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(qA + 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 qв units, firm B receives a payment of s* q3 from the government.) You must show your work at each step, unless the questions is followed by "No work required."
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(qA + 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 qв units, firm B receives a payment of s* q3 from the government.) You must show your work at each step, unless the questions is followed by "No work required."
Chapter10: Monopolistic Competition And Oligoply
Section: Chapter Questions
Problem 9SQP
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just d and e please thank you
Transcribed Image Text: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 A and q. 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 qв units, firm B receives a payment of s* qg from the government.)
You must show your work at each step, unless the questions is followed by "No work required."
Transcribed Image Text:(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 TB(s) and qв(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) — 8 * 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 qв(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 qв(s*)? How does qв (s*) compare to the monopoly output for this market? Explain
why it makes sense that qB (s*) should take this value.
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