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1 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). Ford Aggressive Normal Aggressive Lexus Normal (7, 7) (12,5) (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, Aggressive ) 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.
2 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=10Q. 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=102Q; setting MR=MC we get Q=4 and P=6, so total profit is (62)*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 (42)*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). Mycap e. What is the dominant strategy for Mycap? Yourcap Monopoly P= $4 Monopoly $8, $8 $0,$12 P= $4 $12,$0 $6,$6 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 profitmaximizing price for the first firm is P= $4. Thus, neither firm has an incentive to set the monopolistic price.
3 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. Bill Confess Remain Silent Fred Confess Remain Silent Bill gets 10 years Bill gets 1 year Fred gets 10 years Fred gets 20 years Bill gets 20 years Bill gets 6 months Fred gets 1 year 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 revenue
4 dollars) dollars) (thousands of dollars) 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 be South Africa s production and profit? What would happen to South Africa s profit if it increased its production by 1,000 while Russia stuck to the cartel agreement? If Russia and South Africa formed a cartel, they would set price and quantity like a monopolist, so the price would be $7,000 and the quantity would be 6,000. If they split the market evenly, they would share total revenue of $42 million and costs of $6 million, for a total profit of $36 million. So each would produce 3,000 diamonds and get a profit of $18 million. If Russia produced 3,000 diamonds and South Africa produced 4,000, the price would decline to $6,000. South Africa s revenue would rise to $24 million, costs would be $4 million, so profits would be $20 million, which is an increase of $2 million. d. Use your answer to part c to explain why cartel agreements are often not successful. Cartel agreements are often not successful because one party has a strong incentive to cheat to make more profit. In this case, each could increase profit by $2 million by producing an extra thousand diamonds. However, if both countries did this, profits would decline for both of them. Problem 5: Monopolistic competition Janet lives in Aberdeen and produces EcoIce, a brand of premium lowfat ice cream. Ice cream industry in Aberdeen is monopolistically competitive. In order to retain her market position and differentiate EcoIce from other products, Janet keeps introducing two new natural flavors on the second Friday of each month and offering innovative packaging. The chart below describes the demand for EcoIce at various prices. The marginal cost of producing one scoop of ice cream is $0.40, and there are no fixed costs. Price Quantity demanded $ $ $ $ $0.40 8
5 $ a) How many scoops of ice cream should Janet produce in the short run to maximize profits? What price should she charge? (Hint, this problem will be easiest if you calculate an algebraic expression for demand, given the information in the table). From the table we can get demand equation P = 2 Q / 5 and marginal revenue MR = 2 2Q /5. Set MR=MC to get Q=4, P=1.2 b) Calculate her economic profits in the short run. Profit = Q (PATC) = 4*( ) = 3.2 c) What would be the long run price and quantity if instead this were a perfectly competitive market? Set P = MC to get P = 0.4, Q = 8 Since economic profits are positive, new firms are attracted to the industry. In particular, a new firm that makes ice cream from the Colorado Rocky Mountains water, ColorIce, enters the industry and demand Janet s ice cream decreases by 2 at each price. d) Derive a new demand equation for EcoIce. New demand equation is Q = 8 5P e) According to the economic theory, what should happen to the price of EcoIce after ColorIce entered the market? Price should fall f) Find Janet s new profit maximizing quantity, price, and profits. MR = 8/5 2Q /5, from MR = MC get Q = 3, P = 1 g) Illustrate your solution to parts (a) and (f) with a graph.
6 Problem 6: Monopolistic competition and advertising a) Firms in monopolistic competition often use advertising, expecting to increases demand for a particular product and raise profits. Do you think that advertising makes markets more or less competitive? Critique of Advertising: Manipulates people s tastes Psychological rather than informational Creates a desire that might not otherwise exist Impedes competition by convincing consumers that products are more different that they truly are, fostering brand loyalty (increasing a firm s market power). This makes the demand curve more inelastic allowing the firm to charge a larger markup over marginal cost. Defense of Advertising: Provides information about the goods being offered, existence of new products, and locations of firms. Fosters competition by making customers more aware of all the firms in the industry. Makes customers more aware of price differences, allowing them to exploit these price differences. This pressures the firms to charge similar prices. Also allows new firms to attract customers. b) Now suppose that you are a producer of sunscreen in a monopolistically competitive industry. This industry is monopolistically competitive because each producer uses a unique formula and protects it as a top secret; further, each product has its own brand name. The demand for your brand of sunscreen during the winter months in Wisconsin is described by equation P = 200 2Q. Assume the marginal cost of producing each unit of output is $4.00, and fixed costs are $1,000. i) In the short run, how many bottles of sunscreen should you produce to maximize profits? What price should you charge? MR = 200 4Q = 4, so Q = 49, P = 2002*49 =102 ii) Calculate economic profits. Profits = 49*(1024)1000 = 3,802 Your newly hired marketing director suggests to launch a statewide billboard advertising campaign. As a first time client, you are getting a special price of $4,000 for a month long campaign. The marketing director estimates that the company sales will increase by 30 units at each price. iii) How would advertising affect your cost structure? Would advertising be a fixed or variable cost? How would advertising affect your demand curve? Support your reasoning with a graph. In the case described above advertising is a part of fixed cost as it doesn t depend on the level of output. On a graph ATC curve shifts upwards, demand curve shifts to the right. iv) Find the new profit maximizing quantity, price, and profit levels.
7 New demand equation is Q = 130P/2, MR = 260 4Q, so new Q = 64, P = 132. Profits = 64*(1324) =3,192 v) Would you implement the proposal of marketing director? New short run profits are lower as a result of advertising, so you wouldn t accept proposal, unless you expect demand to decrease without advertising support
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