12 Chapter - The Demand for Resources
Chapter 12 The Demand for Resources
QUESTIONS
1. What is the significance of resource pricing? Explain how the factors determining resource
demand differ from those determining product demand. Explain the meaning and significance of
the fact that the demand for a resource is a derived demand. Why do resource demand curves
slope downward? LO1
Answer: All resources that enter into production are owned by someone, including the
most important resource of all for most people, self -owned labor. The most basic
significance of resource pricing is that it largely determines peoples incomes. Resource
pricing allocates scarce resources among alternative uses. Firms take account of the
prices of resources in deciding how best to attain least -cost production.
Finally, resource pricing has a great deal to do with income inequality and the debate as
to what government should or should not do to lessen this inequality. It is here that the
factors that determine resource demand are most different from those that determine
demand for products. Demand for products is a question of income and tastes. But
resource demand is more passive in the sense that it is derived from the demand for the
products the resource can produce. If a resource cant be used in production of a desired
product, there will not be any demand for it. Additionally, resources are often less
mobile than products, so their geographic location relative to demand for the output they
produce may be an important factor determining demand for resources in particular
geographic areas.
Resources, factors of production, are not hired or bought because their employer or buyer
desires them for themselves. The demand for resources is entirely derived from what the
firm believes the resources can produce. If there were no demand for output, there would
be no demand for input.
The demand for a resource depends, then, on how productive it is in producing output
and on the price of the output. The demand for a resource is downward sloping because
of the diminishing marginal product of the resource (because of the law of diminishing
returns) and, in imperfectly competitive markets, also because the greater the output, the
lower its price.
2. At the bottom of the page, complete the labor demand table for a firm that is hiring labor
competitively and selling its product in a competitive market. LO2
a. How many workers will the firm hire if the market wage rate is $27.95? $19.95? Explain why
the firm will not hire a larger or smaller number of units of labor at each of these wage rates.
b. Show in schedule form and graphically the labor demand curve of this firm.
c. Now again determine the firms demand curve for labor, assuming that it is selling in an
imperfectly competitive market and that, although it can sell 17 units at $2.20 per unit, it must
lower product price by 5 cents in order to sell the marginal product of each successive labor unit.
Compare this demand curve with that derived in question 2b. Which curve is more elastic?
Explain.
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Chapter 12 - The Demand for Resources
Answer: Table:
Units
of
labor
Total
product
Marginal
product
Product
price
0
1
2
3
4
5
6
0
17
31
43
53
60
65
17
14
12
10
7
5
$2
2
2
2
2
2
2
Total
revenue
$0
34
62
86
106
120
130
Marginal
revenue
product
$34
28
24
20
14
10
(a) Two workers at $27.95 because the MRP of the first worker is $34 and the MRP of
the second worker is $28, both exceeding the $27.95 wage. Four workers at $19.95
because workers 1 through 4 have MRPs exceeding the $19.95 wage. The fifth
workers MRP is only $14 so he or she will not be hired.
(b) The demand schedule consists of the first and last columns of the table:
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Chapter 12 - The Demand for Resources
(c) New Table:
Units
of
labor
Total
product
Marginal
product
0
1
2
3
4
5
6
0
17
31
43
53
60
65
17
14
12
10
7
5
Product
price
Total
revenue
$2.25
2.20
2.15
2.10
2.05
2.00
1.95
$0
37.40
66.65
90.30
108.65
120.00
126.75
Marginal
revenue
product
$37.40
29.25
23.65
18.35
11.35
6.75
____
The new labor demand is less elastic. Here, MRP falls because of diminishing
returns and because product price declines as output increases. A decrease in the
wage rate will produce less of an increase in the quantity of labor demanded, because
the output from the added labor will reduce product price and thus MRP.
3. In 2009 General Motors (GM) announced that it would reduce employment by 21,000 workers.
What does this decision reveal about how GM viewed its marginal revenue product (MRP) and
marginal resource cost (MRC)? Why didnt GM reduce employment by more than 21,000
workers? By fewer than 21,000 workers? LO3
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Chapter 12 - The Demand for Resources
Answer: GMs decision suggests that the MRC of those 21,000 workers was greater than
the MRP. GM didnt reduce employment further because the MRP of the remaining
workers exceeds the MRC. Reducing employment by less than 21,000 workers would
have left GM with some employees for whom the MRC exceeded the MRP, reducing the
companys profits.
