Question

The market demand for a good is P = 90 - 2Q. The good can be produced at a constant cost of $50. How much deadweight loss is created if the market is served by a monopolist as opposed to a competitive market?

Answer 1

Market is served by a monopolist

Demand function is as follows -

P = 90 - 2Q

Total revenue function is as follows -

TR = P * Q

TR = (90 - 2Q) * Q

TR = 90Q - 2Q²

Marginal revenue function is as follows -

MR = dTR/dQ

MR = d(90Q - 2Q²)/dQ

MR = 90 - 4Q

Constant cost, MC = $50

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

MR = MC

90 - 4Q = 50

4Q = 40

Q = 40/4 = 10

P = 90 - 2Q = 90 - (2*10) = 90 - 20 = 70

Thus, in case of monopolist,

The profit-maximizing quantity is 10 units and the profit-maximizing price is $70 per unit.

Market is competitive

Demand function is as follows-

P = 90 - 2Q

Constant cost, MC = $50

A firm in competitive market maximizes profit when it produce that level of output corresponding to which price equals marginal cost.

P = MC

90 - 2Q = 50

2Q = 40

Q = 40/2 = 20

P = 90 - 2Q = 90 - (2*20) = 90 - 40 = 50

Thus, in competitive market,

The profit-maximizing quantity is 20 units and the profit-maximizing price is $50 per unit.

Calculate the dead weight loss -

DWL = 1/2 * [Price charged by monopolist - Price charged by competitive firm] * [Quantity produced by competitive firm - Quantity produced by monopolist]

DWL = 1/2 * [$70 - $50] * [20 - 10]

DWL = 1/2 * $20 * 10 = $100

Thus,

The dead weight loss created if the market is served by a monopolist as opposed to a competitive market is $100.