1. (15 points) In the following, let the market demand curve be P = 70 - 2Q, and assume all sellers can produce at a constant marginal cost of c = 10, with zero fixed costs. a) If the market is perfectly competitive, what is the equilibrium price and quantity? b) If the market is controlled by a monopolist, what is the equilibrium price and quantity? How much profit does the monopolist earn? c) Now suppose that Amy and Beau compete as Cournot duopolists. What is the Cournot equilibrium price? What is total market output, and how much profit does each seller earn? 2. (15 points) Let's consider a market in which two firms compete as quantity setters, and the market demand curve is given by Q = 4000 - 40P. Firm 1 has a constant marginal cost equal to MC1 = 20, while Firm 2 has a constant marginal cost equal to MC2 = 40. a) Find each firm's reaction function. b) Find the Cournot equilibrium quantities and the Cournot equilibrium price. 3. (15 points) Suppose that the market demand for cobalt is given by Q=200-P. Suppose that the industry consists of a dominant firm, Braeutigam Cobalt ( BC), which has a constant marginal cost equal to $ 40 per unit. There are nine other fringe producers, each of whom has a marginal cost curve MC = 40 + 10q, where q is the output of a typical fringe producer. Assume there are no fixed costs for any producer. a) What is the supply curve of the competitive fringe? b) What is BC's residual demand curve? () Find BC's profit- maximizing output and price. At this price, what is BC's market share? d) Repeat parts (a) to (c) under the assumption that the competitive fringe consists of 18 firms. 4. (15 points) Two firms, Alpha and Bravo, compete in the European chewing gum industry. The products of the two firms are differentiated, and each month the two firms set their prices. The demand functions facing each firm are: QA = 150 - 10PA + 9P: and Q: = 150 - 10P: + 9PA where the subscript A denotes the firm Alpha and the subscript B denotes the firm Bravo. Each firm has a constant marginal cost of $ 7 per unit. a) Find the equation of the reaction function of each firm. b) Find the Bertrand equilibrium price of each firm. c) Sketch how each firm's reaction function is affected by each of the following changes: i) Alpha's marginal cost goes down (with Bravo's marginal cost remaining the same). ii) Alpha and Bravo's marginal cost goes down by the same amount. 5. (15 points) Suppose that you have a utility function given by the equation U = (50 1)*2 . Consider a lottery that provides a payoff of $ 0 with probability 0.75 and $ 200 with probability 0.25. a) Sketch a graph of this utility function, letting I vary over the range 0 to 200. b) Verify that the expected value of this lottery is $ 50. c) What is the expected utility of this lottery? d) What is your utility if you receive a sure payoff of $ 50? Is it bigger or smaller than your expected utility from the lottery? Based on your answers to these questions, are you risk averse? 6. (15 points) Consider a household that possesses $ 100,000 worth of valuables (computers, stereo equipment, jewelry, and so forth). This household faces a 0.10 probability of a burglary. If a burglary