4. What factors determine the elasticity of resource demand? What effect will each of the
following have on the elasticity or the location of the demand for resource C, which is being used
to produce commodity X? Where there is any uncertainty as to the outcome, specify the causes of
that uncertainty. LO4
a. An increase in the demand for product X.
b. An increase in the price of substitute resource D.
c. An increase in the number of resources substitutable for C in producing X.
d. A technological improvement in the capital equipment with which resource C is combined.
e. A fall in the price of complementary resource E.
f. A decline in the elasticity of demand for product X due to a decline in the competitiveness of
product market X.
Answer: Elasticity of demand for a resource is determined by: (1) ease of resource
substitutability; (2) elasticity of product demand; and (3) ratio of resource costs to total
costs.
(a) Increase in the demand for resource C.
(b) Uncertainty relative to the change in demand for resource C; answer depends upon
which is larger the substitution effect or the output effect.
(c) Increase in the elasticity of resource C.
(d) Increase in the demand for resource C.
(e) Increase in the demand for resource C.
(f) Decrease in the elasticity of resource C.
5. Suppose the productivity of capital and labor are as shown in the accompanying table. The
output of these resources sells in a purely competitive market for $1 per unit. Both capital and
labor are hired under purely competitive conditions at $3 and $1, respectively. LO5
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Chapter 12 - The Demand for Resources
a. What is the leastcost combination of labor and capital the firm should employ in producing 80
units of output? Explain.
b. What is the profitmaximizing combination of labor and capital the firm should use? Explain.
What is the resulting level of output? What is the economic profit? Is this the least costly way of
producing the profitmaximizing output?
Answer:
(a) To answer this question we begin by finding the ratios of the marginal product of each
input to their respective prices for the first unit of each input.
Capital (unit 1): 24/3=8
Labor (unit 1): 11/1=11
Since the ratio is larger for labor we employ the first unit of labor giving us 11 units of
output.
The next step is to calculate the marginal product of labor to price ratio for the second
unit of labor and compare this with the first unit of capital (which we did not select in the
first step).
Capital (unit 1): 24/3=8
Labor (unit 2): 9/1=9
Since the ratio is once again larger for labor we employ the second unit of labor giving us
an additional 9 units of output and a total of 20 (=11 (for the first unit of labor) + 9 (for
the second unit of labor)) .
We continue the process comparing the third unit of labor with the first unit of capital.
Capital (unit 1): 24/3=8
Labor (unit 3): 8/1=8
Here they are equal so we could choose either, or in this case both, to increase output.
Since we now employ the first unit of capital we add 24 units to our total and the third
unit of labor adds 8. This gives is a total of 52 (= 20 (from above) + 24 +8).
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Chapter 12 - The Demand for Resources
Since we are still not at 80 units of output, we continue on down the marginal product of
labor and capital schedules choosing inputs based on the algorithm above.
We will end up employing 2 units of capital and 4 units of labor (the next step in the
process above).
Capital (unit 2): 21/3=7
Labor (unit 4): 7/1=7
Total output is 80 (=52 (from above) + 21 (unit 2 of capital) +7 (unit 4 of labor))
Thus, the least-cost combination is found by equating the marginal product of each input
to their respective prices. Or, employ the product that costs less per unit of output.
(b) To determine the profit maximizing combination of inputs we use the same process
above, except we now need to calculate total cost, total revenue, and profit.
The first step gave us 1 unit of labor and 0 units of capital with 11 units of output. Total
revenue equals $11 and total cost equals $1, which gives us $10 in profit.
Step 2 gave us 2 units of labor and 0 units of capital with 20 units of output. Total
revenue equals $20 and total cost equals $2, which gives us $18 in profit.
Step 3 gave us 3 units of labor and 1 unit of capital with 52 units of output. Total revenue
equals $52 and total cost equals $6 (=$3 (capital) + $3 (3 units of labor)), which gives us
$46 in profit.
Continuing on, Step 4 gives us 4 units of labor and 2 units of capital with 80 units of
output. Total revenue equals $80 and total cost equals $10, which gives us $70 in profit.
This process will continue until we reach 7 units of labor and 7 units of capital with 142
units of output. Total revenue equals $142 and total cost equals $28, with a profit of
$114. You can verify that profit falls adding one more unit of capital or labor.
