Professor Scholz Posted: 11/10/2009 Economics 101, Problem Set #9, brief answers Due: 11/17/2009 Oligopoly and Monopolistic Competition Please SHOW your work and, if you have room, do the assignment on the problem set. Problem 1: Strategic interactions of duopolists Ford and Lexus are competing in the market for SUV’s. For simplicity assume that there are no other rivals in the SUV market. The companies are planning to introduce a new model in this fall. They should decide whether to invest lots of money in advertisements or not. The profits of the two firms are interdependent. The following table describes the situation. Each row represents an action taken by Ford, and each column an action taken by Lexus. The first (second) number in parenthesis means profits for Ford (profits for Lexus respectively). Lexus Aggressive Advertisement Normal Advertisement Ford Aggressive Advertisement (7, 7) (12,5) Normal Advertisement (5,12) (10,10) a. Find the dominant strategy of each firm in noncooperative situation. Dominant strategy for each firm is to run aggressive advertisement b. Find the Nash equilibrium without collusion between two firms. Is there a prisoner’s dilemma in this game? Can the companies achieve an outcome (10, 10) in this game without communications? Explain. From a, we know that (Aggressive Advertisement, Aggressive Advertisement) is a Nash equilibrium, equilibrium payoff is (7, 7). There is a prisoner’s dilemma, as both companies could be better off by cooperating and running normal advertisement – each company would get a payoff 10 rather than 7. However, they can not achieve the outcome (10,10) without a binding commitment, as each player is strictly better off advertising aggressively given that the opponent advertises normally. c. Suppose that both firms make an agreement in advance. Find the optimal outcome. Explain under what situation the agreement can be sustained. If two firms can make an agreement, then they can increase their profit by jointly decreasing their expenditure on advertisement. In this case the optimal outcome (10, 10) can be achieved. We can guess that this agreement is sustained in case of repeated interactions.Problem 2: Oligopoly There are only two companies producing baseball caps in Milwaukee, Mycap and Yourcap. The demand function for baseball caps in this market is P=10-Q. The marginal cost is constant and can be expressed as MC(=ATC) is 2. a. The companies try to coordinate their actions and set quantity and price like a single monopolist. Once they set this profit maximizing price and quantity, the plan is to split the resulting profit equally. What is the profit of each company if they both adhere to the plan? MR=10-2Q; setting MR=MC we get Q=4 and P=6, so total profit is (6-2)*4= $16. Thus, each company’s profit is 16/2= $8. b. One of the companies, Yourcap, deviates from the plan, and sets its price equal to $4. What is the profit of Yourcap? What is the profit of Mycap? (Hint: No one wants to buy overpriced goods!) Mycap’s profit is zero since nobody wants to buys its more expensive product. Yourcap’s price is 4, so from demand function Q=6. Thus, Yourcap’s profit is (4-2)*6= $12. c. Both companies set price equal to $4, and then split profit equally. What is each company’s profit? Now the firms split profits from selling 6 units, so each firm’s profit is 12/2= $6. d. Now the firms have two options: to charge the joint monopoly price as found in part (a), or to set their price equal to $4. Fill in a payoff matrix that represents these choices (use a template provided below). MycapYourcap Monopoly P= $4 Monopoly $8, $8 $0,$12P= $4 $12,$0 $6,$6 e. What is the dominant strategy for Mycap? The dominant strategy for Mycap is to charge P= $4. f. What is the dominant strategy for Yourcap? The dominant strategy for Yourcap is to charge P= $4. g. What is the outcome of this game? The outcome for the game is (P= $4, P= $4). h. Explain the intuition for your answer in part (g). If any of the firms sets the monopoly price, its profit is zero since the other firm will set P= $4. When the other firm sets P= $4, the profit-maximizing price for the first firm is P= $4. Thus, neither firm has an incentive to set the monopolistic price.Problem 3: Game theory Consider the following game. Fred and Bill are arrested and charged with a bank robbery. The district attorney separates them and offers them the deal given in the payoff matrix below. Assume that Fred and Bill are guilty and the penalty is imprisonment. FredConfess Remain Silent Bill Confess Bill gets 10 years Fred gets 10 years Bill gets 1 year Fred gets 20 years Remain SilentBill gets 20 years Fred gets 1 yearBill gets 6 months Fred gets 6 months a. What is the dominant strategy for each player? Neither player has a dominant strategy in this game b. Compute Nash equilibrium of this game. What is predicted outcome of this game? The game has two Nash equilibria (Confess, Confess) and (Remain silent, Remain silent), so we can not predict the outcome of the game Problem 4: Cartels A large share of the world supply of diamonds comes from Russia and South Africa. Suppose that the marginal cost of mining diamonds is constant at $1,000 per diamond, and the demand for diamond is described by the following schedule. Price Quantity 8,000 5,000 7,000 6,000 6,000 7,000 5,000 8,000 4,000 9,000 3,000 10,000 2,000 11,000 1,000 12,000 a. If the market for diamonds was perfectly competitive, what would the price and quantity be? If there were many suppliers of demands, price would equal marginal cost ($1,000), so the quantity would be 12,000. b. If there were only one supplier of diamonds, what would the price and quantity be? (Hint: make a table that lists price, quantity, total and marginal revenue for a monopoly and use it to find monopolist profit maximizing price and quantity). Price (thousands of Quantity (thousands) Total revenue (millions of Marginal revenuedollars) dollars) (thousands of dollars) 8 5 40 - 7 6 42 2 6 7 42 0 5 8 40 -2 4 9 36 -4 3 10 30 -6 2 11 22 -8 1 12 12 -10 With only one supplier of diamonds, quantity would be set where marginal cost equals marginal revenue. The monopolist will maximize profits at a price of $7,000 and a quantity of 6,000. c. If Russia and South Africa formed a cartel, what would be the price and quantity? If the counties split the market evenly, what would
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