Consider the same industry outlined in question 1 except that the marginal cost for each firm is 1. Imagine that firms choose prices rather than quantities. Consumers split themselves evenly across the firms if the firms set the same prices, otherwise all consumers shop at the lower-priced firm. (20 points)

(1) Define a Nash equilibrium in prices 1 and 2.

(2) Explain why the prices 1 and 2 you propose is an equilibrium.