Problem 2. Sub King and Gyro Mart are the only two sandwich shops in town. Their goods are imperfect substitutes. Careful research has found that the demand function for both firms is

qi = 24 5pi + 2pi.

Where i is the firm in question and i is the opponent firm. In other words, while the price of gyros affects demands for subs, consumers do not simply buy the cheapest item, some are willing to pay more to get a sub, and some are willing to pay more to get a Gyro. The marginal cost of production for each firm is 0 and the fixed cost of production is $10.

1. Find the best-response functions for firm Sub King and Gyro Mart. 2. Find the differentiated Bertrand Nash equilibrium outcome. 2. Find the differentiated Bertrand Nash equilibrium outcome.

3. What are the profits of each firm?