final_summer2021_AK

Econ 20100-91: The Elements of Economic Analysis II, Summer 2021 Kenneth C. Griffin Department of Economics, The University of Chicago Final Exam: Answer Key Instructor: Srini Vasudevan Total time : 100 minutes + 20 minutes for submission on Gradescope Total score : 38 points (points given in parentheses) 1. True/False/Uncertain Questions: For each question state whether the statement in italics is true, false or uncertain. Give a precise and concise justification for your answer. Answers without a justification will get no credit. Attempt any two of the three questions. No extra credit for attempting an extra question. Indicate which question you don’t want graded by writing “not attempted.” (a) (3) A monopolist with constant marginal costs faces a demand curve with a constant price elasticity and does not practice price discrimination. If the government imposes an excise tax of $ 1 per unit of goods sold by the monopolist, the monopolist will increase her price by more than $ 1 per unit. (Hint: Inverse Elasticity Pricing Rule.) True. Let the price elasticity of demand be and the marginal cost be c . Monopolist’s problem has a solution only if < - 1. Let p * and p * 0 before and after the tax. p * = c 1+1 / p * 0 = c +1 1+1 / p * 0 - p * = 1 1+1 / , which is 1 only if demand is perfectly elastic (which implies it is not a monopoly) otherwise it greater than 1. Thus, for every dollar tax on the good, the consumer will face a price increase of more than a dollar. (b) (3) A monopolist who is able to practice third-degree price discrimination will make greater profits than a monopolist who is able to practice first-degree price discrimination. False. First-degree price discrimination is perfect, i.e., it captures all possible social surplus as profit. Third-degree price discrimination allows leakage of profit in the form of consumer surplus and deadweight loss. (c) (3) A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist. True. Stackelberg leader has a first-mover advantage by being able to anticipate the follower’s best response. Thus, relative to the simultaneous quantity choice, the Stackelberg leader can only do better. 1

2. Short Questions: Show your work. You may include equations or graphs, if necessary, but final answers must be in words (and numbers where applicable.) Attempt any two of the three questions. No extra credit for attempting an extra question. Indicate which question you don’t want graded by writing “not attempted.” (a) (4) Suppose AMD is considering cloning Intel’s latest CPU chip. If AMD enters Intel’s market, Intel can play Mean by expanding its output, dropping prices, and try to make AMD’s profit as small as possible or play Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves are complete, profits of chip production in billions of dollars are: Intel Mean Nice AMD In 5, 4 9, 17 Out 0, 12 0, 21 Assuming AMD moves first, which of the following is the equilibrium strategies and payoffs of the sequential play? Since it is a sequential game, the relevant equilibrium is the subgame perfect equilibrium (SPE). Through backwards induction, the SPE is { In, (Nice, Nice) } and the payoff is (9,17). (b) (4) An airport is located next to a housing development. Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 38 X - X 2 and profits of the developer are 28 Y - Y 2 - XY . Let H 1 be the number of houses built if a single profit-maximizing company owns the airport and the housing development. Let H 2 be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total “damages” XY done by the planes to the developer’s profits. Find H 1 and H 2 . When the two firms are jointly owned, the joint profit is 38 X - X 2 + 28 Y - Y 2 - XY . Take the FOC with respect to X, 38 - 2 X * - Y = 0 And, with respect to Y, 28 - 2 Y * - X = 0 Solving simultaneously, we get Y * = H 1 = 6. Under independent ownership with damage reimbursement, the developer’s profit is 28 Y - Y 2 , which is maximized at Y * = H 2 = 14 (c) (4) An industry has two colluding firms that act so as to maximize total profit in the industry and then split the profits equally. Firm 1 has cost function c ( y ) = 8 y . Firm 2 has cost function c ( y ) = y 2 . Market demand is given by Y ( p ) = 56 - p . How much is each firm’s profit? Firm 2 will produce the first 4 units (since its marginal cost for the first 4 units is less than that of firm 1) and the remaining will be produced by firm 2. The marginal 2

numbers of web pages (in millions) on Google and Amazon, respectively, and p is the price of hosting a web page. Let Google and Amazon have the cost functions, C 1 ( q 1 ) = 20 q 1 and C 2 ( q 2 ) = 30 q 2 , respectively. (a) (6) Suppose the two firms engage in Cournot competition. What is the equilibrium price, and the equilibrium quantities of the two firms? Google’s best response function is q 1 = 15 - q 2 / 2 and Apple’s is q 2 = 10 - q 1 / 2. Solving simultaneously, q * 1 = 40 / 3 = 13 . 33 and q 2 = 20 / 6 = 3 . 33. The equilibrium price is 200/6=33.33 (b) (6) Suppose that, instead of competing with each other, they decide to collude to form a cartel. What is the equilibrium price and the equilibrium quantities of the two firms? Since Google’s marginal cost is always lower, only Google with produce the entire monopoly quantity. The marginal revenue is 50 - 2 q 1 . Setting it to marginal cost, 20. We get q * 1 = 15 and q * 2 = 0. The equilibrium price is $ 35. 4