UCSD ECON 100C Microeconomics Questions

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Econ 100C, Problem Set 1
1. The inverse demand curve that a monopoly faces is P = 100 – Q. The firm’s 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 firm’s 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 monopoly’s 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 Apple’s 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 Apple’s 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 monopoly’s 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 monopolist’s 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 monopolist’s 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.

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profits

inverse demand curve

facing a monopoly

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