The town of Perkasie, Pennsylvania, has two diners: Emil's Diner and Bobby Ray's Diner. Both sell only chicken pies. Everyone who would consider eating at the diners is aware that they sell the same chicken pies, and knows the prices they charge (PE: PBR). At precisely 5 P.M., each diner (simultaneously) sets its price of chicken pie for that evening. The market demand function for chicken pie is Q = 480 - 40p, where p is the lower of the two diners' prices. If there is a lower-priced diner, then people eat chicken pie at only that diner and the diner sells 480 - 40p chicken pies. If the two diners post the same price, then each sells to one-half of the market: 0.5(480 - 40p). Suppose that prices can be quoted in dollar units only ($0, 4, 6, or 8). Each diner's marginal cost is $4 and fixed cost is $0. If Emil's Diner charges $0 and Bobby Ray's Diner charges $6, then Emil's profit is $and Bobby Ray's profit is $. (Enter numeric responses using integers.) In a second example, if Emil's Diner charges $4 and Bobby Ray's Diner charges $6, then Emil's profit is $and Bobby Ray's profit is $ Next, if Emil's Diner charges $6 and Bobby Ray's Diner charges $6, then Emil's profit is $ and Bobby Ray's profit is $7. 6 $ If Emil's Diner charges $8 and Bobby Ray's Diner charges S6, then Emil's profit is $and Bobby Ray's profit is $0. L Profits for all price combinations are illustrated in the payoff matrix below: Bobby Ray's PBR = 0 PBR = 4 PBR = 6 PBR = 8 4 = Q - 960 0.00 0.00 0.00 PE=0 -960 - 1,920 - 1.920 - 1,920 - 1.920 0.00 0.00 0.00 PE=4 Emil's 0.00 0.00 0.00 1,920 0.00 240 0.00 0.00 PE = 6 480 0.00 0.00 240 - 1,920 0.00 480 320 PE = 8 0.00 0.00 0.00 320 Identify all Nash equilibria. The Nash equilibrium (equilibria) is (are) - O A. (PE = $4, PBR = $4), (PE = $6, PBR = $6), and (PE = $8, PBR = $8). = = = B. (PE = $8, PBR = $8). O C. (PE = $4, PBR = $4). = OD. (PE = $4, PBR = $4) and (PE = $6, PBR = $6). = = = = E. (PE = $6, PBR = $6). = - Suppose that Bobby Ray's Diner is out of business and Emil's is a monopoly. Find Emil's profit-maximizing price. Note that DIE = (480 40p) 40p + 160 = 0. = dp Emil's profit-maximizing price is $ (round your answer to the nearest penny) Now return to the Emil-versus-Bobby Ray's game. Pick one of the Nash equilibria that you identified above. Could Emil and Bobby Ray's collude: set prices different from the particular Nash equilibrium prices and increase both diners' profits? O A. Emil and Bobby Ray could do better than all Nash equilibria by colluding where they set a price of $0. B. Emil and Bobby Ray could do better than all Nash equilibria by colluding where they set a price of $8. C. Emil and Bobby Ray cannot do better than any of the Nash equilibria by colluding. D. Emil and Bobby Ray cannot do better than one of the Nash equilibria (PE = $6, PBR = $6) by colluding. E. Emil and Bobby Ray could do better than all Nash equilibria by colluding where they set a price of $4. = O
