Answers to Final Exam (B)
Intermediate Microeconomics
January 13, 2009
You have 2 hours to solve the exam set. The whole exam set is worth 100 points:
(1)Notice how many points each question is worth and allocate your time appropriately.
(2)To get full credit on answers, you must be clear and rigorous: Define your variables,
thoroughly label any graph, and interpret your graph or math in words.
I. True-False (2 points each)
1. If the supply is perfectly elastic, then an upward shift of the demand curve will lead to a
higher price and quantity in equilibrium.
Correct Answer: False
2. Supply and demand theory shows us that the burden of a sales tax is shared equally
by suppliers and demanders whether the tax is collected from the sellers or collected
from the buyers.
Correct Answer: False
3. In a private-values auction with rational bidders, we can expect the same outcome
from an English auction as from a Vickrey auction.
Correct Answer: True
4. If a quantity tax is collected from competitive suppliers of good, placing a tax on the
good causes the price paid by consumers to increase more than if the tax had been
collected directly from buyers
Correct Answer: False
5. A monopolist who is able to practice third degree price discrimination charges a higher
price in the market that is more elastic.
Correct Answer: False
6. In the Cournot model, each firm chooses its actions on the assumption that its rivals
will react by changing their quantities in such a way as to maximize their own profits.
Correct Answer: False
7 In the Bertrand model of duopoly, each firm sets its price, believing that the other's
price will not change. When both firms have identical production functions and produce
with constant returns to scale, the Bertrand equilibrium price is equal to marginal cost.
Correct Answer: True
7.
8. A life insurance company must be concerned about the possibility that the people who
buy life insurance may tend to be less healthy than those who do not. This is an example
of adverse selection.
Correct Answer: True
9. A natural monopoly occurs when a firm gains ownership of the entire stock of some
natural resource and thus is able to exclude other producers.
Correct Answer: False
10. Price equals marginal cost is a sufficient condition for profit maximization.
Correct Answer: False
II. Multiple Choice (5 points each)
1. Daily demand for gasoline at Billy-Bob's Mobile Station is described by Q = 776 -200p
where Q are gallons of gasoline sold and p is the price in dollars. Billy-Bob's supply is Q
= 890 + 1500p. Suppose the state government places a tax of 20 cents on every gallon
of gasoline sold. What is the deadweight loss resulting from this tax?
(a) 3.53 dollars.
(b) 3.11 dollars.
(c) 0.42 dollars.
(d) 96.12 dollars.
(e) 34.59 dollars.
Correct Answer: A
2. A profit-maximizing monopolist faces the demand curve, q = 100–3p. It produces at a
constant marginal cost of $20 per unit. A quantity tax of $10 per unit is imposed on the
monopolist's product. The price of the monopolist's product:
(a) rises by $5.
(b) rises by $10.
(c) rises by $20.
(d) rises by $12.
(e) stays constant.
Correct Answer: A
3. A profit-maximizing monopolist sets:
(a) price equal to average cost.
(b) price equal to marginal cost.
(c) price equal to marginal cost plus a pro-rated share of overhead.
(d) price equal to marginal revenue.
(e) marginal revenue equal to marginal cost.
Correct Answer: E
4. A monopolist has the total cost function, c(q) = 1300+ 7q. The inverse demand
function is 110 – 2q; where prices and costs are measured in dollars. If the firm is
required by law to meet demand at a price equal to its marginal cost:
(a) the firm's profits will be zero.
(b) the firm will lose $650.
(c) the firm will make positive profit, but not as much profit as it would make if it were
allowed to choose its own price.
(d) the firm will lose $1,300
(e) the firm will lose $780
Correct Answer: D
5. A price-discriminating monopolist sells in two separate markets such that goods sold
in one market are never resold in the other. It charges p1 = 3 in one market and p 2 = 7 in
the other market. At these prices, the price elasticity in the first market is -2.50 and the
price elasticity in the second market is -0.80. Which of the following actions is sure to
raise the monopolists profits?
(a) Lower p 2 .
(b) Raise p 2 .
(c) Raise p1 and lower p 2 .
(e) Raise p 2 and lower p1 .
(d) Raise both p1 and p 2 .
Correct Answer: B
6. Suppose that the market demand curve for bean sprouts is given by P = 3580 - 5Q;
where P is the price and Q is total industry output. Suppose that the industry has two
firms, a Stackleberg leader and a follower. Each firm has a constant marginal cost of $80
per unit of output. In equilibrium, total output by the two firms will be:
(a) 350.
(b) 175.
(c) 525.
(d) 700.
(e) 87.50.
Correct Answer: C
7. According to the First Theorem of Welfare Economics:
(a) Every competitive equilibrium is fair.
(b) If the economy is in a competitive equilibrium, there is no way to make anyone better
off.
(c) A competitive equilibrium always exists.
(d) At a Pareto optimum, all consumers must be equally wealthy.
(e) None of the above.
Correct Answer: E
8. Robinson Crusoe's preferences over coconut consumption, C; and leisure, R; are
represented by the utility function, U(C,R) = CR. There are 48 hours available for
Robinson to allocate between labor and leisure. If he works L hours, he will produce the
square root of L coconuts. He will choose to work:
(a) 8 hours.
(b) 12 hours.
(c) 16 hours.
(d) 20 hours.
(e) 24 hours.
Correct Answer: C
9. A clothing store and a jeweler are located side by side in a shopping mall. If the
clothing store spend C dollars on advertising and the jeweler spends J dollars on
advertising, then the profits of the clothing store will be (30+ J)C – 2C2 and the profits of
the jeweler will be ( 72 + C)J – 2J2. The clothing store gets to choose his amount of
advertising first, knowing that the jeweler will find out how much the clothing store
advertised before deciding how much to spend. The amount spent by the clothing store
will be:
(a) 22.
(b) 44.
(c) 66.
(d) 11.
(e) 33.
Correct Answer: A
10. If the number of persons who attend the club meeting this week is X; then the
number of people who will attend next week is 120+0.20X. What is a long run equilibrium
attendance for this club?
(a) 120
(b) 600
(c) 240
(d) 150
(e) 30
Correct Answer: D
III. Essay
1 (total 15’). Two firms in a grimy Ohio town produce the same product in a competitive
industry. Each has an old factory using an old technology. It still pays to operate these
factories but it would not pay to expand them. The only variable factor used by either firm
is labor. Each firm pollutes the other and thus reduces the output of the other firm. The
production functions of firms A and B respectively are Qa  L0a.5  (2 3)Qb and
Qb  L0b.5  (1 3)Qa where L0a.5 and L0b.5 are the square roots respectively of the amount
of labor used by firms A and B. The wage rate of labor is 1 and the price of the firms'
output is 12.
a (5’). If the two firms each maximize profits independently, what is there total output and
how much quasi-rents do their factories earn?
b (10’). If someone buys them both and maximizes joint profits, how much quasi-rents
are earned in total?
Answer: a) Each produces 48 and quasi-rents are 12 for each.
b) Each produces 36 and quasi-rents total 40.
2 (15’). An economy has 2000 people. 1000 of them have utility functions U(x, y) = x+y
and 1000 of them have utility functions U(x, y) = min{2x, y}. Everybody has an initial
allocation of 1 unit of x and 1 unit of y. Find the competitive equilibrium prices and
consumptions for each type of person.
Answer: Prices are 1 and 1. The first type of person will consume 2/3 units of y and 4/3
units of x and the second type of person will consume 4/3 units of y and 2/3 units of x.