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 qA and qB. Inverse demand is P(9A + 9B) = 18 - 9A-9B 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 q units, firm B receives a payment of s* qB from the government.) You must show your work at each step, unless the questions is followed by "No work required." We now consider the government's choice of s 0. We can see from above that profits and outputs depend upon s. With that in mind, let TB (s) and qB(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) = TB(s) - s* qB(s) 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 > 0. (b) Find qA(s) and qB (s) as function of s. (c) Find TB (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 qB (s*)? How does qp (s*) compare to the monopoly output for this market? Explain why it makes sense that qp (s*) should take this value. 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 qA and qB. Inverse demand is P(9A + 9B) = 18 - 9A-9B 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 q units, firm B receives a payment of s* qB from the government.) You must show your work at each step, unless the questions is followed by "No work required." We now consider the government's choice of s 0. We can see from above that profits and outputs depend upon s. With that in mind, let TB (s) and qB(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) = TB(s) - s* qB(s) 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 > 0. (b) Find qA(s) and qB (s) as function of s. (c) Find TB (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 qB (s*)? How does qp (s*) compare to the monopoly output for this market? Explain why it makes sense that qp (s*) should take this value.