Principles of Microeconomics
|
Economics 111
|
Mr. Beck
|
SUNY College at Oneonta
|
Chapter 8 Solutions
Homepage
1. Marginal physical product (MPP) represents the
change
in quantity resulting from additional labor. Since quantity is increasing,
marginal physical product is positive. However, since quantity (Q)
is increasing at a decreasing rate, marginal physical product is
decreasing. A positive but decreasing marginal physical product is referred
to as diminishing marginal returns.
The correct answer is choice b.
Return to Question
1
2. From point A to B, total output (quantity) is increasing
at an increasing rate. This is illustrated by the fact that the
total physical product (TPP) curve is getting steeper between points A
and B. Since marginal physical product (MPP) represents the change
in quantity resulting from additional labor, marginal physical product
is not just positive, but it is also increasing. Therefore, movements from
point A to B represent increasing marginal returns to labor and the correct
choice is a.
Return to Question
2
3. Marginal returns refers to the change in
quantity resulting from hiring additional labor. Negative marginal returns
means that the change in quantity is negative; that is, quantity is decreasing.
Although quantity produced may decrease, overall quantity itself can never
be negative. The correct answer is e,
quantity
(Q) is positive and decreasing.
Return to Question
3
4. Marginal returns refers to the change in
quantity resulting from hiring additional labor. Diminishing marginal returns
begins when the marginal physical product (MPP) of labor begins to decrease.
We can determine this by adding a 3rd column in our table to represent
the change in quantity resulting from adding each additional laborer. The
3rd column, derived by taking each number in column 2 (quantity) and subtracting
the number in the previous row so as to determine the change in quantity,
illustrates that marginal physical product (MPP) of labor begins to decrease
with the addition of the 3rd
unit of labor (from 9 to 8). The correct answer is choice c.
(Note that marginal physical product only begins with the 1st worker. There
is no value for MPP for 0 labor because MPP only records the change in
quantity produced as additional labor is added.)
|
Labor (L)
|
Quantity Produced (Q)
|
Marginal Physical Product (MPP) |
|
0
|
0
|
|
|
1
|
6
|
6 - 0 = 6 |
|
2
|
15
|
15 - 6 = 9 |
|
3
|
23
|
23 - 15 = 8 |
|
4
|
27
|
27 - 23 = 4 |
|
5
|
25
|
25 - 27 = -2 |
Return to Question
4
5. From point A to B, total output (quantity) is
increasing at a decreasing rate. This is illustrated by the fact
that the total physical product (TPP) curve is positively sloped, but getting
flatter between points A and B. Since marginal physical product (MPP) represents
the change in quantity resulting from additional labor, marginal
physical product is positive but decreasing. Therefore, movements
from point A to B represent diminishing marginal returns to labor and the
correct choice is b.
Return to Question
5
6. Between points A and B the graph illustrates that
marginal physical product (MPP) is positive but decreasing. Since marginal
physical product (MPP) represents the change in quantity resulting
from additional labor, quantity is increasing (the marginal value,
the change, is positive), but quantity is increasing
at a decreasing rate (the marginal value,
the amount of increase, is becoming smaller). The correct choice is b.
Return to Question
6
7. This is the situation illustrated in question
2 and is shown by the fact that the total physical product (TPP) curve
is getting steeper. Since marginal physical product (MPP) represents the
change
in quantity resulting from additional labor, marginal physical product
is not just positive, but it is also increasing.
Therefore, this represents increasing marginal returns
and the correct choice is d.
Return to Question
7
8. From the formula sheet: Marginal Cost (MC) = PL/MPP
(MC is inversely (oppositely) related to MPP because PL
is
assumed to be a constant.) Therefore, if marginal cost is increasing then
marginal physical product (MPP) is decreasing.
However, since additional units of quantity are being produced, marginal
physical product (which represents the change in quantity) must be positive.
The correct choice is c.
Return to Question
8
9. Between points A and B the graph illustrates that
marginal physical product (MPP) is positive and increasing. Since marginal
physical product (MPP) represents the change in quantity resulting
from additional labor, quantity is not only increasing (the marginal value,
the change, is positive), but quantity is increasing
at an increasing rate (the marginal value,
the amount of increase, is getting larger). The correct choice is a.
Return to Question
9
10. Marginal Revenue Product is MPP x Price
of output produced. We can derive the marginal revenue product (MRP) of
the 3rd worker by calculating the 3rd worker's marginal physical product
and multiplying that value by $15.
Marginal physical product (MPP) represents the
change
in quantity resulting from additional labor. By hiring the 3rd worker,
the change in quantity is +5 (Quantity increases from 18 [with 2 workers]
to 23 [with the 3rd worker]).
Multiplying the 3rd worker's marginal physical product
of 5 by the price of output of $15 yields a marginal revenue product of
5 x $15 = $75.
Return to Question
10
11.
|
Labor (L)
|
Marginal Physical Product (MPP)
|
Marginal Revenue Product (MRP)
|
|
1
|
15
|
$60
|
|
2
|
13
|
$52
|
|
3
|
11
|
$44
|
|
4
|
9
|
$36
|
|
5
|
7
|
$28
|
From the formula sheet: Labor-hiring rule: Increase Labor as long as: MRP
> PL. MRP is marginal revenue product which is marginal physical
product (MPP) x Price of output produced. We derive marginal revenue product
(MRP) as a 3rd column on the table above by multiplying each marginal physical
product value by $4, the price of the output.
