Question

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

Market demand: P = 90 - Q

MC = 30

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

Total revenue (TR) = P x Q = 90Q - Q²

MR = dTR/dQ = 90 - 2Q

Setting MR equal to MC,

90 - 2Q = 30

2Q = 90 - 30 = 60

(1) & (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, we get: When Q = 0, P = 90 (Maximum willngness to pay & vertical intercept)

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

(5) A perfectly competitive firm will maximize profit (or minimize loss) by equating P with MC.

90 - Q = 30

Q = 90 - 30 = 60

P = MC = 30

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

= (1/2) x 30 x 30

= 450