Question

Suppose that, in a market of a certain good, there are two firms that are engaged in an infinitely repeated Cournot competition. In each period, the inverse demand function is given by P(Q) = 200 − 4Q, where Q is the total supply of the good. Firm i (i = 1, 2) has the same cost function C(qi) = 8qi and the same discount factor δ, where 0 < δ < 1.

1. What is the Cournot equilibrium profit for each firm? (a) 861. (b) 1422. (c) 968. (d) 1024. (e) 798

2. What is the collusive profit for each firm? (a) 1152. (b) 1328. (c) 1224. (d) 1720. (e) 1352.

3.What is the defection profit for a deviating firm? (a) 1664. (b) 921. (c) 1082. (d) 1752. (e) 1296.

Answer 1

1) p=200-4q1-4q2

MR1=200-8q1-4q2

MC1=8

200-8q1-4q2=8

Q1=24-0.5q2{ best response function of firm1}

By symmetry,

Q2=24-0.5q1

Putting q2 into q1,

Q1=24-0.5(24-0.5q1)=12+0.25q1

Q1=12/0.75=16

Q2=16

Q=16+16=32

P=200-4*32=72

Profit of each firm=(72-20)*16=1024

OptionD is correct

2) In collusion,they will produce jointly monopoly output,

P=200-4Q

MR=200-8Q

MC=8

200-8Q=8

Q=192/8=24

P=200-4*24=104

Q1=q2=24/2=12

Profit of each firm=(104-8)*12=96*12=1152

Option A is correct

3) The defecting firm will produce that QUANTITY that MAXIMIZE its Profit given other firm output fixed at collision output.

Using best response,the best output of defecting firm is,

Qi=24-0.5*12=24-6=18

Q=18+12=30

P=200-4*30=80

Profit of defecting firm=(80-8)*18=72*18=1296

Option e is correct