pepsi, for example ¢ When consumer do not view similar products as perfect substitutes, those products are differentiated ¢ The Bertrand model result of competition driving prices down to marginal cost does not hold with differentiated products ¢ Firms can make a positive profit by raising their price above marginal cost 19 -22

Differentiated Products: Coke and Pepsi Example ¢ Assume there are no other relevant products ¢ Marginal cost to produce a can of either brand is 30 cents ¢ If Pepsi’s price is 30 cents and Coke charges slightly more, it will lose some customers but not all of them ¢ Coke can make a positive profit by raising its price above marginal cost ¢ Coke’s demand curve decreases gradually as its price rises ¢ Coke’s marginal revenue curve is derived from its demand curve ¢ A lower Pepsi price shifts Coke’s demand curve to the left since they are substitutes 19 -23

Figure 19. 12: Coke’s Demand Curves 19 -24

Best Responses and Nash Equilibrium ¢ Obtain Coke’s best response curve by graphing the firm’s best response at each possible price that Pepsi might charge ¢ Coke’s profit-maximizing sales quantity occurs at the intersection of the marginal revenue and marginal cost curves ¢ The corresponding price is found on the firm’s demand curve ¢ Coke’s best response curve is upward sloping ¢ The more Pepsi charges, the more Coke should charge ¢ Follow the same steps to find Pepsi’s best response curve ¢ Graph the two curves with Coke’s price on one axis and Pepsi’s on the other ¢ Nash equilibrium is where the two curves cross ¢ Each firm chooses the price that maximizes its profit given its rival’s price 19 -25

Figure 19. 14: Nash Equilibrium with Differentiated Products 19 -26

Incentives to Differentiate ¢ Competition becomes more intense as products become less differentiated ¢Consumers are more willing to switch in response to price differences ¢ A firm has an incentive to differentiate its products from those of rivals ¢ Product differentiation is an important strategy firms use to ensure a profit 19 -27

Sample Problem 3 (19. 8) Suppose a single monopolist controls the market for Coke and Pepsi in worked out problem 19. 2 (page 722). If the monopolist sets the same price for Coke and Pepsi, what price would maximize its profit? How does that price compare to the equilibrium prices in worked-out problem 19. 2? In that problem: QC = 45 – 50 PC + 200(PP-PC), QP = 45 – 50 PP + 200(PC-PP) and MC=0. 30

Collusion ¢ In the real world firms compete against each other over and over ¢ Repetition can make a big difference in the outcome of oligopolistic competition ¢ In the infinitely repeated Bertrand model, firms play the Bertrand pricing game over and over with no definite end ¢ The noncooperative outcome is the repetition of the Nash equilibrium that would arise if the firms were to compete just one time ¢ There may be other equilibrium outcomes ¢ Sometimes possible for firms to sustain the monopoly price ¢ E. g. , by adopting a grim strategy 19 -29

Collusion, continued ¢ Collusion relies on the credible threat of a future price war to keep firms from undercutting each other’s prices ¢ If future profits are important enough firms will not want to risk a price war ¢ This will be the case if the interest rate is not to high ¢ So future losses are significant from today’s perspective ¢ Factors that inhibit collusion: ¢ With more firms, there is more to gain today and less to lose in the future from undercutting ¢ Differing marginal costs ¢ Observing rivals’ costs imperfectly 19 -30

Tacit vs. Explicit Collusion ¢ What determines which equilibrium prevails when firms compete repeatedly? ¢ Explicit collusion is one possibility ¢Firms engage in explicit collusion when they communicate to reach an agreement about prices ¢Illegal in many countries, including the U. S. ¢ Tacit collusion is another ¢Collusion without communication, sustaining a price above the noncooperative price ¢Generally not illegal, but less likely to be successful 19 -31

Market Entry and Monopolistic Competition ¢ Firms enter an oligopolistic market in response to profit opportunities ¢ Several factors affect the number of firms that enter: ¢Fixed cost associated with becoming active in the market ¢As the fixed cost shrinks and the number of firms grows, the possible profits of an active firm approach zero ¢Size of the market ¢Intensity of competition ¢Because profits are lower in a market with more intense competition, fewer firms will enter 19 -32

Figure 19. 17: Factors Affecting the Number of Firms 19 -33

Market Entry and Social Welfare ¢ Firms’ individual entry decisions in oligopoly markets may not maximize aggregate surplus ¢ Entry may not occur even if it would increase aggregate surplus ¢If entry by the first firm would be unprofitable ¢Government may want to subsidize entry by first firm to increase aggregate surplus ¢ Once one firm has entered the market, excessive entry may result and lower aggregate surplus ¢ Business stealing arises when some of a new entrant’s sales come at the expense of existing firms 19 -34

Figure 19. 19: Entry and Welfare 19 -35

Product Differentiation and Monopolistic Competition ¢ In markets with product differentiation firms must decide what kind of good to produce ¢ Monopolistic competition is a market with: ¢ A large number of firms ¢ Each produces a unique product ¢ Prices above marginal cost ¢ Close to zero profit, net of fixed costs ¢ Firm’s demand curve is downward sloping due to differentiation ¢ At the firm’s profit-maximizing price and quantity, P=AC so the firm breaks even ¢ Entry in monopolistically competitive markets may be excessive or insufficient relative to the level that maximizes aggregate surplus 19 -36

Figure 19. 20: Monopolistic Competition 19 -37

Antitrust Policy ¢ Antitrust legislation focuses on maintaining rules of competition that enable markets to produce good outcomes ¢ Limit welfare losses from market power ¢ Investigation and intervention occur only when the rules may have been violated ¢ Thee U. S. laws provide the foundation of antitrust policy: ¢ Sherman Act (1980), Clayton Act (1914), and Federal Trade Commission Act (1914) ¢ Enforced by the DOJ, FTC, and through private suits ¢ Two categories of antitrust laws: ¢ Collaboration among competitors ¢ Exclusion from the market ¢ Firms engage in price fixing when they agree on the prices they will charge or the quantities they will produce 19 -38

Horizontal Mergers ¢ In a horizontal merger, two or more competing firms combine their operations ¢ A main form of collaboration ¢ In the US, large firms who wish to merge must notify the DOJ and FTC in advance ¢ Concern with horizontal mergers is that they may raise market prices by reducing competition ¢ Can also have beneficial effects: ¢ Cost reductions from reorganized production processes ¢ Increase aggregate surplus ¢ Reduce market prices ¢ Antitrust agencies must weigh these factors when deciding whether to approve a merger ¢ Typical test applied for merger approval in the U. S. requires that prices not rise 19 -39

Figure 19. 23: Welfare Effects of Horizontal Mergers 19 -40

Exclusionary Behavior ¢ Focuses on the ways a dominant firm can reduce competition by excluding rivals from the market ¢ Either fully or by impairing their competitiveness ¢ Recent Microsoft case involved exclusionary behavior ¢ Exclusionary behaviors may include: ¢ Predatory pricing ¢ Exclusive contracts ¢ Bundling ¢ Difficult to restrain dominant firms without limiting their surplus-enhancing actions ¢ Balancing these two concerns is a challenge 19 -41

Sample Problem 4 (19. 18) An economist has found that patients who suffer from diseases that are more prevalent than other diseases are more likely to take the medicine their doctors prescribe. Why might this be so?