Question

1. A monopolist operates in an industry where the demand curve is given by Q = 1000 ? 2P. The monopolist’s has constant marginal cost of $8 (and no fixed costs). What is the monopolist’s profit-maximizing price? How much does the monopolist produce? What are its profits?

Answer 1

Demand curve is as follows -

Q = 1000 - 2P

Inverse demand curve is as follows -

2P = 1000 - Q

P = 500 - 0.5Q

Calculate Total Revenue -

TR = P * Q = (500 - 0.5Q) * Q = 500Q - 0.5Q²

Calculate Marginal Revenue -

MR = dTR/dQ = d(500Q - 0.5Q²)/dQ = 500 - Q

MC = 8

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

MR = MC

500 - Q = 8

Q = 492

P = 500 - 0.5Q = 500 - 0.5(492) = 500 - 246 = 254

When marginal cost is constant, it is equal to ATC.

Calculate Profit -

Profit = TR - TC = (P * Q) - (ATC * Q) = (254 * 492) - (8 * 492) = 124,968 - 3,936 = 121,032

Thus,

The monopolist's profit-maximizing price is $254 per unit.

The monopolist will produce 492 units.

The profits of monopolist is $121,032.