Download Final Exam I Intermediate Microeconomics Fall 2005 I. True

Final Exam I
Intermediate Microeconomics
Fall 2005
I. True-False (2 points each)
1. Mr. Surly consumes only two goods and hates them both. His utility function is
U x, y    max x, y . Mr. Surly has (weakly) convex preferences.
2. Donald's utility function is U(x, y) = x+ y 1 2 . Currently he is buying some of both
goods. If his income rises and prices don't change, he will buy more of both goods.
3. If a good is an inferior good, then an increase in its price will increase the demand for
it.
4. If the demand function is q = 3m/p; where m is income and p is price, then the absolute
value of the price elasticity of demand decreases as price increases.
5. 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.
6. If a profit-maximizing competitive firm has constant returns to scale, then its long run
profits must be zero.
7. 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.
8. If allocation x is a competitive equilibrium at prices p and if everybody likes his
bundle in allocation y better than his bundle in allocation x; then the total value of
allocation y at prices p exceeds the total value of allocation x at prices p.
9. If a pure public good is provided by voluntary contributions, economic theory predicts
that in general too little will be supplied.
10．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.
II. Multiple Choice (2.5 points each)
1. Ambrose has indifference curves with the equation x 2 = constant - 4 x11 2 where larger
constants correspond to higher indifference curves. If good 1 is drawn on the horizontal
axis and good 2 on the vertical axis, what is the slope of Ambrose's indifference curve
when his consumption bundle is (9, 14)?
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(a) -9/14
(c) -0.67
(e) -3
(b) -14/9
(d) -17
2. 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 $300. 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 $500
for a lemon and $1,500 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 $ 1,000.
(b) The only equilibrium is one in which all used cars on the market are lemons and they
sell for 500.
(c) There will be an equilibrium in which lemons sell for 300 and good used cars sell for
900.
(d) There will be an equilibrium in which all used cars sell for 600.
(e) There will be an equilibrium in which lemons sell for 500 and good used cars sell for
1,500.
3. Suppose that Paul and David have utility functions U = 2AP +OP and U = AD + 3OD;
respectively, where AP and OP are Paul's consumptions of apples and oranges and AD and
OD are David's consumptions of apples and oranges. The total supply of apples and
oranges to be divided between them is 18 apples and 20 oranges. The "fair" allocations
consist of all allocations satisfying the following conditions.
(a) AD = AP and OD = OP .
(b) 4AP + 2OP is at least 56 and 2AD+ 6OD is at least 78.
(c) 2AP + OP is at least 56 and 2AD+ 3OD is at least 78
(d) Ap+6Op is at least 19 and AD+ OD is at least 19.
(e) 2Ap+ Op is at least AD+ 3OD and AD+ 3OD is at least 2Ap+ Op .
4. When the price of bananas is 50 cents a pound, the total demand is 100 pounds. If the
price elasticity of demand for bananas is -2; what quantity would be demanded if the
price rose to 60 cents a pound?
(a) 50
(b) 90
(c) 60
(d) 80
(e) 70
5. If the marginal cost of making a photocopy is 2 cents and the elasticity of demand is
2.00, the profit maximizing price is
(a) 3 cents.
(b) 3.33 cents.
(c) 4 cents.
(d) 5 cents.
(e) 6 cents.
6. The demand function for corn is q = 200 - p and the supply function is q = 50+0.5p.
The government sets the price of corn at 150 and agrees to purchase and destroy any
excess supply of corn at that price. How much money does it cost the government to buy
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this corn?
(a) 11,250
(c) 7,500
(e) 14,500
(b) 18,750
(d) 10,750
7. The production function is f ( x1 , x2 )  x11 2 x12 2 . If the price of factor 1 is 8 and the
price of factor 2 is 4, in what proportions should the firm use factors 1 and 2 if it wants to
maximize profits?
(a) x1  x2
(b) x1  2x2
(c) x1  0.5x2
(d) We can't tell without knowing the price of output.
(e) x1  4x2
8. If the short run marginal cost of producing a good is $20 for the first 200 units and $30
for each additional unit beyond 200, then in the short run, if the market price of output is
29, a profit maximizing firm will:
(a) produce a level of output where marginal revenue equals marginal cost.
(b) produce as much output as possible since there are constant returns to scale.
(c) produce up to the point where average cost equals 29.
(d) not produce at all, since marginal cost is increasing.
(e) produce exactly 200 units.
9. Mr. Dent Carr's total costs are 2 s 2 + 75s + 100. If he repairs 25 cars, his average
variable costs will be:
(a) 125.
(b) 129.
(c) 175.
(d) 250.
(e) 87.50.
10. A competitive firm is choosing an output level to maximize its profits in the short run.
Which of the following is not necessarily true? (Assume that marginal cost is not constant
and is well-defined at all levels of output.)
(a) Marginal cost is at least as large as average variable cost.
(b) Total revenues are at least as large as total costs.
(c) Price is at least as large as average variable cost.
(d) Price equals marginal cost.