If the price of labor is $39 per worker, the 4th
worker will not be hired because his marginal revenue product is less
than $39. Each of the first 3 workers have a marginal revenue product greater
than $39 and they will be hired. The correct answer is 3
workers, choice c.
Return to Question
11
12. If the price of labor is only $29 per worker,
the 4th worker will now be hired as his marginal revenue product of $36
exceeds $29. However, the 5th worker will still not be hired as his marginal
revenue product is less than the price of labor of $29. The correct answer
is 4 workers, choice
d.
Return to Question
12
13. The 2nd barber's marginal physical product (MPP)
is 18 haircuts per day. This represents the increase in the number of haircuts
(24 to 42) resulting from hiring him. Marginal revenue product (MRP) is
marginal physical product (MPP) x Price of output produced. Multiplying
his marginal physical product of 18 x $6 per haircut yields his marginal
revenue product of $108.
Return to Question
13
14. The 2nd barber's value to the barbershop is $108.
That is his marginal revenue product (MRP), the additional revenue his
hiring generates. This was determined in question 13. He is paid $80 ($10
per hour x 8 hours per day). $80 represents the additional cost to the
barbershop. The difference ($108 - $80) of $28
represents the additional profit the firm earns by his hiring. The correct
answer is choice c.
Return to Question
14
15.
|
Labor (L)
|
Total Product (Quantity, Q) per day
|
Marginal Physical Product (MPP)
|
Marginal Revenue Product (MRP)
|
|
1
|
10
|
10 - 0 = 10
|
10 x $5 = $50
|
|
2
|
19
|
19 - 10 = 9
|
9 x $5 = $45
|
|
3
|
27
|
27 - 19 = 8
|
8 x $5 =$40
|
|
4
|
34
|
34 - 27 = 7
|
7 x $5 = $35
|
|
5
|
40
|
40 - 34 = 6
|
6 x $5 = $30
|
From the formula sheet: Labor-hiring rule: Increase
Labor as long as: MRP > PL. MRP is marginal revenue product
which is marginal physical product (MPP) x Price of output produced.
On the table above 2 additional columns are derived.
First, we derive marginal physical product (MPP) which represents the change
in quantity resulting from adding each additional laborer. This 3rd column
is derived by taking each number in column 2 (quantity) and subtracting
the number in the previous row so as to determine the change. (Note that
the marginal physical product of the 1st worker is 10 because it is assumed
that 0 labor would produce 0 quantity and 10 - 0 = 10)
We then derive marginal revenue product (MRP) as
a 4th column on the table above by multiplying each marginal physical product
value by $5, the price of the output.
Since the price of labor is $33, each of the first
4
workers will be employed because each of their marginal revenue products
exceeds $33. The 5th worker will not be hired because his marginal revenue
product of $30 is less than the price of labor of $33. The correct answer
is d.
Return to Question
15
16.
|
Labor (L)
|
Total Product (Quantity, Q) per day
|
Marginal Physical Product (MPP)
|
|
0
|
0
|
|
|
1
|
3
|
3 - 0 = 3
|
|
2
|
7
|
7 - 3 = 4
|
|
3
|
15
|
15 - 7 = 8
|
|
4
|
24
|
24 - 15 = 9
|
|
5
|
31
|
31 - 24 = 7
|
|
6
|
30
|
20 - 31 = -1
|
Marginal returns refers to the change in quantity
resulting from hiring additional labor. Diminishing marginal returns begins
when the marginal physical product (MPP) of labor begins to decrease. We
can determine this by adding a 3rd column in our table to represent the
change in quantity resulting from adding each additional laborer. The 3rd
column, derived by taking each number in column 2 (quantity) and subtracting
the number in the previous row so as to determine the change in quantity,
illustrates that marginal physical product (MPP) of labor begins to decrease
with the addition of the 5th
unit of labor (from 9 to 7). The correct answer is choice e.
(Note that marginal physical product only begins with the 1st worker. There
is no value for MPP for 0 labor because MPP only records the change in
quantity produced as additional labor is added.)
Return to Question
16
17. Diminishing marginal returns refers to the situation
in which as additional labor is hired, quantity begins to increase at a
decreasing
rate. Specifically, this occurs when marginal
physical product (MPP) decreases since marginal
physical product represents the change in quantity resulting from
additional labor. The correct choice is d.
Choices a - c all increase because:
a) Total cost always increases as labor increases because the
firm must pay for the labor.
b) From the formula sheet: Marginal Cost (MC) = PL/MPP (MC is
inversely (oppositely) related to MPP because PL
is
assumed to be a constant.). Since marginal physical product (MPP) is decreasing
in this problem, marginal cost (MC) must be increasing.
c) Total physical product (TPP) represents total output or quantity
(Q) produced. The question states that quantity is increasing.
Return to Question
17
18. From the formula sheet: Marginal Cost (MC) =
PL/MPP (MC is inversely (oppositely) related to MPP because PL
is
assumed to be a constant.). Since marginal physical product (MPP) increases
in this problem, marginal cost (MC) must be decreasing.
Total cost always increases as labor increases
because the firm must pay for the labor.
The correct answer is d,
marginal cost (MC) is decreasing, but total cost (TC) is increasing.
Return to Question
18
19. From the formula sheet: Marginal Cost (MC) =
PL/MPP (MC is inversely (oppositely) related to MPP because PL
is
assumed to be a constant.). Since marginal physical product (MPP) is decreasing
in this problem, marginal cost (MC) must be increasing.
