Question

1. A monopolist producer of a drug Zeta has demand P=270 – 0.2q and costs C=5000+50q+0.2q^2.

a. Derive the MC, ATC, and MR functions.

b. Derive the profit-maximizing price, quantity, and profit. Show on a graph.

c. What is the price and quantity if the monopolist loses patent protection and the industry becomes perfectly competitive? What is the size of the deadweight loss in monopoly? Show the deadweight loss triangle in the graph.

Answer 1

(a)

MC = dC/dq = 50 + 0.4q

ATC = C/q = (5,000/q) + 50 + 0.2q

TR = Pq = 270q - 0.2q2

MR = dTR/dq = 270 - 0.4q

In following graph, monopoly profit is maximized at point E where MR intersects MC with price P0 and quantity Q0.

(b)

Setting MR = MC,

270 - 0.4q = 50 + 0.4q

0.8q = 220

q = 275

P = 270 - 0.2 x 275 = 270 - 55 = 215

TR = 215 x 275 = 59,125

TC = 5,000 + 50 x 275 + 0.2 x 275 x 275 = 33,875

Profit = TR - TC = 59,125 - 33,875 = 25,250

Monopoly profit is area P0FHC in graph.

(c)

With perfect competition, P = MC.

270 - 0.2q = 50 + 0.4q

0.6q = 220

q = 366.67

P = 270 - 0.2 x 366.67 = 270 - 73.33 = 196.67

When Q = 275, MC = 50 + 0.4 x 275 = 160

Deadweight loss = Area EFG = (1/2) x (Monopoly price - Monopoly MC) x Change in Quantity

= (1/2) x (215 - 160) x (366.67 - 275) = (1/2) x 55 x 91.7 = 2,521.75