## Microeconomics

Microeconomics (Spring 2017)
Problem Set 7: Monopoly and Market Power
Submit in Recitation or Lecture, April 10/11, whichever comes first
• Write your answers on separate sheets of paper. Please include:
– your recitation teacher’s name
– day and time of your recitation
Part I: Short Answer
1. Show that if a firm is a natural monopoly, a government policy that forces marginal cost pricing will result in
losses for the firm.
2. What type of price discrimination is depicted in the examples below? Please explain your answer.
(a) You can buy an apple for \$1, a pack of 6 apples for \$5, or a pack of 12 for \$8.
(b) When you fly from New York to Los Angeles, the airline charges you \$400 if you buy your ticket 30 days
in advance. However, the airline will charge you \$700 if you buy the ticket on the day of travel.
(c) Tropicana Orange Juice issues a coupon for \$1 off a carton of juice. Only consumers who bring the
coupon to the store and hand it to the cashier at checkout recieve the price discount.
Part II: The Monopolist’s Problem
1. A monopolist sells its good in the US and French markets. The US inverse demand function is
PUS = 20
1
2
QUS
and the French inverse demand function is
PF = 24
1
4
QF
where both prices PUS and PF are measured in dollars. The firm’s marginal cost of production is constant
at MC = 4 in both countries. If the firm can prevent re-sales, what price will it charge in both markets?
(Hint: The monopolist determines its optimal (monopoly) price in each country separately because customers
cannot re-sell the good).
2. Suppose a monopolist’s costs are described by the function C(Q) = 10 + 2Q2 and the monopolist faces a
demand curve of Q = 20
p. Suppose that the firm is able to practice perfect price discrimination. What are
the values of output, profit, and consumer surplus?
3. Consider a monopolist facing two customer groups. The first has demand q1 = 40
2p1 and the second has
demand q2 = 40
p2. The firm has marginal cost MC(q) = q, where q = q1 + q2 is the total amount sold.
(a) Suppose it could first degree price discriminate and charge the full willingness to pay for every unit. How
many units does it sell to each group?
(b) Suppose it can separate customers into the two groups (third degree price discrimination), each with its
own price per unit. How many units does it sell to each group? At what prices?
(c) Suppose instead of MC(q) = q , the firm had exactly 6 units to sell to the two groups (and no costs to
worry about; the 6 units are already produced). How should it split the units between the goods? (we
are still in third degree price discrimination).