Total cost always increases as labor increases
because the firm must pay for the labor.
The correct answer is a,
both
marginal cost (MC) and total cost (TC) are increasing.
Return to Question
19
20.
|
Quantity (Q)
|
Total Cost (TC)
|
Marginal Cost (MC)
|
|
0
|
$12
|
|
|
1
|
$27
|
$27 - $12 = $15 |
|
2
|
$37
|
$37 - $27 = $10 |
|
3
|
$45
|
$45 - $37 = $8 |
|
4
|
$56
|
$56 - $45 = $11 |
|
5
|
$80
|
$80 - $56 = $24 |
Diminishing marginal returns occurs when marginal physical
product (MPP) begins to decrease.
From the formula sheet: Marginal Cost (MC) = PL/MPP
(MC is inversely (oppositely) related to marginal physical product [MPP]
because PL is assumed to be a constant.). Therefore, marginal physical
product will begin to decrease when marginal cost begins to increase.
We can determine marginal cost from the table above
by using the alternative definition: marginal cost (MC) = DTC/DQ.
Since the change in quantity (DQ) is 1 as you
move down the rows on the table, marginal cost (column 3) is derived by
measuring the change in total cost (DTC), the
numerator in the formula. (Note that marginal cost,
MC, only begins with the 1st unit of quantity. There is no value for MC
for 0 quantity because MC only records the change in total cost
as additional quantity is produced.)
Marginal cost begins to increase with the production
of the 4th unit of quantity
(MC increases from $8 for the 3rd unit of quantity to $11 for the 4th unit
of quantity.) Therefore, diminishing marginal returns begins with
the production of the 4th
unit of quantity, choice d.
Return to Question
20
21. Average Cost (AC) = TC/Q in which TC is total
cost. Since quantity produced (Q) = 8, we can determine average cost by
dividing total cost by 8.
Total Cost (TC) = Total Variable Cost (TVC) + Total Fixed Cost (TFC)
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L) = $80 x 3 workers = $240
Total Fixed Cost (TFC) is given as $480.
Total Cost (TC) = $240 + $480 = $720.
Average Cost (AC) = $720/8 = $90.
Return to Question
21
22. From the formula sheet: If Marginal is less than
Average, then average is decreasing.
Therefore, if marginal cost (MC) is less than average cost (AC), then
average cost (AC) is decreasing,
choice
a.
Return to Question
22
23. Choices a, c, and d will always be incorrect
because, as quantity increases, total fixed costs remain constant by definition
and total cost always increases.
If average cost (AC) decreases, then marginal cost
(MC) must be less than average cost. However, marginal cost itself
may be increasing, decreasing, or even remaining constant as quantity increases
from 30 to 40 units. Therefore, although choice b may possibly be correct,
it may also be incorrect. Therefore, it cannot be concluded that
marginal cost decreases.
The correct choice is e, None
of the above can be concluded.
Return to Question
23
24. Average Cost (AC) = TC/Q in which TC is total
cost. Since quantity produced (Q) = 12, we can determine average cost by
dividing total cost by 12.
Total Cost (TC) = Total Variable Cost (TVC) + Total Fixed Cost (TFC)
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L) = $40 x 3 workers = $120
Total Fixed Cost (TFC) is given as $240.
Total Cost (TC) = $120 + $240 = $360.
Average Cost (AC) = $360/12 = $30.
Return to Question
24
25. Choices a, c, d and e will always be incorrect
because, as quantity increases, average fixed costs (AFC) always decrease,
total fixed costs remain constant by definition and total cost always increases.
(Note that average fixed costs always decrease because AFC = TFC/Q and
as quantity (the denominator) increases, TFC (the numerator) remains constant.
Dividing a constant value by an increasing larger value yields a smaller
ratio.)
From the formula sheet: If Marginal = Average, then
Average is constant. Therefore, if average cost (AC) remains constant for
all units form Q = 75 to Q = 80, marginal cost (MC) must be equal
to average cost for each of these 5 units. The correct answer is b,
marginal
cost (MC) is constant.
Return to Question
25
26. Average Cost (AC) = TC/Q in which TC is total
cost. Since quantity produced (Q) = 6, we can determine average cost by
dividing total cost by 6.
Total Cost (TC) = Total Variable Cost (TVC) + Total Fixed Cost (TFC)
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L) = $40 x 5 workers = $200
Total Fixed Cost (TFC) is given as $220.
Total Cost (TC) = $200 + $220 = $360.
Average Cost (AC) = $420/6 = $70.
Return to Question
26
27. If average cost (AC) decreases, then marginal
cost (MC) must be less than average cost. However, marginal cost
itself may be increasing, decreasing, or even remaining constant as quantity
increases
from 20 to 30 units. Therefore, although choices c and d may possibly be
correct, they may also be incorrect.
On the other hand, choice a
is always true. Average Fixed Cost (AFC) = TFC/Q. As quantity
(Q) increases, AFC always decreases because total fixed cost
(TFC) remains constant by definition.
Return to Question
27
28. Choice a is incorrect because as mentioned in
question 27 above, average fixed cost (AFC) always decreases.
Choices b and c are incorrect because total cost (TC) always increases
as quantity increases.
From the formula sheet: If Marginal = Average, then
Average is constant. Although marginal cost (MC) would be the same $6 per
unit for each of these 5 units, we don't know if marginal cost = average
cost for these units. Marginal cost (MC) may be greater or less than average
cost (AC). Although average cost (AC) may be constant, it may also be increasing
or decreasing. Therefore, None of the above
can be concluded, choice e.
