Economics
PART ONE. (3 points each, 30 points total) Please answer the following question in
the space provided with no more than a few sentences. Please note that without an
explanation you will not get full credit.
1. Suppose that market demand is given by = 60 − . The two identical firms in
the market both have zero marginal cost. Draw the reaction curves on a graph and
find the Cournot equilibrium price and quantities.
2. In a Stackleberg Model, is it more advantageous to be the leader and announce
your output decision first, or to be the follower and react to the leader’s
announcement? In what situations is this model more realistic than the Cournot
model?
3. Explain the concept of price rigidity in an oligopoly. Why might an oligopolist be
wary of raising its prices?
4. Consider the following payoff matrix for two firms competing on prices. Explain
why both firms might choose to sell at the low price, even though they earn higher
profits when they both sell at the high price.
Firm 1
Low Price
High Price
Firm 2
Low Price
$10, $10
$5, $25
High Price
$25, $5
$20, $20
5. Explain how asymmetric information in the insurance market can result in moral
hazard.
6. Give an example of a technique that a company can use to signal the quality of
their product. Explain how it is an effective signal of quality.
7. Explain the difference between regulating emissions via fees vs. standards. Which
of the two would a government employ if it cares more about certainty with
regards to emissions levels than certainty about the cost of abatement.
8. Suppose that fishermen have unlimited access to a pond of fish. The market for
fish is competitive, so fishermen take the price as given (face horizontal
individual demand). The fishermen face a private marginal cost, but do not
consider the additional cost of depleting the stock of fish in the pond. Graph the
demand, private cost, and marginal social cost for fish from this pond, showing
the efficient quantity, the actual quantity, and the social cost of common access.
9. Define and explain the difference between the terms “nonrival” and
“nonexclusive.” Which of these properties is likely to result in a free-rider
problem?
10. A local government is considering building new public hiking trails in the town.
Suppose that the trails are public goods. There are two types of people in the
economy, hikers and non-hikers, who face different (aggregate) marginal benefit
curves: = 50 − 10 and = 15 − 5 for the hikers and the non-hikers
respectively, where Q is the miles of trails. On the same graph. draw the marginal
benefit curves for each type of person and the overall economy.
PART TWO. (10 points each, 50 points total) Answer the following problems in the
space provided. Please show your work in an organized way with clearly labeled
graphs should if you choose to use any.
11. Suppose there is a duopoly of two identical firms, A and B, facing a market
demand of = 40 − , and cost functions of = 4 and = 4
respectively.
a. Find the Cournot-Nash equilibrium and profit for each firm.
b. Suppose that A acts as the leader in a Stackleberg model and B responds.
What are the respective prices, quantities and profits of each firm now?
c. What are the prices, quantities and profits for the firms if they decide to
collude and share profits equally?
d. Graph and label the reaction curves for the two firms and the collusion
curve on the same graph. Identify the equilibria from parts a-c.
12. Two firms with differentiated products are competing in price. Firm A and B face
the following demand curves: = 280 − 2 + and = 140 − 2 +
respectively. Both firms have zero marginal costs, but face a fixed cost of 20.
a. Give equations for and graph each firm’s reaction curve.
b. If both firms set their prices at the same time, what is the Nash equilibrium
price and quantity for each firm? What is the profit?
c. Suppose A sets its price first and then B responds. What price and quantity
does each firm set now?
d. Compare the profits from part b and c. Which firm benefits more from the
sequential price choosing?
13. A bank has $500 to lend and is choosing whether to lend to a safe borrower or a
risky borrower. If it lends to the safe borrower, the bank will be paid back the full
amount plus 6% interest for sure. If it lends to the risky borrower, there is an 80%
chance that it is paid back in full plus 25% interest, and a 20% chance that the
borrower defaults on the loan (doesn’t pay anything back).
a. Which borrower would the bank prefer to loan to? Calculate the expected
profits in each case.
b. Suppose the bank knows that if the risky borrower defaults, there will be a
partial government bailout, where the government pays back $300 of the
original $500 loan. Now which borrower will the bank choose, and what is
the expected profit? What is the expected cost for the government?
c. Now consider the case that the bank thinks there is a possibility of a
government bailout (like in part b), but isn’t sure. What probability of
bailout does there have to be in order for the bank to want to make risky
loans?
d. Which market failure concept is exhibited here?
14. Suppose that the market for a certain good has a demand of = 100 − . The
aggregate private marginal cost for the firms that produce the good faces is =
2 + 10. However, production of the good also creates pollution with a marginal
external cost of = 2.
a. If this is a perfectly competitive market with no regulation, what is the
equilibrium price and quantity produced?
b. Suppose instead that the market is a monopoly. Calculate the profitmaximizing price and quantity.
c. Determine the socially efficient price and quantity for the good.
d. Calculate the socially optimal per-unit tax to levy on the competitive firm
and the monopolist respectively to make them produce at the socially
efficient level.
15. Suppose a housing community includes 10 identical households. It is costly to
maintain the sidewalks in the community, but sidewalks are a public good.
Suppose each household faces an individual demand of = 50 − 2 for each
block. The cost of maintaining sidewalks is given by = 100.
a. If the residents have to pay to maintain their own sidewalks, how many
blocks of sidewalk will each household choose to maintain on their own?
b. What is the socially efficient amount of sidewalk for the community as a
whole?
c. Suppose the community were able to charge a flat fee to the households to
fund the maintenance of the sidewalks. How much should this fee be per
household and what is the total cost of maintaining the socially efficient
amount of sidewalks?
d. Draw the individual marginal benefit curves, overall marginal benefit and
the marginal cost curve. Identify and calculate the total social benefit of
the public good.