Answers to Final Exam (A)
Intermediate Microeconomics
January, 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)
!.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 seller or collected from
the buyers..
Correct Answer: False
2.In an English auction, with rational bidders, the object being sold always goes to the
bidder who values it most highly.
Correct Answer: True
3. If the interest rate is 10%, a monopolist will choose a markup of price over marginal
cost of at least 10%.
Correct Answer: False
4. In a monopolistically competitive industry with zero profits, each firm will produce less
than the amount that minimizes average costs.
Correct Answer: True
5. For a monopsonist, the supply curve of a factor of production is less steep than the
marginal cost curve.
Correct Answer: True
6. A Stackelberg leader will necessarily make at least as much profit as he would if he
acted as a Cournot oligopolist..
Correct Answer: True
7.In the prisoners’ dilemma game, if each prisoner believed that the other prisoner would
deny the crime, then both would deny the crime..
Correct Answer: False
8.Partial equilibrium analysis concerns only supply or only demand while general
equilibrium analysis deals with supply and demand at the same time.
Correct Answer: False
9.There are two people and two goods, person A has comparative advantage in the
production of good 1 if and only if it takes person A less time to produce good 1 than it
takes person B.
Correct Answer: False
10. An example of adverse selection is where someone chooses a car that is not as
good as it is claimed to be.
Correct Answer: False
II. Multiple Choice ( 5 points each)
1.If both supply and demand for a good increase at the same time, which of the following
must also increase?
(a) the equilibrium price
(b) the use of substitutes
(c) the use of complements
(d) the equilibrium quantity
(e) all of the above
Correct Answer: D
2. Suppose that a quantity tax is imposed on the monopolist’s product. If the
monopolist’s marginal cost is horizontal in the relevant range, which of the following
statements must be true?
(a) The price will increase by an amount less than the tax
(b) The price will increase by an amount equal to the tax
(c) The price will increase by an amount greater than the tax
(d) The price may either increase or decrease.
(e) A quantity tax will have no effect on the price-output decision of a monopolist.
Correct Answer: D
3 An antique cabinet is being sold to by means of an English auction. There are four
bidders, Natalie, Heidi, Linda, and Eva. These bidders are unacquainted with each other
and do not collude. Natalie values the cabinet at 1200, Heidi values it at 950, Linda
values it at 1700, and Eva values it at 700. If the bidders bid in their rational self-interest,
the cabinet will be sold to
(a) Linda for about 1700
(b) Natalie for about 1200
(c) either Linda or Natalie for about 1200. Which of these two buyers gets it is randomly
determined.
(d) Linda for slightly more than 1200
(e) either Linda or Natalie for about 950. Which of these two buyers gets it is randomly
determined.
Correct Answer: D
4 If demand in the US is given by Q1  23400  900 p1 , where p1 is the price in the US,
and if the demand in England is given by 2800  200 p2 ,where p2 is the price in England,
then the difference between the price charged in England and the price charged in US
will be
(a) 6
(b) 12
(c) 0
(d) 14
(e) 18
Correct Answer: A
5.There are two firms in the apple industry. The demand curve for apples is given by
p=4500-4q。 Each firm has one manufacture plant and each firm i has a cost function
C (qi )  qi 2 where qi is the output of firm i . The two firms form a cartel and arrange to
split total industry profits equally. Under the cartel arrangement, they will maximize joint
profits if
(a) and only if each firm produces 250 units in its plant
(b) they produce a total of 500 units, no matter which firm produces them
(c) and only if they each produce a total of 562.5 units
(d) they produce a total of 375 units, no matter which firm produces them
(e) they shut down one of the two plants, having the other operate as a monopoly, and
splitting the profits
Correct Answer: A
6 In a two-person, two-good, exchange economy, both consumers have quasilinear
utility functions, linear in Good 2. If quantities of Good 1 are measured horizontally and
quantities of Good 2 are measured vertically in the Edgeworth box, the set of Pareto
optimal allocations includes
() a horizontal line through the interior of the box.
(b) a vertical line.
(c) a straight line from the lower left to the upper right corner of the box.
(d) a curved line from the lower left to the upper right corner of the box.
(e) all four edges of the box.
Correct Answer: B
.
