Question

A market has a demand function of Q = 160 - 2p and four firms, each of which has a constant marginal cost of MC = 20. If the firms form a profit-maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output level, how much does each firm produce?

Answer 1

There are four firms and they have formed the cartel.

So, now they will act as monopoly.

A monopoly maximizes profit when it produce that level of outptut corresponding to which MR equals MC.

Demand function is as follows -

Q = 160 - 2p

2p = 160 - Q

p = [160 - Q]/2

p = 80 - 0.5Q

Total revenue function is as follows -

TR = p * Q

TR = [80 - 0.5Q] * Q

TR = 80Q - 0.5Q²

Marginal revenue function is as follows -

MR = dTR/dQ

MR = d(80Q - 0.5Q²)/dQ

MR = 80 - Q

Equating MR and MC

80 - Q = 20

Q = 80 - 20

Q = 60

Thuhs,

The profit maximizing output for cartel is 60 units.

It has been stated that each firm in the cartel will produe the same level of output.

Calculate the output of each firm -

Output of each firm = Total output of cartel/Number of firms in the cartel

Output of each firm = 60/4 = 15 units

Thus,

Each firm will produce 15 units.