In: Economics
\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 + 2p−i . 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 zero. 1. Find the best-response functions for firm Sub King and Gyro Mart. 2. Find the Nash equilibrium outcome. 3. What are the profits of each firm? 4. Suppose that the firms merge, so now they set prices jointly. What prices should the merged firm choose to maximize total profits? What are post-merger profits? Compare them with Bertrand profits. (Hint: Write out total profits of the merged firm and find marginal profits with respect to both prices. Then solve the resulting system of 2 equations for p1 and p2 by substituting one into the other.)