Economics 370 Microeconomic Theory Problem Set 7 Due 19 July 2004. Please hand it in at the end of the 19 July 2004 lecture. 1) A firm is a monopoly in its output market and a monopsony in its input market. Its only input is the finished good, which it buys from a competitive market with an upward sloping supply curve. The firm sells the same good to competitive buyers in the output market. Determine its profit-maximizing output. What price does it charge in the output market? What price does it pay to its suppliers? 2) Southwest Airlines’ cost to fly one seat one mile is 7.5¢ compared to 15¢ for USAir. Assume that Southwest and USAir are the only two firms competing on a single route. The distance traveled on the route is 500 miles. If the market demand function is q = 600 – p, what is the Cournot equilibrium (where p is in dollars)? 3) Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of q1 = 100 – 2p1 + p2Where q1 is firm 1’s output, p1 is firm 1’s price, and p2 is firm 2’s price. Similarly, the demand firm 2 faces is: q2 = 100 – 2p2 + p1a) Solve for the Bertrand equilibrium. b) Solve for the Bertrand equilibrium if both firms have a marginal cost of $0 per unit. c) Solve for the Bertrand equilibrium if firm 1 has a marginal cost of $30 and firm 2 has a marginal cost of $10 per unit. 4) Suppose that Panasonic and Zenith are the only two firms than can produce a new type of high-definition television. The payoffs (in millions of dollars) from entering this product market are shown in the following payoff matrix. Be sure to consider both pure and mixed strategies below as appropriate. PanasonicDo not EnterEnter0025000250-40-40EnterZenith Do notEntera) If both firms move simultaneously, what is/are the Nash equilibrium(s)? b) If the US government commits to paying Zenith a lump-sum subsidy of $50 million if it enters this market, what is/are the Nash equilibrium(s)? c) If Panasonic is first-mover (and Zenith does not have the subsidy), what is/are the Nash equilibrium(s)? 5) There are many buyers who value high-quality used cars at the full-information market price p1, and lemons at p2. There are a limited number of potential sellers who value high-quality cars at v1 ≤ p1 and lemons at v2 ≤ p2. Everyone is risk-neutral. The share of lemons among all the used cars that might be sold is θ. a) Under what conditions are all cars sold? b) Under what conditions are only lemons sold? c) Under what conditions are no cars sold? Suppose that buyers incur a transaction cost of $200 to purchase a car. This transaction cost is the value of their time to find a car. What is the d) Under what conditions are all cars sold? e) Under what conditions are only lemons sold? f) Under what conditions are no cars