Question

Assume there are two firms, 1 and 2, that compete in output, products are homogeneous, and the inverse market demand is p = a – Q, where Q = q1 + q2. Assume that production costs are zero for simplicity.

1. Find the NE (Cournot) price, output, and profits of each firm if this is a static game.

2. Find the SPNE if this is a dynamic game where firm 1 chooses output first.

3. Find the cartel equilibrium to this game.

4. Use a graph of best-reply and isoprofit functions to describe the NE, SPNE, and cartel equilibrium for problems A, B, and C above.

5. Use a graph of best-reply and isoprofit functions to show that each firm has an incentive to increase its output from the cartel level.

Answer 1

(po ha 10)-au a mala - 9 p=a-Q, Q = 4 + 42 MC=0 1 TI = (P-o) q = (a-9-92) u = (a-qa) u-91² anila =) (a-q2) - 24 =0 q BR = a -92/2 - Similarly q BR = (a-12 so sowing two BR 29 = a- (ay) 49= atau q=213 * = 213 Q = 2a = 4 + q P = a-Q = a-da = ala 80 Ti = Tg = (P-MC) q = a/9 Ang .. Stackelben Game, Max II St Q BR . T= (P-MC) 9 = (a-q-9₂BB)

4) graph

02 BR1(92) cournot Nash eqm BR2(912 isoprofit of Firm 1 stackelberg (SPNE) & MONOPOLY Q1