Scenario: Two Firms, Firm 1 and Firm 2, Make Differentiated

Multiple Choice

Scenario: Two firms, Firm 1 and Firm 2, make differentiated products and compete in a duopoly market. The firms do not have a fixed cost. Firm 1's cost is $30 per unit, while Firm 2's cost is $25 per unit. (So they are the marginal cost and the average total cost) . There are 1,000 consumers in this market. The demand is divided between the two firm in the following way:
• If Firm 1's price is less than twice Firm 2's price, then everyone buys from Firm 1.
• If Firm 1's price is more than twice Firm 2's price, then everyone buys from Firm 2.
• If Firm 1's price is equal to twice Firm 2's price, then half of the consumers buy from Firm 1 and the other half buy from Firm 2.
-Refer to the scenario above.Suppose Firm 1 sets its price at $50 and Firm 2 sets its price at $25.Is this a Nash equilibrium? Why?

A) No, because if Firm 1's price is $50, then Firm 2 should set its price below $25.
B) No, because if Firm 2's price is $25, then Firm 1 should set its price below $50.
C) Yes, because (a) if Firm 1's price is $50, then setting price at $25 is Firm 2's best response, and (b) if Firm 2's price is $25, then setting price at $50 is Firm 1's best response.
D) Yes, because (a) if Firm 1's price is $50, then setting price at $25 or below is Firm 2's best response, and (b) if Firm 2's price is $25, then setting price at least $50 is Firm 1's best response.