Return to Question
28
29. Marginal returns refers to the change
in quantity resulting from hiring additional labor. Diminishing marginal
returns begins when the marginal physical product (MPP) of labor begins
to decrease.
From the formula sheet: Marginal Cost (MC) = PL/MPP
(MC is inversely (oppositely) related to marginal physical product [MPP]
because PL is assumed to be a constant.). Therefore, when marginal
physical product decreases, marginal cost increases and choice a
is definitely incorrect for this problem.
However, although marginal cost (MC) is increasing,
marginal cost (MC) might still be less than average cost (AC).
From the formula sheet: If Marginal is less than Average, then average
is decreasing. Therefore, average cost (AC) might
be decreasing. Choice b
is correct.
Note that choices c and d
are always incorrect because as quantity increases, total fixed cost (TFC)
remains constant and total cost (TC) increases.
Return to Question
29
30. As quantity (Q) increases, total cost (TC) always
increases. Since marginal is the slope of total, if marginal cost (MC)
is increasing, the slope of the total cost curve is increasing. A steeper
total cost curve (larger slope) indicates that total cost (TC) is increasing
at an increasing rate, choice e.
Return to Question
30
31. As quantity increases, total
cost (TC) always increases because the additional labor hired must
be paid. The correct choice is a.
The other choices are incorrect for the following reasons:
b) Increasing returns to labor mean that marginal physical product
(MPP) is increasing. From the formula sheet: Marginal Cost (MC) = PL/MPP
(MC is inversely (oppositely) related to marginal physical product [MPP]
because PL is assumed to be a constant.). Therefore, when marginal
physical product increases, marginal cost decreases and choice b
is definitely incorrect for this problem.
c) Total fixed costs (TFC) always remain constant as quantity increases.
d) Average Fixed Cost (AFC) = TFC/Q. As quantity (Q) increases, AFC
always decreases because total fixed cost (TFC) remains constant by
definition.
Return to Question
31
32. Marginal returns refers to the change
in quantity resulting from hiring additional labor. Diminishing marginal
returns begins when the marginal physical product (MPP) of labor begins
to decrease.
From the formula sheet: Marginal Cost (MC) = PL/MPP
(MC is inversely (oppositely) related to marginal physical product [MPP]
because PL is assumed to be a constant.). Therefore, when marginal
physical product is decreasing, marginal cost
is increasing.
Also from the formula sheet: If Marginal is less
than Average, then average is decreasing. Therefore, since the question
states that average cost (AC) is decreasing, then marginal
cost (MC) is less than average cost (AC). The correct choice is
a.
Return to Question
32
33. Average Fixed Cost (AFC) = TFC/Q. As quantity
(Q) increases, AFC always decreases because total fixed cost (TFC)
remains constant by definition. The correct answer is d.
The other choices are incorrect for the following
reasons:
a) Total cost (TC) always increases as quantity increases because the
additional labor must be paid.
b) Diminishing returns to labor mean that marginal physical product
(MPP) is decreasing. From the formula sheet: Marginal Cost (MC) = PL/MPP
(MC is inversely (oppositely) related to marginal physical product [MPP]
because PL is assumed to be a constant.). Therefore, when marginal
physical product decreases, marginal cost increases.
c) Total fixed costs (TFC) always remain constant by definition as
quantity increases.
Return to Question
33
34. The total output (quantity, Q) produced by the
2 workers is 10, 4 by the first worker and an additional 6 by the second
worker.
Average Cost (AC) = TC/Q in which TC is total cost. Since quantity
produced (Q) = 10, we can determine average cost by dividing total cost
by 10.
Total Cost (TC) = Total Variable Cost (TVC) + Total Fixed Cost (TFC)
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L) = $50 x 2 workers = $100
Total Fixed Cost (TFC) is given as $500.
Total Cost (TC) = $100 + $220 = $500.
Average Cost (AC) = $600/10 = $60.
Return to Question
34
35. Total Cost (TC) = Total Variable Cost (TVC) +
Total Fixed Cost (TFC)
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L) = $100 x 5 workers = $500
Total Fixed Cost (TFC) is given as $200.
Total Cost (TC) = $500 + $200 = $700.
Return to Question
35
36. From the formula sheet: If Marginal is less than
Average, then average is decreasing. Therefore, since marginal cost is
less than average cost (AC) in this question, average
cost (AC) is decreasing.
Total cost (TC) always
increases as quantity increases because the additional labor must
be paid.
The correct answer is d,
average
cost (AC) is decreasing, but total cost (TC) is increasing.
Return to Question
36
37. From the formula sheet: If Marginal = Average,
then Average is constant. If average cost (AC) remains the same at $10
per unit, then marginal cost (MC) is equal to average
cost (AC), choice d.
Choices a and c are incorrect for the following
reasons:
a) Average Fixed Cost (AFC) = TFC/Q. As quantity (Q) increases, AFC
always decreases because total fixed cost (TFC) remains constant by
definition.
c) Total cost (TC) always increases as quantity increases because
the additional labor must be paid.
Return to Question
37
38.
|
Labor (L)
|
Total Physical Product (Quantity, Q)
|
|
0
|
0
|
|
1
|
10
|
|
2
|
30
|
|
3
|
60
|
|
4
|
84
|
|
5
|
90
|
Average Cost (AC) = TC/Q in which TC is total cost. Since quantity produced
(Q) = 30, we can determine average cost by dividing total cost by 30.
