04 Jun Question ECN121A (INDUSTRIAL ORGANIZATION) PROBLEM SET 1
Question
ECN121A (INDUSTRIAL ORGANIZATION)
PROBLEM SET 1
DUE BEGINNING OF CLASS: JANUARY 16, 2015
Question 1: [30 points] Consider the production of some product A. (Assume if q A = 0, then
C (q A ) = 0).
(a) [10 points] Does the cost function C (q A ) = 1 + q A exhibit economies of scale? Explain
why/why not.
(b) [10 points] Does the cost function C (q A ) = q2 exhibit economies of scale? Explain why/why
A
not.
(c) [10 points] Does the cost function C (q A ) = (1 + q A )0.5 + 100 exhibit economies of scale?
Explain why/why not.
Question 2: [35 points] A monopolist faces demand of q( p) = 230 p and has cost function
C (q) = 30q.
(a) [5 points] What is the monopolists maximization problem?
(b) [5 points] What is the rst order condition corresponding to this problem?
(c) [5 points] Draw a diagram showing demand, and the relevant curves corresponding to the
monopolists problem. Indicate the (price, quantity) chosen by the monopolist.
(d) [5 points] What are the monopolists prots, consumer surplus, and deadweight loss of
monopoly?
(e) [5 points] How much would consumers be willing to pay to have the monopolist set price
equal to its marginal cost?
(f) [5 points] If the monopolist set price equal to marginal cost, but had a membership fee
equal to what you found in part e, how would total surplus change compared to part d?
Question 3: [35 points] There are two groups of consumers who have inverse demands p1 =
120 q1 and p2 = 60 0.5q2 . The monopolist has cost function C (q) = 20q.
(a) [5 points] If the monopolist can choose a separate p1 and p2 for each group, what will they
be?
(b) [10 points] If the monopolist can only charge a single price, what will it be? Do both
groups purchase? If so, how much does each group buy? [Hint: Add up demands, not
inverse demands.]
(c) [5 points] How do the prices p1 and p2 compare to the uniform price you found in part b?
(d) [5 points] Does the monopolist prefer to set a separate p1 and p2 , or does the monopolist
prefer to set a single price?
1
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