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| L^{2} 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.**

A monopoly is facing inverse demand given by P = 40−0.5Q and
marginal cost given by MC = 7+0.1Q. Illustrate these on the graph
and answer the questions below.
(a) If the monopolist is unable to price discriminate, what is
the profit-maximizing quantity? What is the price? What is consumer
surplus? Producer surplus? Deadweight loss?
(b) Suppose instead the monopolist is able to perfectly price
discriminate. How many units will be sold? What is consumer
surplus? Producer surplus? Deadweight loss?

A monopolist has the following cost function C(q) = 2000 + 40q.
The demand for its product is given by: q = 100 ? p/2.
(a) Find the optimal quantity, price, and profit.
(b) Find the elasticity of demand at the monopoly quantity and
the Lerner index.
(c) Find the dead-weight loss due to the monopoly.

Given information, cost equation C(Q), Marginal cost MC(Q), and
its demand for elasticity equation
Q(p). ?(?) = 0.5?3 − 20?2 + 282.5?
MC(?) = 1.5?2– 40? + 282.50
?d(?) = 16 − (1/20)?
The government decides that the lack of competition in this
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(i) A monopolist has the following total cost function:
C=50+10Q+0.5Q2
They face the market demand of: P= 210-2Q
a. What is the profit maximizing price and quantity set by
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a. If this good is produced in a monopoly market, provide a
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a. If this good is produced in a monopoly market, provide a
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