(a) What is each firm\'s strategic variable and what is firm A\'s profit maximiz
ID: 1195393 • Letter: #
Question
(a) What is each firm's strategic variable and what is firm A's profit maximization problem as a function of each firm's strategic variable? (b) What is each firm's best response function? (c) how much does each firm produce at the Nash equilibrium? (d) What is the market equilibrium price at the Nash equilibrium? Short Answer/Numerical 2. The inverse demand function for the market is P 120-2Q. There are two firms: A and B. The costs for firm A are C(ga) 180A, and the costs for firm B are CGp) = 184B. Assume that both firms choose quantities simultaneously (a) What is each firm's strategic variable and what is firm A's profit maximization problem as a function of each firm's strategic variable? (b) What is each firm's best response function? (c) How much does each firm produce at the Nash equilibrium? (d) What is the market equilibrium price at the Nash equilibrium?Explanation / Answer
a) Strategic variables are qa and qb
Firm A's profit = qa(120 - 2qa - 2qb) - 18qa
b) Maximize firm A's profit w.r.t qa
120 - 4qa - 2qb = 18
2qa + qb = 51
Firm B's profit: qb(120 - 2qa - 2qb) - 18qb
Maximize w.r.t qb,
120 - 2qa - 4qb = 18
qa + 2qb = 51
Best response for firm A: (51 - qb)/2
Best response for firm B: (51-qa)/2
c) Solving the best responses: qa* = 17
qb* = 17
d) P* = 120 - 2(34) = 52
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