Econ 301
Homework #3
1)
due by June 16, 04
Efficient production occurs if a firm
(a)
cannot produce its current level of output with fewer inputs.
(b)
given the quantity of inputs, cannot produce more output.
(c)
maximizes profit.
(d)
All of the above.
Answer: d
2)
Which of the following statements best describes a production function?
(a)
the maximum profit generated from given levels of inputs
(b)
the maximum level of output generated from given levels of inputs
(c)
all levels of output that can be generated from given levels of inputs
(d)
all levels of inputs that could produce a given level of output
Answer: b
Labor
1
2
3
4
5
Output
10
18
24
28
30
Table 6.1
3)
Table 6.1 shows the short-run production function for Albert’s Pretzels. The marginal
productivity of labor
(a)
rises then falls as the amount of labor increases.
(b)
falls then rises as the amount of labor increases.
(c)
is greater than or equal to the average productivity of labor for all amounts of labor.
(d)
is less than or equal to the average productivity of labor for all amounts of labor.
Answer: d
4)
Table 6.1 shows the short-run production function for Albert’s Pretzels. The law of
diminishing marginal productivity
(a)
appears with the second worker.
(b)
has not yet appeared for any of the levels of labor.
(c)
first appears with the fifth worker.
(d)
is refuted by this evidence.
Answer: a
5)
Average productivity will fall as long as
(a)
(b)
(c)
(d)
marginal productivity is falling.
it exceeds marginal productivity.
it is less than marginal productivity.
the number of workers is increasing.
Answer: b
Figure 6.2
6)
The table in Figure 6.2 shows the levels of output resulting from different levels of inputs.
Which of the following conclusions can be drawn from this information?
(a)
Increasing returns to scale exist when 100 units of output are produced.
(b)
Constant returns to scale exist throughout all levels of production.
(c)
Labor is subject to diminishing marginal productivity in the short run.
(d)
No firm conclusions can be drawn.
Answer: a
7)
The table in Figure 6.2 shows the levels of output resulting from different levels of inputs.
Returns to scale are greatest at which level of output?
(a)
100–200 units
(b)
200–400 units
(c)
400–600 units
(d)
There is insufficient information to answer the question.
Answer: a
8)
The table in Figure 6.2 shows the levels of output resulting from different levels of inputs.
At which level of input are there constant returns to scale?
(a)
400–600 units
(b)
Constant returns to scale exist throughout all levels of production.
(c)
Constant returns to scale do not exist at any level of production.
(d)
No firm conclusions can be drawn.
Answer: a
Q: Total Output
*
*
C
B
A
Labor
Figure 6.3
9)
Between points A and B, the total product curve in Figure above exhibits
(a)
Increasing marginal returns to labor.
(b)
Decreasing marginal returns to labor. Capital and labor can be substituted for one
another.
(c)
An increasing marginal rate of substitution.
(d)
A decreasing marginal rate of substitution.
Answer: a
10)
Between points A and B, the total product curve in Figure above exhibits
(a)
Increasing returns to scale.
(b)
Constant returns to scale.
(c)
Decreasing return to scale.
(d)
None of the above.
Answer: d
11)
At point C,
(a)
The marginal product of labor is greater than the average product of labor.
(b)
The marginal product of labor is less than the average product of labor.
(c)
The marginal product of labor equals the average product of labor.
(d)
One cannot determine whether the marginal product of labor is greater than, less
than, or equal to the average product of labor.
Answer: b
Skilled labor
3
2
*A
* B
q=50
9
11
unskilled labor
Figure 6.4
12)
Moving downward along the isoquant in Figure 6.4,
(a)
Skilled labor and unskilled labor are perfect substitutes.
(b)
The marginal rate of technical substitution between skilled labor and unsikilled
labor is diminishing.
(c)
The ratio of the marginal product of unskilled labor to the marginal product of
skilled labor is falling.
(d)
Both b and c.
Answer: d
13)
As we move from point A to point B in Figure 6.4, if the marginal product of skilled labor
is 1, then the marginal product of unskilled labor
(a)
Is ½.
(b)
Is also 1.
(c)
Is 2.
(d)
Cannot be determined.
Answer: a
Calculation:
14)
Calculate the average product of labor and the marginal product of labor.
Labor
0
2
4
6
8
10
15)
Total Product
0
7
27
42
49
47
MPL
3.5
10
7.5
3.5
-1
The product function is q  50 L0.4 K 0.6 . Find the isoquant q=50, and find the marginal rate
of technical substitution (MRTS) on that isoquant curve when L=1.
Answer: K 
1
3
L2
MRTS=2k/3L=2/3
above isoquant curve.
16)
APL
0
3.5
6.75
7
6.125
4.7
because when q=50, and L=1, k is equal to 1 from the
The table below gives production relationships for the production of Dr. Cure-All’s tablets.
Draw isoquants based on this information. What are the returns to scale? Does the table
exhibit the law of diminishing marginal products?
Capital
1
2
3
4
5
L 1
13
17
20
22
23
A 2
20
23
26
28
29
B 3
24
28
31
33
34
O 4
28
32
35
37
38
R 5
23
28
32
36
39
Answer: Decreasing return to scale. From (1,1) to (2,2), inputs have been doubled, while the
output is less than doubled output. By same reasoning, decreasing return to scale appears
for other combinations of inputs, for example, from (2,2) to (3,3), from (3,3) to (4,4) and
from (4,4) to (5,5).
17)
Mike regards Gatoraid and Crocaid as perfect substitutes. Assume that he has $10 per
month to spend on sports drinks and that the price of a bottle of Gatoraid is $.60, while the
price of a bottle of Crocaid is initially $.70.
a. Draw a graph showing his budget line and how it changes as the price of Crocaid falls
from $.70 to $.60 to $.50 to $.40. Mark the consumption bundles that Mike chooses.
b. Draw a second graph showing the demand curve for Crocaid.
c. Explain which part of the increase in consumption is due to the income effect and which
part is due to the substitution effect.
Answer: When price of Crocaid falls from $.70 to $.60, the slope of budget line is
equal to the one of isoquant, so consumers will buy any combination of two goods on
that budget line. There is only substitution effect.
If price falls from $.60 to $.50, budget line will rotate outward and
consumer will use all his money to buy Crocaid, and 0 of Gatoraid. If we draw a
budget line parallel to the new one while intersect the previous isoquant at the same
point, we can see the substitution effect is 0, and the total effect is equal to income
effect.
Note: It is quite inconvenient to draw graph by using Microsoft word, so I ignore the
graph here. If you have any question, please feel free to ask me.
18)
What is the production function if L and K are perfect substitutes and each unit of q
requires 1 unit of L or 1 unit of K. (or a combination of these inputs that adds up to 1)?
Answer: q=K+L