A producer is hiring 20 units of labor and 6 units of capital (bundle A).

HOMEWORK CHAPTER
9

1. A producer is
hiring 20 units of labor and 6 units of capital (bundle A). The price of labor is
$10, the price of capital is $2, and at A,
the marginal products of labor and capital are both equal to 20. Beginning at A, if the producer increases labor by
one unit and decreases capital by 1 unit, then
a. cost remains constant and output
increases by 20 units.
b. cost remains constant and output
decreases by 20 units.
c. output remains constant and cost
increases by $8.
d. output remains constant and cost
decreases by $8.
e. both cost and output remain constant.

2. A producer is
hiring 20 units of labor and 6 units of capital (bundle A). The price of labor is
$10, the price of capital is $2, and at A,
the marginal products of labor and capital are both equal to 20. Beginning at
A, if the producer increases expenditures on labor by $1 and decreases
expenditures on capital by $1, then
a. cost remains constant and output
decreases by 8 units.
b. cost remains constant and output
increases by 12 units.
c. cost remains constant and output
increases by 20 units.
d. output remains constant and cost
increases by $8.
e. output remains constant and cost
decreases by $2.

3. A producer is
hiring 20 units of labor and 6 units of capital (bundle A). The price of labor is
$10, the price of capital is $2, and at A,
the marginal products of labor and capital are both equal to 20. The producer
a. is using the optimal combination of
capital and labor.
b. should use more labor and less capital.

c. should use more capital and less labor.

d. cannot determine without more
information.

4. A producer is
hiring 20 units of labor and 6 units of capital (bundle A). The price of labor is
$10, the price of capital is $2, and at A,
the marginal products of labor and capital are both equal to 20. In
equilibrium,
a. MPL
will be less than 20.
b. MPK
will be more than 20.
c. MPL
will be 5 times MPK.
d. a
and b
e. none of the above

5. Which of the
following is FALSE?
a. A change in input prices shifts the
isoquant map.
b. Convex isoquants mean that the marginal
rate of technical substitution decreases as the firm substitutes labor for
capital.
c. A change in cost shifts the isocost
curve.
d.
At the optimal input choice, the rate at which the firm can
substitute labor for capital in production is equal to the rate at which the
firm can substitute labor for capital in the market.
e. none of the above.

6.
The expansion path shows
a. how input prices change as the firm’s
output level changes.
b. how the marginal products change as the
firm’s output level changes.
c. how the cost-minimizing input choices
change as the firm’s output level changes.
d. how the profit-maximizing input choices
change as the firm’s output level changes.
e. how the cost-minimizing input prices
change as the firm’s output level changes.

Refer to the following figure to answer questions 7-15. The
price of capital is $50 per unit:

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7.
What is the price per unit of labor?
a. $25
b. $20
c. $10
d. $ 2

8.
How many units of labor should the firm use in order to
produce 400 units of output at the least cost?
a. 100

b. 105
c. 110
d. 115

9. The minimum cost
of producing 800 units of output is
a. $
6,000.
b. $
7,500.
c. $
8,000.
d. $10,000.

10. Which of the
following combinations of capital and labor lies on the expansion path?
a. 110K,
120L
b. 60K,
120L

c. 130K,
200L
d. 130K,
175L
11. How many units
of capital should the firm use to produce 800 units of output at least cost?
a. 110
b. 98
c. 108
d. 102
e. 120

12. What is the
minimum cost of producing 400 units of output?
a. $3,000
b. $4,000
c. $5,000
d. $6,000
e. none of the above

13. What is the
minimum cost of producing 1,200 units of output?
a. $7,000
b. $8,000
c. $9,000
d. $10,000
e. $11,000

14. How many units of
labor should the firm use to produce 1,200 units of output at least cost?
a. 120
b. 500
c. 240
d. 128
e. 175

15. What is the
marginal rate of technical substitution at each cost minimizing equilibrium
point?
a. 0.80
b. 0.40
c. 2.50
d. 2.00
e. impossible to tell without marginal
products

16. The marginal
rate of technical substitution is
a. the rate at which the firm can
substitute labor for capital while holding total cost constant.
b. the rate at which the firm can
substitute labor for capital while holding output constant.
c. the slope of the isocost curve.
d. both a and c
e. none of the above

17.
A firm is using 500 units of capital and 200 units of labor
to produce 10,000 units of output.
Capital costs $100 per unit and
labor $20 per unit. The last unit of
capital added 50 units of output, while the last unit of labor added 20 units
of output. The firm
a. is using the cost-minimizing
combination of capital and labor.
b. should
use more of both inputs in equal proportions.
c. should use less of both inputs in equal
proportions.
d. could produce the same level of output
at a lower cost by using more capital and less labor.
e. could produce the same level of output
at a lower cost by using less capital and more labor.

18. Suppose that
when a firm increases output by 50%, long-run total cost increases by less than
50%. The firm will experience
a. diminishing
marginal returns.
b. decreasing
marginal rate of technical substitution.
c. economies of scale
d. diseconomies
of scale

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Refer to
the following graph to answer questions 19-23. The price of labor is $3 per
unit:
19. What is the
price per unit of capital?
a. $1.50
b. $2.00
c. $2.10
d. $5.00

20. How many units
of capital should a firm use in order to produce 300 units of output at the
least cost?
a. 17 units of capital
b. 18 units of capital
c. 19 units of capital
d.
20 units of capital

21. What is the
marginal rate of technical substitution at point B?
a. 0.6
b. 0.75
c. 1
d. 1.7

22. What is the
minimum cost of producing 100 units of output?
a. $150
b. $105
c. $ 75
d. $ 60

23. How many units
of labor should a firm use in order to produce 100 units of output at the least
cost?
a. 5 units of labor
b. 10 units of labor
c. 15 units of labor
d. 20 units of labor
Refer to the
following graph to answer question 24-30. The price of capital (r) is $20.
.0/msohtmlclip1/01/clip_image006.gif”>

24. What is the
price of labor (w)?
a. $20
b. $30
c. $25
d. $35
e. none of the above

25. What combination
of labor (L) and capital (K) can produce 5,000 units of output at
lowest cost?
a. 90K,
60L
b. 110K,
10L
c. 42K,
52L
d. 60K,
20L
e. 10K,
110L

26. What is the
lowest possible cost of producing 5,000 units of output?
a. $1,800
b. $2,400
c. $2,600
d. $1,400
e. $3,000

27. Why wouldn’t the
firm choose to produce 5,000 units of output with the combination at A?
a. At A, MRTS
< 3/2. b. At A, MPK / r > MPL/ w.
c. At A, MPL
> MPK.
d. both
a and b
e. none
of the above

28. Why wouldn’t the
firm choose to produce 5,000 units of output with the combination at B?
a. At B, MRTS
< 3/2. b. At B, MPK / r > MPL/ w.
c. At B, MPL
< MPK. d. both a and b e. none of the above 29. What is the lowest possible cost at which 14,000 units of output can be produced? a. $8,600 b. $2,400 c. $3,600 d. $4,200 e. none of the above 30. What combination of K and L should the firm choose to produce 14,000 units of output at the lowest cost? a. 180K, 120L b. 180K, 0L c. 60K, 120L d. 90K, 60L e. none of the above  

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