Question

Consider two firms competing in a market with a demand function P=150-Q. Both firms have constant marginal cost c>0. There are no fixed costs. They compete by setting prices p₁ and p₂ simultaneously. (Bertrand game.) Which of the following statements is not correct?

Select one:

a. Both firms charging charging p = c is a Nash equilibrium.

b. When firm 1 sets  where  is the industry monopoly price, firm 2's best response is to set .

c. When p₁=c, any price p₂≥c can be firm 2's best response.

d. For any price , firm 2 wants to undercut p₁ marginally.

Answer 1

correct answer is (C)

when price set by frim1 is equal to marginal cost, then firm 2 will have to set its price equal to marginal cost because at at any price higher than marginal cost, firm 1 will capture the entire market. if the price set by both firms is the same but the marginal cost is lower, there will be an incentive for both firms to lower their prices and seize the market. Therefore, the only equilibrium in which none of the firms will be willing to deviate is when price equals marginal cost.