QUESTION ONE 1. Let the market demand function for two companies namely Patriots for e Heritage be given by; Q(p) = 380 - P where Q = q1 + 92. The cost function for each firms in the industry is C (qi) = 47qi where i = 1,2. REQUIRED: A. Find the best reaction functions for firm 1 and firm 2. B. Graph each firm's reaction function. Show the Stackelberg equilibrium C. Find the optimal output for both firm 1 and firm 2 D. Find the profit levels for both firm one and firm two? E. Where do you find more output produced and profits made Stackelberg model? Give a reason for your answer. [To STION TWO wani is a student at the University of Lusaka who wants to buy food ia. Kondwani's preference is given by U(x,y)= 2xy, where x uts and y is the amount of pies. The price of a doughnut is ZMV W 2. Kondwani only has ZMW 30 to spend. ing Lagrangian methodology, obtain the optimal amounts ofQUESTION Consider the normal-form, one-shot game shown in Figure E13.2, involving two firms that have entered into a collusive agreement. The payoffs in the parentheses are in millions of dollars. Having entered into the agreement, both firms must decide whether to remain faithful to the agreement (Don't cheat) or to violate the agreement (Cheat). a) Does either firm have a dominant strategy? b) If both firms follow a maximin strategy, what is the strategy profile for this game? Is this strategy profile a Nash equilibrium? c) Suppose that firm 8 were to cheat on the agreement. What would firm A do? d) How might your answer be different if this were an infinitely repeated game?What factors not presented here must be considered? Firm B Dordt cheat Cheat Dod t cheat (10, 10) (-5,20) Firm A Cheat (20.-5) (5. 5) Payoffs: (Firm A. Firm B) FIGURE E13.2 Payull matrix for chapter excerise 132