7 Suppose Tip can write 4 pages of term papers or solve 4 workbook problems in an
hour, while Spot can write 2 pages of term papers or solve 4 workbook problems in an
hour. If they each decide to work a total of 6 hours, and to share their output then if they
produce as many pages of term paper as possible given that they produce 20 workbook
problems.
(a) Spot will spend all of his time writing term papers and Tip will spend some time at
each task.
(b) Tip will spend all of his time writing term papers and Spot will spend some time at
each task.
(c) Both students will spend some time at each task.
(d) Spot will write term papers only and Tip will do workbook problems only.
(e) Tip will write term papers only and Spot will do workbook problems only.
Correct Answer: A
8. A parent has two children living in cities with different costs of living. The cost of living
in city B is 4 times the cost of living in city A. The child in city A has an income of 5000
and the child in city B has an income of 20000. The parent wants to give a total of $4000
to her two children. Her utility function is U(CA, CB) = CACB, where CA and CB are the
consumptions of the children living in cities A and B respectively. She will choose to:
(a) give each child 2000, even though this will buy less goods for the child in city B.
(b) give the child in city B 4 times as much money as the child in city B.
(c) Give the child in city A 4 times as much money as the child in city B.
(d) Give the child in city B 2 times as much money as the child in city A.
(e) Give the child in city A 2 times as much money as the child in city B.
Correct Answer: A
9 An apiary is located next to an apple orchard. The apiary produces honey and the
apple orchard produces apples. The cost function of the apiary is
CH ( H , A)  H 2 /100  3 A , and the cost function of the apple orchard is
C A ( H , A)  A2 /100 , where H and A are the number of units of honey and apples
produced respectively. The price of honey is 7 and the price of apples is 1 per unit. Let
A1 be the output of apples if the firms operate independently, and let A2 be the output
of apples if the firms are operated by a profit-maximizing single owner. Then,
(a) A1 =25 and A2 =50
(b) A1  A2  50
(c) A1  100 and A2  50
(d) A1  50 and A2  200
(e) A1  350 and A2  50
Correct Answer: D
10 In Rustbucket, Mi there are 200 used cars for sale, half of them are good and half of
them are lemons. Owners of lemons are willing to sell them for $500. Owners of good
used cars are willing to sell them for prices above $900 but will keep them if the price is
lower than $900. There is a large number of potential buyers who are willing to pay $700
for a lemon and $1,900 for a good car. Buyers can't tell good cars from bad, but original
owners know.
(a) There will be an equilibrium in which all used cars sell for $ 1300.
(b) The only equilibrium is one in which all used cars on the market are lemons and they
sell for 700
(c) There will be an equilibrium in which lemons sell for 500 and good used cars sell for
900.
(d) There will be an equilibrium in which all used cars sell for 700.
(e) There will be an equilibrium in which lemons sell for 700 and good used cars sell for
1,900.
Correct Answer: A
III. Essay
1(total 20 points) In a 2X2 (2 consumers and 2 goods) pure exchange economy, both
consumers’ utility function is of Cobb-Douglas form, u A ( x1A , x A2 )  ( x1A ) a ( x A2 )1 a
and uB ( x1B , xB2 )  ( x1B )b ( xB2 )1b . The initial endowment of player A and B is (1A ,  A2 ) ,and
(1B , B2 ) .
(1) (5’)Try to solve out good 1 and good 2’s aggregate excess demand function
(2) (5’)Show that it satisfies Walras’ Law.
(3) (10’)Find the relative price of two goods in equilibrium.
Answer
(1) z1 ( p1 , p2 )  a
p11A  p2 A2
p 1  p2B2
b 1 B
 1A  B1
p1
p1
z2 ( p1 , p2 )  (1  a)
p11A  p2 A2
p  1 p2B 2 2
 (1  b) 1 B
  A  B2
p2
p2
(2) p1 z1  p2 z2  0
a A2  bB2
(3) p 
(1  a)1A  (1  b)B1
*
1
2 (total 10’). Suppose that the inverse demand function for wool is p = A/q for some
constant A. Suppose that 1/4 of the world's wool is produced in Australia.
a(5’). If Australian wool production increases by 1% and the rest of the world holds its
output constant, what will be the effect on the world price of wool?
b(5’). How is the marginal revenue to Australia from an extra unit of wool relate to the
price of wool?
Answer
a) Price will fall by about one fourth of one percent.
b) Marginal revenue is three fourths of price.