Question

If the duopolists in question 24behave 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.Show Work

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

P = 90 - Q

A monopolist will maximize profit by equating Marginal Revenue (MR) with MC.

Total revenue (TR) = P x Q = 90Q - Q²

MR = dTR/dQ = 90 - 2Q

Equating with MC,

90 - 2Q = 30

2Q = 60

(1) and (2)

Q = 30

P = 90 - 30 = 60

(3) Profit = Q x (P - MC) = 30 x (60 - 30) = 30 x 30 = 900

(4) From demand function, when Q = 0, P = 90 (Reservation price)

Consumer surplus = Area between demand curve & market price = (1/2) x (90 - 60) x 30 = 15 x 30 = 450

(5) If the firm were perfectly competitive, profit would be maximized when P = MC.

90 - Q = 30

Q = 60

P = MC = 30

Deadweight loss = (1/2) x Change in price x Change in quantity = (1/2) x (60 - 30) x (60 - 30) = (1/2) x 30 x 30 = 450