ECON 515: Industrial Organization
Midterm 1 Graduate Exam Supplement
Due February 27, 2023
Question 1 (10 pts)
Recall the markup of the multiproduct monopolist that sells two goods:

1
p1 ? mc1
( p2 ? mc2 ) ? 1,2 Q2
.
=?
1?
°1
? 1,1
p1
Q1
Prove the statements below. (To keep things simple, you may assume that p2 ? mc2 > 0, and
p ?mc ?
2
| ( 2 p1 2 ) 1,2
Q1 | < 1.)
a. If goods 1 and 2 are unrelated,
p1 ?mc1
1
= ? ? 1,1
.
p1
b. If goods 1 and 2 are substitutes,
p1 ?mc1
1
> ? ? 1,1
.
p1
c. If goods 1 and 2 are complements,
p1 ?mc1
1
< ? ? 1,1
p1
Question 2 (10 pts)
Return to the model of optimal patent duration that we discussed in class. Prove that if ? < 12 ,
the optimal patent life is finite. (Hint: Just show that the welfare level under a patent life of one
period (T = 1) is greater than the welfare level at T ? ?.)
Question 3 (10 pts)
A monopolist firm faces two groups of consumers. Group 1 is a homogeneous group of consumers with an inverse market demand curve of p1 = 40 ? q1 while Group 2 is a homogeneous
group of consumers with an inverse market demand curve of p2 = 20 ? q2 . This monopolist has
a cost function c( Q) = 2Q with Q = q1 + q2 .
The consumeràtotal payment Ti (q) is Ti (q) = Ai + pi q with lump sum payment A and per unit
price p.
a. Assume that the monopolist can perfectly distinguish between the two groups of consumers
and can utilize a lump sum payment A > 0. Find the two part tariff the monopolist charges
consumer i, consumer iàsurplus, and the monopolistàprofit.
1
b. Suppose the monopolist cannot distinguish between the consumers and offers a single two
part tariff to both consumers. What is the profit maximizing two-part tariff? What is
consumer iàsurplus, and what is the monopolistàprofit?
c. Compare the consumer surplus for each group of consumers in part a to those in part b. Explain why one group of consumers seems to gain when the monopolist cannot distinguish
between consumers.
2

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