Question

Monopoly, markup formula, Lerner index, deadweight loss] Megasoft makes a word-processing program. Marginal cost of producing the program is $10. The elasticity of demand for the program is ε = -1.5.

a. What price should Megasoft charge for the program, to maximize profit? $

b. Compute the Lerner index (also called the "price-cost margin" or the "markup ratio") for this monopolist. Recall that the Lerner index is defined as L = (P-MC) / P . L =

c. Compute social deadweight loss using Harberger's approximation formula: DWL = (1/2) |ε| L2 P Q, where  denotes the elasticity of demand, L denotes the Lerner index, P denotes the price charged, and Q denotes the quantity sold.1 Assume Q = 10 million copies of the program are sold. $ million

Answer 1

(a)

Marginal cost, MC = $10

Elasticity of demand, e = -1.5

MC = P[1+(1/e)]

10 = P[1+(1/-1.5)]

10 = 0.33P

P = 10/0.33 = 30.30

In order to maximize profit, Megasoft should charge $30.30 for the program.

(b)

Calculate Lerner's Index -

L = (P-MC) / P

L = (30.30 - 10)/30.30

L = (20.30/30.30)

L = 0.67

The Lerner Index for this monopolist is 0.67.

(c)

Calculate Social deadweight loss -

DWL = (1/2) |ε| L² P Q

DWL = (1/2) * 1.5 * (0.67)² * 30.30 * 10 million

DWL = $102.01 million

The social deadweight loss is $102.01 million.