Consider a Bertrand oligopoly with two firms (Firm 1 and Firm 2) both selling goods that are imperfect substitutes for each other and competing by choosing prices simultaneously. Their market demands are 3 3 1 91 = 1,200 92 = 800 – 2p2 + %D - For simplicity, assume the marginal cost is zero for both firms (MC, = MC2 = 0). %3D a. Find the best response curve for each firm. Hint: The marginal revenue curves will be 3 MR, = 1,200 – 3p1 +5P2. 1 MR2 = 800 – 4p2 +5P1 %3D And the condition MR = MC will give the optimal price (best response) for each firm. b. Find the optimal price for each firm. Hint: Find the Nash equilibrium, that is, the combination of mutual best responses. c. Find the quantity sold by each firm.
Consider a Bertrand oligopoly with two firms (Firm 1 and Firm 2) both selling goods that are imperfect substitutes for each other and competing by choosing prices simultaneously. Their market demands are 3 3 1 91 = 1,200 92 = 800 – 2p2 + %D - For simplicity, assume the marginal cost is zero for both firms (MC, = MC2 = 0). %3D a. Find the best response curve for each firm. Hint: The marginal revenue curves will be 3 MR, = 1,200 – 3p1 +5P2. 1 MR2 = 800 – 4p2 +5P1 %3D And the condition MR = MC will give the optimal price (best response) for each firm. b. Find the optimal price for each firm. Hint: Find the Nash equilibrium, that is, the combination of mutual best responses. c. Find the quantity sold by each firm.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider a Bertrand oligopoly with two firms (Firm 1 and Firm 2) both selling goods that are
imperfect substitutes for each other and competing by choosing prices simultaneously. Their
market demands are
3
1
92 = 800 – 2p2 +
91 = 1,200 –
For simplicity, assume the marginal cost is zero for both firms (MC,
= MC2 = 0).
a. Find the best response curve for each firm. Hint: The marginal revenue curves will be
3
MR 3 1,200 -Зр, +
1
MR2 = 800 – 4p2 +5P1
And the condition MR = MC will give the optimal price (best response) for each firm.
b. Find the optimal price for each firm. Hint: Find the Nash equilibrium, that is, the combination
of mutual best responses.
c. Find the quantity sold by each firm.
99-
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