# CLASS 18: PRICE DISCRIMINATION. OLIGOPOLY, AND GAME THEORY PRICE DISCRIMINATION

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1 GSD 5203/KSG API-105 CLASS 18: PRICE DISCRIMINATION. OLIGOPOLY, AND GAME THEORY PRICE DISCRIMINATION Until now we have assumed that a firm charges every customer the same price Price discrimination: Charging different customers different prices for the same product Purposes: For private firm: to capture more consumer s surplus For government regulatory agency: to allow firm to price at MC without incurring losses (if IRS) or excess profits (if DRS) Limitations: 1. Need market power (barrier to entry, no close substitutes) Otherwise competitors will steal your cream customers 2. Must know different consumer s maximum willingness to pay 3. Must keep customers separate and prevent resale among them TYPES OF PRICE DISCRIMINATION (1) FIRST DEGREE (also known as PERFECT PRICE DISCRIMINATION) Definition: charge each customer exactly what he is willing to pay and thus capture all the consumers surplus. Examples: a car salesperson bargaining over the price, or a college that gives financial aid according to the ability of each student to pay D = MR with perfect Price discrimination D market (2) SECOND DEGREE (also known as BLOCK OR MULTIPART PRICING) Definition: charge every customer the same price but you charge one rate for the first block or units of service they require and a different rate for subsequent blocks. For example, a water company might charge \$2 per cubic meter for the first 10 cubic meters per month and \$1 per cubic meter for the 11 th and on. There are several forms of second degree price discrimination: 1

2 (A) Descending blocks: where you charge less per unit for the second block than the first, and for the third than the second, etc. The graph to the left shows a typical customer s demand curve with P 1 descending two block pricing P 2 P 1 is the unit price for the first block, P 2 the unit price for subsequent units, and Q* the Q* amount the consumer chooses D individual Note: Sometimes mandated by public agency regulating a private natural monopoly. Natural monopoly means IRS, so MC is below AC. P 2 can be set at MC and P 1 just high enough so the firm can recover its total costs from its customers. (B) Two-part pricing: a variant of descending block pricing in which the first block is to merely subscribe and the second block is priced at marginal cost. In theory, the first part could be set to capture all the consumers surplus of the customer. P 2 P 1 is the price to subscribe, D individual P 2 the price per unit, and Q* the amount the consumer chooses Q* (unless P 1 absorbs all consumer s surplus) (C) Ascending or inverted block pricing: when the unit price for the first block is less than the unit price for the subsequent blocks. The graph to the right shows a two-block ascending block system P 2 P 1 D individual Q* Note: Never voluntarily used by a monopolist. But public firm (or regulator) may require if firm has decreasing returns to scale. With DRS, MC greater than AC. P 2 can be set at MC and P 1 just low enough so the firm recovers costs but does not earn huge profits. 2

3 (3) THIRD DEGREE (also known as INVERSE ELASTICITY or RAMSEY PRICING) The firm operates in two or more different markets and charges a different price in each market. For example, a pharmaceutical company charges different prices in third world than first world countries. Or a movie theater sells tickets at different prices for adults, senior citizens and children: \$ \$ \$ D ADULT D CHILD MC MC MC MR ADULT D SENIOR MR CHILD Q ADULT Q SENIOR Q CHILD MR SENIOR Often it is called inverse elasticity pricing because the relative prices charged are higher in the less elastic markets. MR ADULT = MR CHILD = MC Remember from class 16 that the monopolist will charge a markup over MC that is inversely related to the elasticity of demand: (P MC)/P = -1/e D If movie theaters serve both adults and children, the MC of a seat for either is the same. But the adults will be charged more because their demand is less price elastic. An aside on Ramsey pricing: Ramsey pricing is a related pricing strategy named after an economist Frank Ramsey who invented it in the 1930s. Suppose that marginal cost pricing will not raise enough money to meet the financial needs of the enterprise. Ramsey asked what third-degree discriminatory pricing scheme would raise the required revenue while minimizing the allocative inefficiencies (deadweight losses) from doing so? He found that the relative mark-up over marginal cost for each submarket should be inversely related to the relative absolute value of the elasticity in that submarket. In the simple case where there were no cross price elasticities of demand between different submarkets, Ramsey showed that the optimal mark up over marginal cost in each submarket i would be: (P i - MC i ) / P i = - K / e Di where (P i is the price charged in submarket i, MC i is the marginal cost of serving submarket i, e Di is the price elasticity of demand in submarket I, and K is a constant determined by the amount of revenue that must be raised. 3