Total Cost (TC) = Total Variable Cost (TVC) + Total Fixed Cost (TFC)
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L). Since row 3 of the table above indicates that 2 units of labor produce
30 units of quantity, TVC = $55 x 2 workers = $110
Total Fixed Cost (TFC) is given as $100.
Total Cost (TC) = $110 + $100 = $210.
Average Cost (AC) = $210/30 = $7.
Return to Question
38
39. From the formula sheet: Marginal Cost (MC) =
PL/MPP. The price of labor (PL) is $55 per
laborer and the marginal physical product (MPP) of the 4th laborer is 24.
Marginal physical product (MPP) represents the change in quantity resulting
from additional labor. Since the table above indicates that 3 units of
labor can produce 60 units of quantity and 4 units of labor can produce
84 units of quantity, the additional quantity produced by the 4th laborer
is 84 - 60 = 24.
Marginal Cost (MC) = $55/24 = $2.2917. Rounding
off to the nearest cent yields the answer of $2.29.
Return to Question
39
40.
|
Units of Labor (L)
|
Marginal Physical Product (MPP)
|
|
1
|
8
|
|
2
|
10
|
|
3
|
9
|
|
4
|
7
|
|
5
|
5
|
|
6
|
2
|
|
Labor (L)
|
Marginal Physical Product (MPP)
|
Marginal Revenue Product (MRP)
|
|
1
|
8
|
8 x $8 = $64
|
|
2
|
10
|
10 x $8 = $80
|
|
3
|
9
|
9 x $8 = $72
|
|
4
|
7
|
7 x $8 = $56
|
|
5
|
5
|
5 x $8 = $40
|
|
6
|
2
|
2 x $8 = $16
|
From the formula sheet: Labor-hiring rule: Increase Labor as long as: MRP
> PL. MRP is marginal revenue product which is marginal physical
product (MPP) x Price of output produced. We derive marginal revenue product
(MRP) as a 3rd column on the table above by multiplying each marginal physical
product value by $8, the price of the output.
If the price of labor is $60 per worker, the 4th
worker will not be hired because their marginal revenue product is less
than $60. Each of the first 3 workers has a marginal revenue product greater
than $60 and each of them will be hired. The correct answer is 3
workers, choice c.
Return to Question
40
41.
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
|
0
|
0
|
|
1
|
10
|
|
2
|
24
|
|
3
|
37
|
|
4
|
42
|
|
5
|
45
|
|
6
|
45
|
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
Marginal Physical Product (MPP)
|
Marginal Revenue Product (MRP)
|
|
0
|
0
|
|
|
|
1
|
10
|
10 - 0 = 10
|
10 x $12 = $120
|
|
2
|
24
|
24 - 10 = 14
|
14 x $12 = $168
|
|
3
|
37
|
37 - 24 = 13
|
13 x $12 =$156
|
|
4
|
42
|
42 - 37 = 5
|
5 x $12 = $60
|
|
5
|
45
|
45 - 42 = 3
|
3 x $12 = $36
|
|
6
|
45
|
45 - 45 = 0
|
0 x $12 = $0
|
From the formula sheet: Labor-hiring rule: Increase
Labor as long as: MRP > PL. MRP is marginal revenue product
which is marginal physical product (MPP) x Price of output produced.
On the table above 2 additional columns are derived.
First, we derive marginal physical product (MPP) which represents the change
in quantity resulting from adding each additional laborer. This 3rd column
is derived by taking each number in column 2 (quantity) and subtracting
the number in the previous row so as to determine the change.
We then derive marginal revenue product (MRP) as
a 4th column on the table above by multiplying each marginal physical product
value by $12, the price of the output.
Since the price of labor is $55 per worker, each
of the first
4 workers will be employed because
each of their marginal revenue products exceeds $55. The 5th worker will
not be hired because their marginal revenue product of $36 is less
than the price of labor of $55. The correct answer is d.
Return to Question
41
42. Diminishing marginal returns refers to a situation in which, as
labor increases, quantity produced increases at a decreasing rate. Since
marginal physical product (MPP) represents the change in quantity produced,
the change is positive (Quantity is still increasing) but the change is
decreasing (since each additional labor adds less to production). The correct
choice is b, diminishing
marginal returns since quantity (Q) is increasing at a decreasing rate.
Return to Question
42
43.
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
|
0
|
0
|
|
1
|
5
|
|
2
|
13
|
|
3
|
23
|
|
4
|
34
|
|
5
|
43
|
|
6
|
42
|
Diminishing marginal returns refers to a situation in which, as labor increases,
quantity produced increases at a decreasing rate. Since marginal physical
product (MPP) represents the change in quantity produced, diminishing marginal
returns occurs when marginal physical product begins to decrease. We can
determine this by adding a 3rd column in our table to represent the change
in quantity resulting from adding each additional laborer. The 3rd column,
derived by taking each number in column 2 (quantity) and subtracting the
number in the previous row so as to determine the change in quantity, illustrates
that marginal physical product (MPP) of labor begins to decrease
with the addition of the 5th
unit of labor (from 11 to 9). The correct answer is choice e.
