Question

A monopoly has an inverse demand function given by p = 120 - Q and a constant marginal cost of 10. a) Graph the demand, marginal revenue, and marginal cost curves. b) Calculate the deadweight loss and indicate the area of the deadweight loss on the graph. c) If this monopolist were to practice perfect price discrimination, what would be the quantity produced? d) Calculate consumer surplus, producer surplus, and deadweight loss for this monopolist under perfect price discrimination.

Answer 1

(a) p = 120 - Q

Total revenue (TR) = p x Q = 120Q - Q²

Marginal revenue (MR) = dTR/dQ = 120 - 2Q

From demand function,

When Q = 0, p = 120 (Vertical intercept) & when p = 0, Q = 120 (Horizontal intercept).

From MR function,

When Q = 0, p = 120 (Vertical intercept) & when p = 0, Q = 120/2 = 60 (Horizontal intercept).

The demand, MR & MC curves are as follows.

(b) A perfect competitor maximizes profit by equating price with MC.

120 - Q = 10

Q (= Qc) = 110

p (= Pc) = MC = 10

A monopolist maximizes profit by equating MR with MC.

120 - 2Q = 10

2Q = 110

Q (= Qm) = 55

p (= Pm) = 120 - 55 = 65

Deadweight loss = Area BDE = (1/2) x (110 - 55) x (65 - 10) = (1/2) x 55 x 55 = 1,512.50

(c) With perfect price discrimination, monopolist charges a price equal to MC, and earns a profit equal to entire consumer surplus (CS).

When p = MC = 10, Quantity (Qc) = 110

(d) With perfect price discrimination,

Consumer surplus = Area between demand curve & price = Area AEPc = (1/2) x (120 - 10) x 110 = 55 x 110 = 6,050

Producer surplus = Area between MC curve and price = 0 (Since Market price = MC)

Deadweight loss = 0