Description

1 attachmentsSlide 1 of 1attachment_1attachment_1.slider-slide > img { width: 100%; display: block; }

.slider-slide > img:focus { margin: auto; }

Unformatted Attachment Preview

Econ 100C, Problem Set 1

1. The inverse demand curve that a monopoly faces is P = 100 Q. The firms cost curve is

C(Q) =10 + 5Q. What is the profit-maximizing price and quantity? How does your answer change

if C(Q) = 100 + 5Q?

2. The inverse demand curve that a monopoly faces is P = 10Q-1/2. The firms cost curve is

C(Q) = 5Q. What is the profit-maximizing price and quantity?

3. If the inverse demand function facing a monopoly is P(Q) and its cost function is C(Q), show

the effect of a specific tax ??, on the monopolys profit-maximizing output. How does imposing

affect its profit?

4. Suppose that all iPod owners consider only two options for downloading music to their MP3

players: purchasing songs from iTunes or copying songs from friends CDs. With these two

options, suppose the weekly inverse market demand for the Rolling Stones song Satisfaction

is p = 1.98 0.00198Q. The marginal cost to Apple Inc. of downloading a song is zero.

a. What is Apples optimal price of Satisfaction? How many downloads of Satisfaction

does Apple sell each week?

b. Now suppose that Apple sells a version of the iPod equipped with software in which songs

played on the iPod must be downloaded from iTunes. For this iPod, the inverse market

demand for Satisfaction is p = 2.58 0.0129Q. What is Apples optimal price of downloads

of Satisfaction for this new player? How many downloads of Satisfaction does Apple sell

each week?

5. A monopoly manufactures its product in two factories with marginal cost functions MC1(Q1)

and MC2(Q2), where Q1 is the quantity produced in the first factory and Q2 is the quantity

manufactured in the second factory. The monopolys total output is Q = Q1 + Q2. Use a graph (or

math) to determine how much total output the monopoly produces and how much it produces

at each factory.

6. A monopolist has the cost function of C(Q) = A+Q2, where A > 0. Inverse market demand is

equal to P(Q) = 60 4Q.

a. Assuming no shutdown find the monopolists profit maximizing price and quantity.

b. For what values of A will the monopolist shutdown? Explain.

For the rest of the problem assume A = 0.

c. Give the monopolists profit maximizing price and quantity.

d. Calculate the demand elasticity at the point you found in (c). Verify that this elasticity is in

the elastic region.

e. Calculate the Lerner index using elasticity, and then using price and marginal cost.

f. Calculate consumer surplus, producer surplus and deadweight loss at the monopoly price

and quantity.

7. Suppose the market demand for gasoline is Q=100-P/2. A monopolist firm has a cost of C(Q)=Q

for procuring gasoline. Suppose the government wants to maximize tax revenue by imposing a

specific tax on gasoline per unit. Find the optimal specific tax and the resulting tax revenue.

Purchase answer to see full

attachment

Tags:

profits

inverse demand curve

facing a monopoly

User generated content is uploaded by users for the purposes of learning and should be used following FENTYESSAYS.COM ESSAY’s honor code & terms of service.