(e) The marginal cost curve is rising.
11. A firm has the long run cost function C(q) = 7 q 2 + 112. In the long run, it will
supply a positive amount of output, so long as the price is greater than:
(a) 112
(b) 120
(c) 28
(d) 56
(e) 61
12. The bicycle industry is made up of 100 firms with the long run cost curve
c(y) = 2+( y 2 /2) and 80 firms with the long run cost curve c(y) = y 2 /6. No new firms can
enter the industry. What is the long run industry supply curve at prices greater than 2?
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(a) y = 360p
(c) y = 170p
(e) y = 375p
(b) y = 340p
(d) y = 240p
13. The cheese business in Lake Fon-du-lac, Wisconsin is a competitive industry. All
cheese manufacturers have the cost function C = Q 2 + 9; while demand for cheese in the
town is given by Q d = 120 - P. The long run equilibrium number of firms in this industry
is
(a) 19
(b) 38
(c) 34
(d) 120
(e) 39
14. A monopolist faces the inverse demand function described by p = 32 - 5q where q is
output. The monopolist has no fixed cost and his marginal cost is 7 at all levels of output.
Which of the following expresses the monopolist's profits as a function of his output?
(a) 32 - 5q - 7
(b) 32 - 10q
2
(c) 25q - 5 q
(d) 32q - 5 q 2 - 7
(e) None of the above.
15. 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 .
(d) Raise both p1 and p 2 .
(e) Raise p 2 and lower p1 .
16. The labor supply curve faced by a large firm in a small city is given by w = 40+0.05L
where L is the number of units of labor per week hired by the large firm and w is the
weekly wage rate that it pays. If the firm is currently hiring 1000 units of labor per week,
then the marginal cost of a unit of labor to the firm is:
(a) equal to the wage rate.
(b) is twice the wage rate.
(c) equals the wage rate plus 100.
(d) equals the wage rate plus 50.
(e) equals the wage rate plus 150.
17. An industry has two firms. The inverse demand function for this industry is
p = 92 - 2 q . Both firms produce at a constant unit cost of $32 per unit. What is the
Cournot equilibrium price for this industry?
(a) 32
(b) 34
(c) 52
(d) 26
(e) None of the above.
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18. Suppose that the market demand curve for bean sprouts is given by P = 3, 580-5Q;
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.
19. 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.
20. 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 - 2 C 2 and the profits of
the jeweler will be ( 72 + C)J - 2 J 2 . 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.
III. Essay
1(10 points). A competitive firm has a production function described as follows. "Weekly
output is the square root of the minimum of the number of units of capital and the number
of units of labor employed per week." Suppose that in the short run this firm must use 16
units of capital but can vary its amount of labor freely.
a)Write down a formula that describes the marginal product of labor in the short run as a
function of the amount of labor used. (Be careful at the boundaries.)
b) If the wage is w = 1 and the price of output is p = 4; how much labor will the firm
demand in the short run?
c) What if w = 1 and p = 10?
d) Write down an equation for the firm's short run demand for labor as function of w and
p.
2 (10 points). Two firms produce a homogenous product. Let p denote the product’s price.
The output level of firm 1 is denoted by q1; and the output level of firm 2 by q2: The
aggregate industry output is denoted by Q; Q = q1 +q2: The aggregate industry (inverse)
demand is given by p = a - bQ: The cost functions of the two firms are c1 (q1) = q12 and
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c2 (q2) = q2 2:
(a) Suppose that firm 1 is a Stackelberg leader in choosing its quantity (i.e., firm 1
chooses it’s quantity first, knowing that firm 2 will observe firm 1’s quantity when it
chooses its own output.) How much output will each firm produce in equilibrium?
(b) Now assume that the firms choose their output levels simultaneously (i.e., we have
Cournot competition). What are the equilibrium output levels in this case?
(c) Now suppose the firms collude and agree to share total profits equally. What is the
optimal total industry output?
3 (10 points). 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.
1/ 2
The production functions of firms A and B respectively are Qa  La  (2 3)Qb and
and Lb
are the square roots respectively of the
Qb  Lb  (1 3)Qa where La
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) If the two firms each maximize profits independently, what is their total output and
how much are their profits?
b) If someone buys them both and maximizes joint profits, what are the outputs and
profit?
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Ⅰ.True-False Answer：1. True 2. False
6. True 7. False 8. True 9. True
3. False
10. True
4. False
Ⅱ.Multiple Choice Answer：1.C 2.A 3.B
4.C 5.C
9.A 10.B 11.D
12.B 13.B 14.C
15.B 16.D
20.A
6.A
17.C
5. False
7.C 8.E
18.C 19.E
Ⅲ.Essay
1. Answer: a) MP = 1/(2 L1 2 ) if L < 16; MP = 0 if L > 16. b) 4 ;c) 16; d) L = ( p 2w) 2 .
2. Answer: a)
,
b)
c)
and
3. Answer: a) Each produces 48 and quasi-rents are 12 for each.
b) Each produces 36 and quasi-rents total 40.
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