PSET 6 2.1 ) ply, 3.) : 90- 31-42 -24,=- 80 +42 2.5 IT , (90 - 9. - J= 1 Ly, 1 - 10 9, 24 , =80 - 42 4 90/ 2y, = 90 - 24, - 42 - 10 3 50-24,-42=0 4, (9 2) = 80 -12 2.2 60 242 = 60-4, 40 4 2 64 1 ) OT = 90-41- 242 - 30 42 = 60 -41 3 60 - 41 -242 = 0 (yzly, ) = 60 -3, 80 90 -242 = -60+4, 2.6 2. 3 4 , . 60 - 4. 60 -180-72 TT = TT, + 1 2 2 2 = y1 ( 90- 4, - 4= ) (y, + 42) - 10g, - 30 yz 2 60 -1 80-32) = 242 9, : 50 - 31 91 80-24,-292 =0 /15 251 :60- 241- 242 0 2 -291 5 -90 + 242 y, = 80-(49 - 247= -60+2y, 120 - 180 - 42 ) = 4 yz 42 = 60-24. J = 100 2 40 = 34 2 ~ 33.33 3 12 = 60- 241 (60-180-24- ]) 42=40 ~ 13.31 120 - 140 - 2) = 242 2 2.4 120 - 40 +4 2 = 292 80 = 42 P ( y , , y 2 ) = 90 - 3, - yz 80 - 2180) - to -40 =4 90 - 40 190 2 3 - 2.7) 3 = 13.3 90 -80 - 1-40) = 502. Assume that in a duopoly market two firms compete by choosing quantities. Suppose that the inverse market demand is p(y1,y2) = 90 y1 y2. Suppose that firm 1's cost function is C1(y1) = 10y; while firm 2's cost function is Cs(y2) = 30y2. Suppose initially that firms simultaneously choose quantities (i.e. Cournot competition) 2.1. 2.2, 2.3. 24. 2.5. What is firm 1's reaction function y,(y,) to any given quantity y, of firm 27 What is firm 2's reaction function y,(y,) to any given quantity y; of firm 17 What is the Cournot equilibrium of this game? What is the market price and the profits of each firm in the Cournot equilibrium? Plot the reaction functions that you found in (a) and (b) on the same graph with firm 1's quantity on the z axis and firm 2's quantity on the y axis (like we did in the lecture notes). Label the Cournot equilibrium. Suppose that the firms could collude by setting y; and y, to maximize joint profits. (Hint: will the firms ever want to choose y, > 072 Think about marginal costs...) 2.6. o 2.8. 2.9. 2.10. What is the joint profit maximizing level of output at the two firms? What is the market price? What are the profits for each firm? Why would it be hard for firms to sustain the joint profit maximizing levels of output? Specifically, which firm might want to deviate? Suppose these firms interacted repeatedly (perhaps infinitely often) would that make it possible to sustain the joint profit maximizing output levels? Could repeated inter- action at least help firms do better than repeated play of the Cournot equilibrium? Hint: what would the profits be for firm 2 in every round? Could they do better