Problem 4. (Challenge Question, not graded) Sub King and GyroMart are the only two sandwich shops in town. Their goods are imperfect substitutes. Careful research has found that the demand function for both rms is (1?; = 16 229.; +294. Where 7; is the rm in question and z' is the opponent rm. 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 rm is zero. Firms set prices simultaneously. 1. Find the best-response functions for rm Sub King and GyroMart. 2. Find the differentiated Bertrand Nash equilibrium outcome. 3. What are the prots of each rm? 4. Is this outcome efcient? Explain your answer. 5. Suppose that the rms merge, so now they set prices jointly. What prices should the merged rm choose to maximize total prots? What are postmerger prots? Compare them with Bertrand prots. (Hint: Write out total prots of the merged rm and nd marginal prots with respect to both prices. Then solve the resulting system of 2 equations for 191 and p2 by substituting one into the other.)