Problem 3 [40 points] Two firms compete by choosing the prices. Their demand functions are Q1 = 20 - P1 + P2 and Q2 = 20 + Py - P2, where P1 and P2 are the prices charged by each firm, respectively, and Q1 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted and earn infinite profits. Marginal costs are zero. This implies that total profit equals total revenue for each firm. Marginal revenues are MR1 = 20 - 2P, + P2 and MR2 = 20 - 2P2 + P1. a. Suppose the two firms set their prices at the same time. Determine each firm's reaction curve. (Hint: set each marginal revenue equals marginal cost). [10 points] b. Using your answers from a., show that at the Nash equilibrium, each firm charges $20 per unit. How much will each firm sell, and what will its profit be? [10 points] c. Suppose Firm 1 sets its price first and then Firm 2 sets its price. By taking Firm 2's reaction curve into account, Firm 1's profit function becomes IT1 = 30P1-Py-/2, so that the new marginal revenue is MR1 = 30-P1. 1. Determine what price each firm will charge. (Hint: set new MR = MC for Firm 1 and use Firm 2's reaction curve from a.) to find P2 ). [5 points] 2. Using c.1.) determine how much each firm will sell. What will each firm's profit be? [5 points] d. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set the price at the same time; (ii) You set a price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why. [10 points] Bonus Problem [100 points] I. What are the characteristics of a monopolistically competitive market? What happens to the equilibrium price and quantity in such a market if one firm introduces a new, improved product? [20 points] Il. In the Stackelberg model, the firm that sets output first has an advantage. Explain why. [20 points] Ill. What do the Cournot and Bertrand models have in common? What is different about the two models? [20 points] IV. Why has the OPEC oil cartel succeeded in raising prices substantially while the CIPEC copper cartel has not? What conditions are necessary for successful cartelization? What organizational problems must a cartel overcome? [20 points] V. Explain the meaning of a Nash equilibrium when firms are competing with respect to price. Why is the equilibrium stable? Why don't the firms raise prices to the level that maximizes joint profits? [20 points]