All question are with regards to the following set up. There are two firms A and B. Firms compete in a Cournot Duopoly in Karhide. They set quantities g, and ga. Inverse demand is P(QA + 98) = 18 -4A - 95 and costs are C(q) = 3 = q for both firms. Firm B is a domestic firm (in Karhide,) and firm A is a foreign firm (from Orgoreyn.) The government of Karhide engages in a strategic trade intervention by giving firm B a per unit subsidy of s. (That is, when firm B produces and sells ge units, firm B receives a payment of s *go from the government.) You must show your work at each step, unless the questions is followed by "No work required." (1) (20 points) We begin by examining the model with an unspecified s 2 0. (a) Find profit functions for both firms. (No work required.) (b) Use first order conditions to find each firm's best response function. (2) (25 points) Assume that s = 0 (there is no subsidy.) (a) Write down firm A's profit function. (No work required.) (b) Find each firm's best response function. (You may do this directly or by setting s to zero in your expressions from (1b). (c) Solve for equilibrium outputs (q), q;). You may either use the symmetry in this problem to assume a symmetric solution, or solve for firm B's best response and solve the two best responses simultaneously. (I recommend the first approach.) (d) Solve for the equilibrium price. (e) Solve for the equilibrium profits. (3) (25 points) Assume that s = 3. (a) Find firm B's profit function under the subsidy. (No work required.) (b) Find firm B's best response function. (You may do this directly or by setting s to zero in your expressions from (1b). (c) Why don't I need to ask you to solve for A's best response? (d) Solve for the equilibrium outputs (4A. of)- (e) Solve for the equilibrium price. (f) Solve for firm B profits. (4) (30 points) We now consider the government's choice of s 2 0. We can see from above that profits and outputs depend upon s. With that in mind, let as(s) and qp(s) denote firm B's profit and output as a function of the subsidy s. Let qa(s) denote firm A's equilibrium output as a function of s. Let G(s) = Is(s) -s*95(#) denote the government's objective function. (a) We first assume that the government must choose either s = 0 or s = 3. Which of these two choices makes G(s) bigger? For (b) through (e) we allow the government to choose any s 2 0. (b) Find ga(s) and qa(s) as function of s. (c) Find wa(s) as a function of s. (d) Use a first order condition to find the value of s that maximizes G(s). Call this value s". (e) What is go(s")? How does go(s") compare to the monopoly output for this market? Explain why it makes sense that ge(s* ) should take this value. Some mathematical tips for (4d) Let A, B, and C be constants. Let f(x) = B * (A+ C * x] . By the chain rule dx - = 28 * (A+C*x) *C. Let g(x) = B * (A+ C * x) = r. By the product rule df 19 = B * (A +C = x) + B : C *I