Microeconomics II

Problem set 2
Due on May 14
Note: PS will be graded solely on COMPLETION, and not CORRECTNESS.
Name: __________________
Student ID: ______________

A. Multiple Choices
1. When firms price discriminate they turn ________ into ________.
A) producer surplus, revenue
B) consumer surplus, profit
C) total cost, profit
D) producer surplus, consumer surplus

2. If consumers are identical, then

A) price discrimination is impossible.
B) price discrimination can occur if each consumer has a downward-sloping demand curve
for the product.
C) perfect price discrimination is the only form of price discrimination that can increase a
monopoly's profit.
D) tie-in sales cannot increase a monopoly's profit.

3. For a monopoly, marginal revenue is less than price because

A) the demand for the firm's output is downward sloping.
B) the firm has no supply curve.
C) the firm can sell all of its output at any price.
D) the demand for the firm's output is perfectly elastic.

4. A perfect price discriminator

A) charges each buyer her reservation price.
B) charges different prices to each customer based upon different costs of delivery.
C) generates a deadweight loss to society.
D) charges lower prices to customers who buy greater quantities.

5. One difference between a monopoly and a competitive firm is that

A) only a monopoly is a price taker.
B) only a monopoly maximizes profit by setting marginal revenue equal to marginal cost.
C) only a monopoly faces a downward-sloping demand curve.
D) None of the above.

6. If two identifiable markets differ with respect to their price elasticity of demand and resale
is impossible, a firm with market power will
A) set a higher price in the market that is more price elastic.
B) set a lower price in the market that is more price elastic.
C) set price so as to equate the elasticity of demand across markets.
D) set price equal to marginal cost in both markets.

7. Suppose a profit-maximizing monopoly is able to employ group price discrimination. The

marginal cost of providing the good is constant and the same in both markets. The marginal
revenue the firm earns on the last unit sold in the market with the higher price will be

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A) greater than the marginal revenue the firm earns on the last unit sold in the market with
the higher price.
B) less than the marginal revenue the firm earns on the last unit sold in the market with the
higher price.
C) equal to the marginal revenue the firm earns on the last unit sold in the market with the
higher price.
D) greater than the marginal cost of the last unit.

8. Quantity discrimination makes sense if

A) buyers of smaller quantities are more price sensitive than buyers of larger quantities.
B) buyers of smaller quantities are less price sensitive than buyers of larger quantities.
C) demand for the good is perfectly elastic.
D) the lower price for larger quantities encourages all consumers to purchase the larger
quantity.

9. Two-part pricing offer a mechanism whereby the firm can

A) charge two different prices to distinct groups of customers.
B) collect two times as much from consumers as a single-price monopoly can.
C) capture some or all of the consumer surplus.
D) reduce some of its fixed costs.

10. Suppose all individuals are identical, and their monthly demand for Internet access from a
certain leading provider can be represented as p = 5 - (1/2)q where p is price in $ per hour
and q is hours per month. The firm faces a constant marginal cost of $1. Potential consumer
surplus equals
A) $4.
B) $8.
C) $16.
D) $32.

11. If Ben values good X more than good Y, and Catherine values good Y more than good X,
a firm can increase its profits by
A) charging the same price for both goods.
B) bundling the goods.
C) selling the goods in a competitive market.
D) charging one price per good.

12. A profit-maximizing monopolist will never operate in the portion of the demand curve
with price elasticity equal to
A) -3.
B) -1.
C) -1/3.
D) None of the above—the price elasticity does not matter.

13. A monopolist will spend resources to advertise its product so long as

A) net profits increase.
B) gross profits increase.
C) demand increases.
D) total revenue increases.

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14. Perfect competition and monopolistic competition are similar in that firms in both types
of market structure will
A) act as price takers.
B) produce a level of output where price equals marginal cost.
C) earn zero profit in the long run.
D) act as price setters.

15. Regardless of market structure, all firms

A) consider the actions of rivals.
B) maximize profit by setting marginal revenue equal to marginal cost.
C) produce a differentiated product.
D) have the ability to set price.

16. The more elastic the demand curve, a monopoly

A) will have a larger Lerner Index.
B) will face a lower marginal cost.
C) will earn more profit.
D) will lose more sales as it raises its price.

17. If the inverse demand curve a monopoly faces is p = 100 - 2Q, and MC is constant at 16,
then the deadweight loss from monopoly equals
A) $21.
B) $441.
C) $882.
D) $1,764.

