University of California, Davis
Department of Agricultural and Resource Economics
ARE 100B
Winter 2010
Dr. Larson
Problem Set 2
Answers
Be sure to explain what you are doing and show your work in the numerical problems, and provide a brief but
complete answer to the discussion questions.
Each part of a problem is weighted equally.
Be sure to express the
appropriate units for your answers.
You should draw graphs for each problem to help guide your analysis.
1.
You are a monopolist producing video game software and know you can segment your market into two distinct
groups of consumers: kids who will pay almost any price for your software, and older consumers who are very
price-sensitive.
Your investigation of the market has shown that the demand by kids is
100
,
kk
qp
=
−
while the
demand by adults is
800 40
.
aa
=
−
Your marginal cost of producing videos is
5.
MC
=
(a)
If you were to engage in third-degree price discrimination, what prices would you charge to each
market segment?
To third-degree price discriminate, you would determine a separate price for each market that maximizes your
producer surplus (and profit).
In the kids market, by inspection you can tell that the marginal revenue function is
100 2 .
k
MR
q
=
−
(
Be sure you know why
.)
Setting this equal to the MC, the monopoly quantity
is
(100 5)/ 2
47.5.
km
q
=−=
Evaluating price on the demand curve for this quantity, the monopoly price is
100 47.5 52.50.
km
p
=
−=
In the adult market, the inverse demand is
20 .025 ,
pq
=
−
so
20 .05 .
MR
q
=
−
Setting this equal
to MC, the monopoly quantity in the adults market is
(20 5)/.05 300;
am
q
=
from the inverse adults demand,
the corresponding monopoly price is
20 .025(300) 12.50.
km
p
=
(b)
How many units would you sell to each market?
In part (a), we found the monopoly quantities to be
47.5
km
q
=
and
300.
km
q
=
(c) What would your total producer's surplus be?
Total revenue in the kids market is
k
TR
=
(52.50)(47.5) = 2493.75, while total variable cost is
k
TVC
=
5(47.5)
= 237.50, so producer's surplus in this market is
2256.25
k
PS
TR
TVC
=
.Total revenue in the adults
market is
a
TR
=
(12.50)(300) = 3750, while total variable cost is
a
TVC
=
5(300) = 1500, so producer's surplus in
this market is
2250.
a
PS
=
Your total producer's surplus from this strategy therefore is the sum of the surpluses
from each market, or 4506.25.
2.
Assuming all the same relationships as in problem 1, are you better off by price discriminating or by charging
a single price to the entire market?
To answer this question,
(a) Determine the aggregate demand for videos.
[Hint: Be careful to account for the kink.]
In determining the aggregate demand, you have to be aware that because the two groups have different reservation
prices, they will “drop out” of the market at different prices.
This means that for low prices, both groups will be