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
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.
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.
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.
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