18. The benefits from cartelizing are greater if

A) the market demand elasticity is higher.
B) the market demand elasticity is lower.
C) the market price is higher.
D) each firm cuts its output more.

19. If a Cournot duopolist announced that it will double its output,

A) it becomes the leader.
B) the other firm does not view the announcement as credible.
C) the other firm will shut down.
D) the other firm will double output also.

20. The concept of Nash equilibrium states that

A) no firm can improve their outcome holding the other firm's actions constant.
B) all firms are earning the highest possible profit.
C) firms make alternating output decisions.
D) None of the above

21. Suppose two Cournot duopolist firms operate at zero marginal cost. The market demand
is p = a - bQ. Firm 1's best-response function is
A) q1 = (a - bq2)/2b.
B) q1 = (a - 2bq2)/2b.
C) q1 = a/b.

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D) q1 = a/2b.

22. In a Nash-Cournot equilibrium where firms produce identical products with unequal
costs,
A) the firm with lower costs charges a higher price.
B) the firm with higher costs charges a higher price.
C) the firm with lower costs produces more.
D) the firm with higher costs produces more.

23. In the Stackelberg model, the leader has a first-mover advantage because it
A) has lower costs than the follower.
B) commits to producing a larger quantity.
C) reacts to the follower's decision.
D) differentiates its output.

24. If only two identical firms operate in a market, consumers prefer

A) a Cournot equilibrium.
B) a Stackelberg equilibrium.
C) a collusive equilibrium.
D) any equilibrium, since they all result in the same consumer surplus.

25. As the number of firms increases in a market, the differences between the Cournot,
Stackelberg, and price-taking market structures
A) decrease.
B) increase.
C) remain the same.
D) cannot be determined.

B. Analytical Problems
1. A monopolist faces the inverse demand for its output: p = 30 – Q
The monopolist also has a constant marginal and average cost of $4/unit. The government is
seeking ways to collect tax revenue from the monopolist and faces two proposals:
i. Impose a specific tax of t on the monopolist.
ii. Impose an ad valorem tax of a on the monopolist.
a. Suppose the government imposes a 20% ad valorem tax on the monopolist. What
price and quantity does the monopolist choose and how much revenue does the
government generate from the tax?
b. Rather than an ad valorem tax, what is the government's revenue from a specific tax
of t imposed on the monopolist? Your answer should be in terms of t.
c. Show that a specific tax of $3.70/unit generates the same revenue as a 20% ad
valorem tax (approximately).

2. Suppose Jerry sells gasoline, which have the following demand: pJ = 170 – 3qJ – qE, where
pJ is the price of Jerry's gasoline and qJ is the number of gasoline Jerry sells. qE is the number
of gasoline James's rival, Ethan, sells. Ethan's demand is given by: pE = 170 – 3qE – qJ,
where pE is the price Ethan can sell his gasoline for. Suppose each seller has a cost per unit
(average and marginal) of $20.
a. How does this game differ from the Cournot model with same products? Why do the
demand curves point that the goods are differentiated – not perfect substitutes for one

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 another?
b. Derive the best response functions for Jerry and Ethan and compute the Nash
Equilibrium outputs and prices for Jerry and Ethan.
c. Suppose the two firms merge. By doing so, the newly merged firm will maximize the
joint profits ((qA,qB) = A(qA,qB) + B(qA,qB)). Find the joint-profit maximizing quantities
and price.
d. Are the combined profits greater or smaller with the firms merging? (compute total
profits before merging and after merging)
e. Are consumers better or worse off with the firms merging? (briefly explain)

3. Suppose the demand for pizza in a small isolated town is p = 10 - Q. There are only two
firms, A and B. Each has a cost function TC = 2 + Q.
a. Determine the equilibrium quantities of each if firm A is the Stackelberg leader.
b. If the government wants to subsidize firm A to raise its output to that of a Stackelberg
leader, how large should the subsidy be?

C. Short Answer Problems

1. Draw a graph that shows the effect on the equilibrium quantities if the government
subsidizes one firm in a Cournot duopoly with a per-unit subsidy. Assume that the best-
response functions are linear. Explain the new equilibrium quantities.

2. Consumers of laundry detergent view brands as different and so each brand effectively has
some market power. Prices are set much higher than marginal cost, yet detergent firms earn a
normal rate of return. Use a diagram with demand for the output of a single firm, marginal
cost and average cost curves to show a monopolistically competitive firm in equilibrium.