(Note that marginal physical product only begins with the 1st worker. There
is no value for MPP for 0 labor because MPP only records the change in
quantity produced as additional labor is added.)
|
Labor (L)
|
Total Physical Product
(Quantity, Q) per day
|
Marginal Physical Product (MPP)
|
|
0
|
0
|
|
|
1
|
5
|
5 - 0 = 5
|
|
2
|
13
|
13 - 5 = 8
|
|
3
|
23
|
23 - 13 = 10
|
|
4
|
34
|
34 - 23 = 11
|
|
5
|
43
|
43 - 34 = 9
|
|
6
|
42
|
42 - 43 = -1
|
Return to Question 43
44.
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
Marginal Physical Product (MPP)
|
|
3
|
35
|
|
|
4
|
42
|
42 - 35 = 7
|
Labor-hiring rule: Increase Labor as long as: MRP > PL. MRP
is marginal revenue product which is marginal physical product (MPP) x
Price of output produced. The 4th worker's marginal physical product is
7 units. This is determined by subtracting the quantity without him (35)
from the quantity that can be produced with him (42). Since his marginal
revenue product must be greater than the $77 price of labor, the price
of the product he produces must be greater than $11.
This is because MRP = MPP x Price of output produced. If the price of output
is $11, MRP = 7 x $11 = $77. Any price greater than $11 will make his marginal
revenue product greater than the $77 necessary for the firm to find it
profitable to hire him.
Return to Question
44
45.
The graph above illustrates that marginal physical product (MPP) is
positive, but decreasing, between points V and W.
Since marginal physical product is positive, then total physical product
(quantity) is increasing.
Since marginal physical product (which represents the change in quantity)
is decreasing, then total physical product is increasing at a decreasing
rate.
On the graph of total physical product below, only
between points C and D is quantity increasing at a decreasing rate.
The correct choice is b.
Return to Question
45
46.
A firm with the following table can sell its product at $15 per unit:
|
Units of Labor (L)
|
Marginal Physical Product (MPP)
|
|
1
|
9
|
|
2
|
10
|
|
3
|
9
|
|
4
|
8
|
|
5
|
7
|
From the formula sheet: Labor-hiring rule: Increase Labor as long as: MRP
> PL. MRP is marginal revenue product which is marginal physical
product (MPP) x Price of output produced. We derive marginal revenue product
(MRP) as a 3rd column on the table above by multiplying each marginal physical
product value by $15, the price of the output:
|
Labor (L)
|
Marginal Physical Product (MPP)
|
Marginal Revenue Product (MRP)
|
|
1
|
9
|
9 x $15 = $135
|
|
2
|
10
|
10 x $15 = $150
|
|
3
|
9
|
9 x $15 = $135
|
|
4
|
8
|
8 x $15 = $120
|
|
5
|
7
|
7 x $15 = $105
|
If the firm hires only 4 workers, then it decides not to hire the 5th worker.
Therefore, the 5th worker's marginal revenue product (MRP) of $105 must
be less than the price of labor (PL).
However, the 4th worker is hired so her marginal revenue product (MRP)
of $120 must be greater than the price of labor (PL).
Since the price of labor (PL) is the same for all workers, we have
determined that the price of labor is less than $120
and
is greater than $105.
Return to Question
46
47. Marginal returns refers to the value of the marginal product of
labor (MPP). The marginal product of labor represents the change
in quantity resulting from adding an additional unit of labor.
Zero marginal returns is equivalent to a zero value of the marginal
product of labor. A zero change in quantity means that
quantity produced (Q) remains constant,
choice d.
Return to Question
47
48. Diminishing marginal returns refers to a situation in which marginal
physical product (MPP) decreases as additional labor is hired. The formula
sheet indicates that marginal cost (MC) is inversely (oppositely) related
to MPP. This is because Marginal Cost (MC) = PL/MPP. PL (the price of labor)
is assumed to be constant. Therefore, if MPP, the denominator of the ratio,
is decreasing, then marginal cost (MC) will be increasing.
Total cost (TC) always increases as a firm hires more labor because
the labor must be paid.
The correct choice is d, both
its marginal cost (MC) and total cost (TC) curves are increasing.
Return to Question
48
49. Average fixed cost (AFC), choice c,
always
decreases as quantity increases. AFC is inversely (oppositely) related
to quantity (Q).
This is because Average Fixed Cost (AFC) = TFC/Q.
Total fixed cost (TFC) is independent of quantity so it remains constant
as quantity (Q) increases. Dividing a constant value (TFC) by a larger
denominator (Q) will always yield a smaller value.
Return to Question
49
50. Since Average Cost (AC) = Total Cost/Quantity, to compute
average cost we first compute total cost.
Total Cost (TC) = Total Variable Cost (TVC) + Total Fixed Cost (TFC)
Since total fixed costs are given as $270/day, to determine total cost
we must compute total variable cost.
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L).
TVC = $150 x 3 = $450.
Adding total variable cost of $450 to the total fixed cost of $270
yields a total cost (TC) of $720.
Therefore, since the 3 workers product a quantity of 80 units per day,
AC = $720/80 = $9.
Return to Question
50
51. Diminishing marginal returns refers to a situation in which
marginal physical product (MPP) decreases as additional labor is hired.
The formula sheet indicates that marginal cost (MC) is inversely (oppositely)
related to MPP. This is because Marginal Cost (MC) = PL/MPP. PL (the price
of labor) is assumed to be constant. Therefore, if MPP, the denominator
of the ratio, is decreasing, then marginal cost (MC) will be
increasing.
