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Simon Fraser University Spring 2016 Econ 302 Assignment 3 Due: in Lecture, Tuesday February 2, 2016. Show all your work. In this assignment, assume that firms set their quantities or prices simultaneously. 1. (4 points) The market (inverse) demand function for a homogenous good is P (Q) = a − b · Q, where a, b > 0, and Q is the total quantity of the good on the market. There are n firms each with a constant marginal cost of c (for producing each unit of the good). (a) Suppose that n = 1 (say, due to a merger). Calculate the monopolist’s price and quantity. (b) Suppose that n > 1. The n firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. Calculate the symmetric Nash equilibrium in this game and the corresponding market price. Your answers must be a function of n. (c) Calculate the deadweight loss in (a) and (b). (d) What happens to the price and the deadweight loss in part (b) as n → ∞? 2. (2 points) Assume that the market (inverse) demand function for a homogenous good is P (Q) = 10−Q. There are now 2 firms. Firm 1 has a constant marginal cost of 2: C1 (q) = 2q. Firm 2 has a quadratic cost function: C2 (q) = q 2 . And assume that the firms compete by setting quantities as in Problem 1(b). Calculate the (asymmetric) Nash equilibrium and the corresponding market price. 3. (4 points) Assume that the market demand for a homogenous good is still Q(P ) = 10−P . There are n firms which compete by setting prices, and the firm with the lowest price captures the whole market (if multiple firms have the same lowest price, they split the market evenly). Firm i has a constant marginal cost of ci , 1 ≤ i ≤ n. Assume that the price that each firm sets must be in the increments of cents: for example, 1.98, 1.99, 2, 2.01, 2.02, 2.03, . . .. Calculate the pure-strategy Nash equilibria in this game and the corresponding market quantities when: (a) n = 2, c1 = 2 and c2 = 3; 1 (b) n = 5, c1 = 2, c2 = 3, c3 = 5, c4 = 6, and c5 = 9; (c) n = 2, c1 = 2, c2 = 7. 2