Question

Suppose there are two firms, 1 and 2, each with M C = AC = 10. They each choose quantities of output, y1 and y2. The market demand is p= 70−2y, where y=y1+y2. Each firm discounts the future at rate δ <1per period.

a. [6 marks] First calculate the Cournot equilibrium outputs. Call these y∗1 and y∗2.

b. [4 marks] Next, calculate how much each firm would produce if the two firms colluded to act as a monopoly. Call these y1^c and y2^c.

c. [6 marks] Now suppose (as a simplification), each period the firms can choose one of two strategies: produce either yi^c or y∗i, where i= 1, 2 denotes the firm in question. Draw a two-by-two simultaneous game showing what payoffs would be in each outcome, and briefly explain why collusion can’t occur if the game is played exactly one time.

. [6 marks] Finally, assume that the two firms plan on playing the game in (c) an ‘infinite’ number of times. Each has the dynamic strategy ‘collude if we colluded last period, otherwise never collude again.’ Calculate the minimum value of δ which supports collusion as a dynamic equilibrium. Be sure to show your work.

Answer 1

a) MC=10

P=70-2y

Y=y1+y2

Output:-

TR=70y-2y^2

MR=70-4y

MC=MR

10=70-4y

4y=60

Y=60/4

=15

Y*1 , Y*2

15*1=15

15*2=30

P=70-2*15

=40

b) Y1^c=15^10 =9

Y2^c=30^10 = 36