However, even though marginal cost is increasing, average
cost (AC) may possibly be decreasing. This
is because if marginal is less than average, then average is decreasing.
And, despite the fact that marginal cost is increasing, it may still be
less than average cost. The correct choice is e.
Return to Question
51
52. Total fixed cost (TFC) is independent of quantity so it remains
constant as quantity (Q) increases. Since costs (expressed in $) is on
the vertical axis and quantity (expressed in units per time) is on the
horizontal axis, total fixed cost (TFC) is graphed as a horizontal line.
Average Fixed Cost (AFC) = TFC/Q. Dividing a constant value (TFC) by
a larger denominator (Q) will always yield a smaller value. Therefore,
doubling Q will exactly halve AFC. Average fixed cost (AFC) is a negatively
sloped curve which is asymptotic to both axes; that is, as quantity increases,
AFC gets continually smaller, but always remains positive. It never touches
the X-axis.
The correct choice is a, total
fixed cost (TFC) is a horizontal line and average fixed cost (AFC) is a
negatively sloped curve.
Return to Question
52
53. A firm notices that if it increases quantity (Q) from 80 to 90
units per day its average cost (AC) per unit of quantity decreases. It
can thus conclude that from 80 to 90 units of quantity (Q)
-
total variable cost (TVC) decreases.
-
marginal cost (MC) decreases.
-
total cost (TC) decreases.
-
total fixed cost (TFC) decreases.
-
marginal cost (MC) increases.
-
None of the above can be concluded.
The correct answer is f, None
of the above can be concluded. Let's exam why none of the five choices
is correct:
Choice a: As quantity increases, total variable cost (TVC) always increases
because the labor used to produce the additional quantity must be paid.
Choices b and e: Since average cost (AC) decreases, marginal cost must
be less than average cost. However, we cannot conclude whether marginal
cost itself is increasing or decreasing.
Choice c: As quantity increases, total cost (TC) always increases because
there is no free good. The labor used to produce the additional quantity
must be paid.
Choice d: Total fixed cost (TFC) is independent of quantity. It always
remains
constant as quantity increases.
Return to Question
53
54.
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
|
2
|
24
|
|
3
|
33
|
Marginal Cost (MC) = PL/MPP. Since the price of labor (PL) is given at
$66, then to solve for marginal cost we must divide $66 by the marginal
physical product (MPP) of the 3rd unit of labor. The marginal physical
product of labor represents the change in quantity resulting from
adding an additional unit of labor. By adding the 3rd unit of labor, quantity
increases from 24 units to 33 units. The MPP of the 3rd unit of labor is
33 - 24 = 9.
MC = PL/MPP
MC = $66/9
MC = $7.33.
Return to Question
54
55. From the formula sheet: If Marginal is less than Average, then
average is decreasing.
Therefore, if marginal cost (MC) is less than average cost (AC), average
cost is being pulled down, even if marginal cost itself is increasing.
The correct choice is d.
Return to Question
55
56.
Marginal physical product (MPP) = DQ/DL
(Q is quantity, L is units of labor). Thus, MPP is the slope of the total
physical product (TPP) curve since Q is measured on the vertical axis and
L is measured on the horizontal axis.
From point A to point B, total physical product is increasing, but
at a decreasing rate. The curve is getting flatter; that is, the slope,
although still positive, is becoming smaller.
As labor increases, if marginal physical product is decreasing, but
is still positive, then diminishing marginal returns is occurring.
The correct choice is b.
Return to Question
56
57. Average Cost (AC) = TC/Q [TC is total cost and Q is quantity
of output produced.]
TC = Total Variable cost (TVC) + Total Fixed Cost (TFC)
Total Variable Cost (TVC) = Price of Labor (PL) x Number of Laborers
(L)
Since each worker is paid $80/day and there are 5 workers, TVC = $80
x 5 = $400
TFC is given as $300.
TC = $400 + $300 = $700
Dividing the total cost of $700 by the 14 units of quantity produced
yields average cost:
AC = $700/14 = $50.00.
Return to Question
57
58. Diminishing marginal returns refers to a situation in which, as
labor increases, total physical product is positive and increasing,
but it is increasing at a decreasing rate. Marginal physical product (MPP)
describes the change in total physical product and is represented by the
slope of the total physical product curve. If total physical product is
increasing, marginal physical product is positive, and if total
physical product is increasing at a decreasing rate, marginal physical
product (the slope) is decreasing.
The correct choice is d.
Return to Question
58
59. Given the following table for a firm which can
sell its quantity (Q) at $10 per unit:
|
Units of Labor (L)
|
Marginal Physical Product (MPP)
|
|
1
|
9
|
|
2
|
10
|
|
3
|
8
|
|
4
|
7
|
|
5
|
5
|
|
6
|
2
|
|
Labor (L)
|
Marginal Physical Product (MPP)
|
Marginal Revenue Product (MRP)
|
|
1
|
9
|
9 x $10 = $90
|
|
2
|
10
|
10 x $10 = $100
|
|
3
|
8
|
8 x $10 = $80
|
|
4
|
7
|
7 x $10 = $70
|
|
5
|
5
|
5 x $10 = $50
|
|
6
|
2
|
2 x $10 = $20
|
From the formula sheet: Labor-hiring rule: Increase Labor as long as: MRP
> PL. MRP is marginal revenue product which is marginal physical
product (MPP) x Price of output produced. We derive marginal revenue product
(MRP) as a 3rd column on the table above by multiplying each marginal physical
product value by $10, the price of the output.
