Question Industrial Organization June 4, 2014

Industrial Organization

June 4, 2014

Problem Set 2

Due: Monday, June 9

1. A monopoly with constant marginal costs of $50 can sell to three groups of potential con-

sumers, with demandsQ1= 800????0:2p,Q2= 400????p, andQ3= 700????0:4prespectively.

Find the optimal price-quantity combination in each market

(a) if the rm is able to price-discriminate;

(b) if it is not able to price-discriminate.

2. A rm with costsC(Q) = 1;000 + 60Q+ 0:1Q2is able to price-discriminate between two

groups of customers, with demandsQ1= 3;000????2p, andQ2= 350????0:5prespectively. How

much does it sell to each group, and at what price? What would happen if it were forced to

charge all its customers the same price?

3. A marketing order for oranges has a xed total supply ofQ= 1;000 crates a month. Demand

in the market for fresh oranges isQ1= 220????0:2pand that in the market for processed orange

products isQ2= 1;000????2p. Calculate the competitive market-clearing price. What is the

deadweight loss in both markets if the price of a crate of fresh oranges is raised to $200?

4. A monopolist has two sets of customers. The inverse demand for Group 1 is described by

P= 200????X. For Group 2, the inverse demand isP= 100????2X. The monopolist faces

constant marginal cost of 40

(a) Show that the monopolist’s total demand, if the two markets are treated as one is:

X= 0;P200

X= 200????P; 100< P200

X= 250????(3=2)P; 0< P100

(b) Show that the monopolist’s prot maximizing price isP= 120 if both groups are to be

charged the same price. At this price, how much is sold to members of Group 1 and

how much to members of Group 2? What is the consumer surplus of each group? What

are total prots?

5. Now suppose that the monopolist in #4 can separate the two groups and charge separate,

prot-maximizing prices to each group

(a) What will these prices be? What is consumer surplus? What are total prots?

(b) If total surplus is consumer surplus plus prot, how has price discrimination a
ected

total surplus?

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