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Solve for equilibrium prices in the following differentiated product Bertrand model.
Q1 = 300 - 12P1 + 4P2 + 3P3
Q2 = 275 - 10P2 + 2P1 + P3
Q3 = 250 - 8P3 + 2P1 + P2
Assume that each firm has a marginal cost of 10.
a. Write down each firm's profit function. (Ignore question)
b. Write down the profit-maximization conditions. (Ignore question)
c. Use an equation solver to get the equilibrium prices. (Ignore question)
d. Show the equilibrium graphically. (ignore question)
e. Suppose that Firm 1's marginal cost rises from 10 to 15, but Firm 2 and Firm 3's marginal costs remains at 10. Do Firm 2 and 3 undercut Firm 1 and take all its business away?
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