= All question are with regards to the following set up. There are two nrms A and B. compete in a Cournot Duopoly in Karhide. They set quantities A and qB. Inverse de P(9A + 9B) = 18 - 9A-9B and costs are C(q) = 3* q for both firms. Firm B is a domes (in Karhide,) and firm A is a foreign firm (from Orgoreyn.) The government of Karhide in a strategic trade intervention by giving firm B a per unit subsidy of s. (That is, when produces and sells q3 units, firm B receives a payment of s* qp from the government.) You must show your work at each step. unless the questions is followed by "No work requi
(4) 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 πB(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) = πB(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 πB(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 qB(s*) compare to the
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