Simon Fraser University Spring 2016 ECON 302 S. Lu

Simon Fraser University
ECON 302
Spring 2016
S. Lu
Problem Set 8
Due on March 21, at 2:30pm
Remember to show your work on all questions.
1. Consider a profit-maximizing monopoly, and assume that there is no resale market, so that
the firm can charge each customer a different price. Consumers have unit demand, and the
good is homogeneous. (So neither quantity nor quality discrimination is possible.)
The firm has constant marginal cost 5 and no fixed costs. It faces two groups of consumers,
A and B. Group A has demand QA = 25-P, and group B has demand QB = 75-P.
a) What are the firm’s pricing strategy and profit if it can tell every customer apart?
b) What are the firm’s pricing strategy and profit if it can only tell the two groups apart?
c) What are the firm’s pricing strategy and profit if it cannot tell anybody apart?
2. Suppose that there are two types of customers, High and Low, served by a monopolist. High
types have utility 𝑢𝐻 (𝑥, 𝑃) = 2√𝑥 − 𝑃, while low types have utility 𝑢𝐿 (𝑥, 𝑃) = √𝑥 − 𝑃,
where x is the quantity of the good consumed, and P is the total (not per unit) amount paid.
Fraction q of the population has High type, and fraction 1-q has Low type. The monopolist
has constant marginal cost c and no fixed cost.
a) Suppose consumer types are observable. Find the monopolist’s first-best quantity and
price for each type.
Now suppose consumer types are not observable.
b) Suppose the monopolist wants both types to buy, but must offer the same bundle to
everyone. What quantity and price does it pick?
c) Is it possible for the monopolist to sell only to the Low type and not to the High type?
Defend your answer mathematically.
d) If the monopoly chooses to only serve the High type, what price and quantity would it
pick? Explain why the Low type wouldn’t buy without using your answer.
e) Suppose the firm wants to engage in second-degree price discrimination (that is, the firm
offers a menu and intends for each type to choose a different item from the menu). Write
down the firm’s maximization problem. Your answer should include the firm’s choice
variables, its objective function, the two IR constraints, and the two IC constraints.