EC 301, Spring 2015. Problem set 6 Page 1 of 2

Note: Your score will be based on your overall performance in answering all questions in this
problem set. Answers to specific questions will not be individually graded. Show all logical steps
in your arguments. Answers without any explanation will get zero credit. You must work in
groups of two and you can consult any other resources (internet, other text books, etc.). You need
to turn in one home work per group. Make sure you write the names of all group members on
your home work.
There are seven problems in total. Several questions are from your text book “Microeconomics”
by Bernhiem and Whinston.
A remark on plagiarism: While you are allowed to use any resource you like to solve these
problems, please note that each group must write their answers in their own words. Copying
from other groups’ work or from any document that you have not produced by yourself is
considered to be a case of plagiarism and may result in a ZERO grade.
A few sample questions and answers are posted on ANGEL to give you hints on how to solve
some of these problems.
Questions from Chapter 19
1. Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function
is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number
of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and
Rebecca compete in quantities and competition in this market is described by Cournot model.
What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do
they each earn as profit? How does the price compare to the marginal cost?
2. Consider question 1 again but assume that Joe’s and Rebecca’s firms compete in prices rather
than in quantities. Consumers perceive the ready-mix concrete produced by the two firms as
identical products. Find the Nash equilibrium prices when the two firms set their prices
simultaneously.
Questions from Chapter 20
3. Two hundred paper mills compete in the paper market. The total cost of production (in
dollars) for each mill is given by the formula TC = 500Qmill + (Qmill)2 where Qmill indicates
the mills annual production in thousands of tons. The marginal cost of production is MC =
500 + 2Qmill. The external cost of a mill’s production (in dollars) is given by the formula EC
= 40Qmill + (Qmill)2 and the marginal external cost of production is MEC = 40 + 2Qmill.
Finally, annual market demand (in thousands of tons) is given by the formula Qd = 150,000 –
100P where P is the price of paper per ton. Using algebra, find the competitive equilibrium
EC 301, Spring 2015. Problem set 6 Page 2 of 2
price and quantity, as well as the efficient quantity. Calculate the magnitude of the
deadweight loss resulting from the externality. Illustrate your solution with graphs.
4. Three stores have a problem with theft, and security is a public good. Let’s use S to stand for
the number of person-hours of security patrols per week. The marginal benefit of security
patrols to each of the stores is given by the formula MB = 100 – 2S, and the cost of patrols is
$30 per hour. What is the socially efficient level of security? If security is left to the
independent decisions of the stores, what will they choose? How would your answer change
if there were 5 stores?
5. Students receive two types of benefits from standardized test preparation services: first, they
learn useful material; second, they score better on the test relative to other students. Because
relative performance matters, their improved performance creates a negative externality for
other students. Suppose that the market demand function for test preparation services is Qd =
30 – P/2, where Qd is millions of hours of services and P is the price per hour. Suppose also
that the market for these services is competitive and that the market supply function is Qs =
2P – 30. Finally, suppose that the marginal external cost of test preparation is given by MEC
= 5 + 1.5Q. Find the socially efficient level of test preparation, the competitive equilibrium,
and the deadweight loss created by the externality. Draw a figure to illustrate your answer.
6. Consider the same market described in Q. 5 above, but now assume that test preparation
services are monopolized. Also assume that the monopolist’s marginal cost curve coincides
with the market supply curve in the last problem. How does the monopoly output compare
with the socially efficient output? Calculate the deadweight loss of monopoly.
7. Fifty residents of a college dorm all like espresso. An espresso machine costs $1,000. Each
dorm resident is willing to pay up to $50 for the machine. However, the resident’s
willingness to pay is their “private information.” One resident, Eugene, decides to take up a
collection. Assuming there is no way to make other residents contribute (and Eugene does
not know what the residents’ willingness to pay is), is Eugene likely to raise the necessary
$1,000? Why or why not? What could be done to improve his chances of success? [Hint: a
simple argument can be made in the lines of the “non-excludability” nature of a public good.
If one student pays for the coffee maker in the pantry, all will use it! Eugene can do better by
ensuring this does not happen.]