4 OLIGOPOLIES, CARTELS AND GAMES OLIGOPOLY Definition: Structural: a few competing firms Behavioral: so few firms that each firm realizes that its behavior is likely to induce a reaction by other firms in the industry. Recognizing their interdependence, the oligopolists can earn more profits if they can collude to act is if they were a monopolist. (1) EXPLICIT: CARTELS FORMS OF COLLUSION The firms join together to set prices and outputs so as to maximize industry profits as a monopolist would. Examples: Organization of Petroleum Exporting Countries, or OPEC (oil prices) Ivy League colleges until 1991 (coordinating financial aid offers) Difficulties: 1. Cartels are unstable because members have incentives to cheat on their production quotas if they think they might not get caught. 2. Fixing prices and outputs with competitors is illegal under US and EU antitrust law Cartels are more stable and cheating harder if: 1. high concentration (few firms in industry to gain agreement from) 2. barriers to entry (so that colluders don t face new entrants) 3. homogeneous products (so it is harder to cheat on agreement) (2) TACIT COLLUSION AND SIGNALING To avoid legal problems, firms try to reach a tacit understanding about prices and quantities by signaling. Example:s tit for tat signaling among the firms: -- You cut prices a bit, and your partner does by just the same amount to signal that he won t stand for price cutting, or -- You raise prices a bit and your partner follows to signal that he too thinks it time for a price increase. Tacit collusion easier with the same three conditions above that favor cartels, plus 4. A recognized industry leader who can be the price setter or signaler. 4

5 MODELS OF OLIGOPOLISTIC INTERACTION The formal models are simplistic but offer interesting insights. They usually assume: a duopoly (two firms, although the models can be generalized to several firms), each firm produces identical products, and simple assumptions about how a firm will respond to the other firm s behavior. BERTRAND MODEL: Firm assumes competitor s price is fixed You assume your competitor will not change her price and you price accordingly. The rational strategy is to price just under your competitor. If each firm acts this way, they will gradually bid the price down to MC, the same as in a competitive industry. COURNOT/NASH MODEL: Firm assumes competitor s quantity is fixed. You assume that your competitor will not change the quantity she is producing, and you produce accordingly. This game does not always result in the competitive market solution The rational strategy depends on how much you competitor produces. In the example below, your MC curve is flat and your D, MR and optimal Q depend on whether your competitor produces 0, 25 or 50 units. \$ \$ \$ D 0 MC MC MC MR 0 D 25 Q 0 Q 25 Q 50 D 50 MR 25 MR 50 Reaction function: You can summarize the quantity that each firm will produce as a function of the quantity that their competitor produces in a reaction function. Q FIRM 1 Q FIRM 1 Firm 1 s Firm 2 s reaction function reaction function Q FIRM 2 Q FIRM 2 Nash equilibrium: If the two reaction functions intersect then there is an equilibrium: Q FIRM 1 Equilibrium Q FIRM 2 5

