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(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 qв (s*) compare to the monopoly output for this market? Explain why it makes sense that qB (s*) should take this value.

(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 qв (s*) compare to the monopoly output for this market? Explain why it makes sense that qB (s*) should take this value.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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just D and E please thank you

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 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 q 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: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 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 q 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."
(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) = 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 qв (s*) compare to the monopoly output for this market? Explain why it makes sense that qB (s*) should take this value.
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) = 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 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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