Question

Monopoly Deadweight Loss and Elasticity The demand and cost information for a patented drug developed and sold by the monopolist BigPharma are given below: Demand: P = 80 – 6Q Total cost: TC = 2Q2 Marginal Cost: MC = 4Q, where Q is measured in millions of pills per year and P is measured in dollars per pill.

a. Calculate the monopoly profit-maximizing price and quantity and the monopoly deadweight loss triangle. Illustrate your answer, showing demand, marginal revenue, marginal cost, monopoly price and quantity, competitive price and quantity, and deadweight loss.

b. Calculate the elasticity of demand at the monopolist’s profit-maximizing price. Explain why it is that if demand is linear (and marginal cost is not zero), the monopolist will always price in the elastic portion of the demand curve.

Answer 1

(a)

TR = P x Q = 80Q - 6Q²

MR = dTR/dQ = 80 - 12Q

Setting MR = MC,

80 - 12Q = 4Q

16Q = 80

Q = 5

P = 80 - 6 x 5 = 80 - 30 = 50

TR = 50 x 5 = 250

TC = 2 x 5 x 5 = 50

Profit = TR - TC = 250 - 50 = 200

In competitive equilibrium, P = MC.

80 - 6Q = 4Q

10Q = 80

Q = 8

P = 4 x 8 = 32

TR = 32 x 8 = 256

TC = 2 x 8 x 8 = 128

Profit = 256 - 128 = 128

Monopoly deadweight loss = (1/2) x Change in P x Change in Q = (1/2) x (50 - 32) x (8 - 5) = (1/2) x 18 x 3 = 27

In following graph, monopoly profit is maximized at point E where MR intersects MC with price P0 (= 50) and output Q0 (= 5), with profit of area P0BFG. Competitive profit is maximized at point H where Demand (D) intersects MC with lower price P1 (= 32) and higher output Q1 (= 8), with profit of area P1HGK. Monopoly deadweight loss is area BEH.

(b)

P = 80 - 6Q, so

Q = (80 - P)/6

Elasticity = (dQ/dP) x (P/Q) = - (1/6) x (50/5) = - 1.67

If monopolist produces at inelastic range, to sell additional output, the monopolist has to accept a more-than-proportionately lower price, therefore he produces at the elastic portion only.