MB 515: Economic Theory and Application Problem Set 5 5.1 Alcoa and Kaiser, duopolists in the market for primary aluminum ingot, choose prices of their 500 foot rolls of sheet aluminum on the first day of the month. The following payoff table shows their monthly payoffs resulting from the pricing decisions they can make. Alcoa High price Low price A B Kaiser - = 5 Low price $525, 5200 $273, 5250 Payoffs in millions of dollars of profits per month. a. What 15 the cooperative outcome? What 15 the noncooperative outcome? What payoff will each recerve for the cooperative and noncooperative outcomes, respectively? b. If Alcoa and Kaiser make their pricing decision just one time, will they choose the cooperative outcome? Why or why not. 5.2 Sony and Toshiba must each decide which video technology to use in producing their 2018 model Ultra HDTVs: Alpha technology or Beta technology. The pavoff table below shows the profit outcomes for both Sony and Toshiba 1 the four possible technology choice outcomes: Toshiba Alpha Beta Alpha Sony Beta Payoffs in bilions of dollars of profits. a. Suppose that Toshiba successfully makes a strategic commitment to one of the technologies so that 1t can make the first move in a sequential decision game. Complete the following game tree for the sequential game in which Toshiba mowves first, by filling in the blanks below using the information in the payoff table. Sony Toshiba K Use the roll-back method to find the Nash equilibrium decision path. Mark all best decisions and then circle the solution (Nash) decision path on the game tree above. Sony earns a profit of $_ and Toshiba earns a profit of $_ 5.3 Managers at Firm A and Firm B must make pricing decisions simultaneously. The following demand and long-run cost conditions are common knowledge to the managers: QA = 600 - 2PA + PB and LACA = LMCA = 32 QB = 400 -2.5PB + 2PA and LACB = LMCB = 24 The accompanying figure shows Firm A's best-response curve, BRA. Only one point on Firm B's best-response curve, point J, is shown in the figure: PB BRA 300 - 200 Firm B's price 100- L 100 200 300 Firm A's priceFind a second point on Firm B's best-response curve by finding the best response when Firm B believes Firm 4 will set a price of $100. Plot this price pair on the graph, label it K, draw the best-response curve for Firm B, and label 1t BR.. . What prices do you expect the managers of Firm A and F to set? Why? Label this point on the graph M. Compute each firm's profit at point N