6 (3) STACKLBURG MODEL: First mover A variant of the Cournot-Nash which recognizes that the sequence of moves maters and that there are advantages to moving first. If your competitor takes your quantity as fixed (as in Cournot-Nash) then moving first allows you grab a big chunk of the market and your competitor has to optimize with what is left. Your competitor will reduce the price you get by producing something, but it will never be worth his while to drop price down to MC and you will have the larger market share. This model is unrealistic if this is a repeat game. The second mover might punish the first mover to encourage restraint in future games. GAME THEORY AND THE PRISONERS DILEMMA Game theory is the analysis of games between interdependent players, and is used to understand a variety of other topics besides oligopoly, including business and diplomatic negotiations. The prisoners dilemma is a simple game that illustrates many of the issues in oligopoly. Prisoners Dilemma: Two burglars who work together are arrested and held in separate cells so they can t communicate. The sentences they will get depend on whether they confesses and give evidence against one another The possible outcomes of games are usually summarized in a payoff matrix. For our prisoner s dilemma it might be: Prisoner A remains silent Prisoner A confesses Prisoner B remains silent A gets 2 years B gets 2 years A gets 1 year B gets 10 years Prisoner B confesses A gets 10 years B gets 1 year A gets 5 years B gets 5 years They are better off if they both keep silent but how can they be sure the other will? Confessing is the Nash equilibrium! Doupolist version: Two airlines serving the same route consider offering discount fares. The payoff matrix might be: Airline A offers no discounts Airline A offers big discounts Airline B offers no discounts A profits \$100 B profits \$100 A profits \$200 B profits -\$50 Airline B offers big discounts A profits -\$50 B profits \$200 A profits \$0 B profits \$0 The airlines would be better off avoiding a fare war, but it is difficult for one airline to be sure the other won t offer discounts if agreements or communication between them is illegal under anti-trust law. Players are more likely to avoid the prisoners dilemma to the extent that they can make binding agreements with each other before hand 6

7 can communicate with each other during the game, or play the game repeatedly, so that they can, through trial and error and the threat of retaliation in the next round avoid the worst cells of the payoff matrix. AN ILLUSTRATION OF OLIGOPOLY MODELS (courtesy of George Borjas) Only two firms make photographic film: Kodak and Fuji. The marginal and average cost of producing film is \$1 per roll. The industry-wide demand curve is given by P = 31 -Q. This implies the following schedule of industry-wide demand and profits: Quantity Price Profit MR The profit maximizing output for the industry as a whole is 15 (where MR = MC). A competitive industry would produce at 30 (where P=MC). The profits are divided between the two firms according to how much each firm sells with the following payoff matrix: Fuji s 5 Strategy 7.5 K: \$87.5 F: \$ Is to 10 K: \$75 Produce: K: \$25 Kodak s strategy is to produce K: \$ F: \$87.5 F: \$ K: \$93.75 F: \$125 K: \$56.25 F: \$112.5 K: \$18.75 K: \$125 F: \$93.75 F: \$56.25 K: \$75 F: \$25 F: \$ You can calculate MR by brute force or by recognizing that if P = 31 Q then TR = Q (31- Q) = 31Q Q 2 and MR = dtr/dq = 31 2Q. 7

8 The colluding equilibrium: together they produce 15 units and have a profit of \$225. This is an example of a prisoners dilemma the firms are better off if they can collude: Kodak s strategy is to produce Fuji s 5 Strategy 7.5 K: \$87.5 F: \$ Is to 10 K: \$75 Produce: K: \$25 K: \$ F: \$87.5 F: \$ K: \$93.75 F: \$125 K: \$56.25 F: \$112.5 K: \$18.75 K: \$125 F: \$93.75 F: \$56.25 K: \$75 F: \$25 F: \$18.75 The Cournot-Nash equilibrium is where each firm sells 10 units and has a profit of \$100. It is the only point where neither firm wants to deviate given what the other does: Kodak s strategy is to produce Fuji s 5 Strategy 7.5 K: \$87.5 F: \$ Is to 10 K: \$75 Produce: K: \$25 K: \$ F: \$87.5 F: \$ K: \$93.75 F: \$125 K: \$56.25 F: \$112.5 K: \$18.75 K: \$125 F: \$93.75 F: \$56.25 K: \$75 F: \$25 F: \$18.75 The Stackelberg equilibrium if, for example, Kodak is the dominant firm and moves first will be with Kodak producing 15 and Fuji 7.5 as shown below: Kodak s strategy is to produce Fuji s 5 Strategy 7.5 K: \$87.5 F: \$ Is to 10 K: \$75 Produce: K: \$25 K: \$ F: \$87.5 F: \$ K: \$93.75 F: \$125 K: \$56.25 F: \$112.5 K: \$18.75 K: \$125 F: \$93.75 F: \$56.25 K: \$75 F: \$25 F: \$18.75 To see this, note that all the gray cells are feasible. If Kodak produces 5 units, for example, then Fuji will produce either 10 or 15. Of the gray cells, the one where Kodak produces 15 gives Kodak the maximum profit. Notice also that Kodak produces and profits more than Fuji it s an example of first mover advantage. 8

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