Question

27. If the duopolists in question 24 behave as a shared monopoly, determine the (1) equilibrium price, (2) quantity, and (3) economic profits for the total market and (4) the consumer surplus, and (5) dead weight loss.

24:Cournot duopolists face a market demand curve given by P = 90 - Q where Q is total market demand. Each firm can produce output at a constant marginal cost of 30 per unit. There are no fixed costs. Determine the (1) equilibrium price, (2) quantity, and (3) economic profits for the total market, (4) the consumer surplus, and (5) dead weight loss.

Answer 1

When the firms behave as a shared monopoly, the duopolist combine to form a monopoly and behave like one firm. They charge price, quantity as a monpolist and then divide amongst themselves.

A monopolist would produce profit maximising level of output at a point where the marginal cost equals the marginal revenue.

P = 90 - Q

TR = P * Q

TR (90 - Q) * Q

TR = 90Q - Q²

MR = TR/Q.

MR = 90 - 2Q

MC = 30

MR = MC

90 - 2Q = 30

90 - 30 = 2Q

60 = 2Q

Q = 60/2

Q = 30 units.

Each firm would then produce 30/2 or 15 units each.

P = 90 - 30

P = $60.

Profit = TR - TC

Profit of total market = (60 * 30) - (30 * 30)

Profit = 1800 - 900

Profit = $900

Profit of each firm would thus be $450.

Orange shaded is the consumer surplus, above the price line and below the demand curve.

Green shaded is the deadweight loss.

Area of triangle = 1/2 * base * height.

CS = 1/2 * (30-0) * (90-60)

CS = $450.

DWL = 1/2 * (60-30) * (60-30)

DWL = $450.