If the price of labor is $65 per worker, the 5th
worker will not be hired because their marginal revenue product is less
than $65. Each of the first 4 workers has a marginal revenue product greater
than $65 and each of them will be hired. The correct answer is 4
workers, choice d.
Return to Question
59
60. As quantity (Q) increases, total cost (TC) always increases.
Diminishing marginal returns refers to a situation
in which marginal physical product (MPP) is positive, but decreasing.
If MPP is decreasing, then marginal cost (MC) must
be increasing.
Marginal Cost (MC) = PL/MPP in which PL is the price per unit of labor.
Marginal cost always is inversely (oppositely) related to MPP because PL
is
assumed to be a constant.
The correct choice is d,
both marginal cost (MC) and total cost (TC) are increasing.
Return to Question
60
61.
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
|
0
|
0
|
|
1
|
10
|
|
2
|
22
|
|
3
|
30
|
Marginal Cost (MC) = PL/MPP in which PL is the price per unit of labor.
PL is given as $100 per laborer per day.
The marginal physical product (MPP) of the 3rd unit of labor is the
additional quantity produced by the 3rd unit of labor.
MPP = 8 because quantity of 30 with the 3rd laborer is 8 units greater
than the quantity (22) with only 2 units of labor.
MC = $100/8 = $12.50.
Return to Question
61
62. Since total cost (TC) always increases as quantity increases
(as there is no free good), this provides no useful information. The correct
choice is therefore e,
None of the above can be concluded.
Note that while choices b and c are both possible,
choices a and d are both incorrect. As quantity increases, total fixed
cost (TFC) always remains constant, by the very definition of fixed
costs. Similarly, as quantity increases, average fixed cost (AFC) always
decreases. AFC = TFC/Q. As quantity (the denominator) increases, AFC decreases
because the numerator (TFC) remains constant by definition. Dividing a
constant value by a larger denominator will always yield a smaller ratio.
Return to Question
62
63.
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
|
0
|
0
|
|
1
|
10
|
|
2
|
24
|
|
3
|
37
|
|
4
|
45
|
|
5
|
51
|
|
6
|
55
|
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
Marginal Physical Product (MPP)
|
Marginal Revenue Product (MRP)
|
|
0
|
0
|
|
|
|
1
|
10
|
10 - 0 = 10
|
10 x $25 = $250
|
|
2
|
24
|
24 - 10 = 14
|
14 x $25 = $350
|
|
3
|
37
|
37 - 24 = 13
|
13 x $25 =$325
|
|
4
|
45
|
45 - 37 = 8
|
8 x $25 = $200
|
|
5
|
51
|
51 - 45 = 6
|
6 x $25 = $150
|
|
6
|
55
|
55 - 51 = 4
|
4 x $25 = $100
|
From the formula sheet: Labor-hiring rule: Increase
Labor as long as: MRP > PL. MRP is marginal revenue product
which is marginal physical product (MPP) x Price of output produced.
On the table above 2 additional columns are derived.
First, we derive marginal physical product (MPP) which represents the change
in quantity resulting from adding each additional laborer. This 3rd column
is derived by taking each number in column 2 (quantity) and subtracting
the number in the previous row so as to determine the change.
We then derive marginal revenue product (MRP) as
a 4th column on the table above by multiplying each marginal physical product
value by $25, the price of the output.
Since the price of labor is $105 per worker, each
of the first
5 workers will be employed because
each of their marginal revenue products exceeds $105. The 6th worker will
not be hired because their marginal revenue product of $100 is less
than the price of labor of $105. The correct answer is e.
Return to Question
63
64. AFC = TFC/Q. As quantity (the denominator)
increases, AFC decreases because the numerator (TFC) remains constant by
definition. Dividing a constant value by a larger denominator will always
yield a smaller ratio. Therefore, the correct choice is e,
because as quantity increases, average fixed cost (AFC) always decreases.
Return to Question
64
65.
|
Labor (L)
|
Total Physical Product (Quantity, Q) per day
|
|
0
|
0
|
|
1
|
5
|
|
2
|
13
|
|
3
|
23
|
|
4
|
32
|
|
5
|
35
|
|
6
|
34
|
Diminishing marginal returns refers to a situation in which, as labor increases,
quantity produced increases at a decreasing rate. Since marginal physical
product (MPP) represents the change in quantity produced, diminishing marginal
returns occurs when marginal physical product begins to decrease. We can
determine this by adding a 3rd column in our table to represent the change
in quantity resulting from adding each additional laborer. The 3rd column,
derived by taking each number in column 2 (quantity) and subtracting the
number in the previous row so as to determine the change in quantity, illustrates
that marginal physical product (MPP) of labor begins to decrease
with the addition of the 4th
unit of labor (from 10 to 9). The correct answer is choice d.
(Note that marginal physical product only begins with the 1st worker. There
is no value for MPP for 0 labor because MPP only records the change in
quantity produced as additional labor is added.)
|
Labor (L)
|
Total Physical Product
(Quantity, Q) per day
|
Marginal Physical Product (MPP)
|
|
0
|
0
|
|
|
1
|
5
|
5 - 0 = 5
|
|
2
|
13
|
13 - 5 = 8
|
|
3
|
23
|
23 - 13 = 10
|
|
4
|
32
|
32 - 23 = 9
|
|
5
|
35
|
35 - 32 = 3
|
|
6
|
34
|
34 - 35 = -1
|
Return to Question 65
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