A less time intensive approach is to recognize that the Marginal Revenue Product (MRP)
for labor and capital equal their respective Marginal Product schedules since the price of
each unit of output is $1. Profit maximization occurs where the Marginal Resource Cost
(MRC) equals Marginal Revenue Product (MRP). Since the MRC is $3 for capital and $1
for labor, equate these values with the MRP for capital and labor. This occurs at 7 units
of capital (MRP=$3=MRC) and 7 units of labor (MRP=$1=MRC). This rule is MRP L/PL
= MRPK/PK =1.
Finally, since MPL/PL = MPL/PL for profit maximization the least-cost rule also applies.
6. In each of the following four cases, MRPL and MRPC refer to the marginal revenue products
of labor and capital, respectively, and PL and PC refer to their prices. Indicate in each case
whether the conditions are consistent with maximum profits for the firm. If not, state which
resource(s) should be used in larger amounts and which resource(s) should be used in smaller
amounts. LO5
a. MRPL = $8; PL = $4; MRPC = $8; PC = $4
b. MRPL = $10; PL = $12; MRPC = $14; PC = $9
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Chapter 12 - The Demand for Resources
c. MRPL = $6; PL = $6; MRPC = $12; PC = $12
d. MRPL = $22; PL = $26; MRPC = $16; PC = $19
Answer: To answer this question use the profit maximization rule MRPL/PL = MRPK/PK
=1.
(a) Use more of both; capital: $8/$4 =2 (more capital) Labor: $8/$4=2 (more labor)
(b) Use less labor and more capital; capital: $14/$9 =1.56 (more capital) Labor:
$10/$12=0.83 (less labor)
(c) Maximum profits obtained; capital: $12/$12 =1 (optimal capital) Labor: $6/$6=1
(optimal labor)
(d) Use less of both; capital: $16/$19 =0.84 (less capital) Labor: $22/$26=0.85 (less
labor)
7. Florida citrus growers say that the recent crackdown on illegal immigration is increasing the
market wage rates necessary to get their oranges picked. Some are turning to $100,000 to
$300,000 mechanical harvesters known as trunk, shake, and catch pickers, which vigorously
shake oranges from the trees. If widely adopted, what will be the effect on the demand for human
orange pickers? What does that imply about the strengths relative of the substitution and output
effects? LO5
Answer: The effect of the adoption of the mechanical pickers will be to decrease the
demand for human pickers. If this occurs, the substitution effect will have been greater
than the output effect.
8. LAST WORD Explain the economics of the substitution of ATMs for human tellers. Some
banks are beginning to assess transaction fees when customers use human tellers rather than
ATMs. What are these banks trying to accomplish?
Answer: These banks are trying to produce using the least cost combination of resources.
Given two resources, labor and capital, the least cost combination requires that the
marginal product per dollar spent on each is equal.
MPLabor MPATM (Capital)
=
PLabor
PATM (Capital)
With the introduction of the highly productive ATM machines, the MP/P of capital was
greater than the MP/P of labor, to regain productive efficiency, (the least cost
combination) the banks had to substitute capital for labor until the ratios are again equal.
MPLabor MPATM (Capital)
<
PLabor
PATM (Capital)
Recall that using more of a resource lowers its marginal product and using less raises it.
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Chapter 12 - The Demand for Resources
PROBLEMS
1. A delivery company is considering adding another vehicle to its delivery fleet, all the vehicles
of which are rented for $100 per day. Assume that the additional vehicle would be capable of
delivering 1500 packages per day and that each package that is delivered brings in ten cents
($.10) in revenue. Also assume that adding the delivery vehicle would not affect any other costs.
LO2
a. What is the MRP? What is the MRC? Should the firm add this delivery vehicle?
b. Now suppose that the cost of renting a vehicle doubles to $200 per day. What are the MRP and
MRC? Should the firm add a delivery vehicle under these circumstances?
c. Next suppose that the cost of renting a vehicle falls back down to $100 per day but, due to
extremely congested freeways, an additional vehicle would only be able to deliver 750 packages
per day. What are the MRP and MRC in this situation? Would adding a vehicle under these
circumstances increase the firms profits?
Answers: (a) The MRP = $150/1 since 1,500 packages at ten cents each will yield $150 per
day in revenue. The MRC = $100/1 since renting the van will add $100 per day to total
costs. Since MRP > MRC, the firm should add this vehicle. (b) The MRP = $150/1; the
MRC = $200/1; the firm should not add this vehicle because MRP < MRC. (c) The MRP =
$75/1; the MRC = $100/1; the firm should not add a vehicle because MRP < MRC.
Feedback: Consider the following example: A delivery company is considering adding
another vehicle to its delivery fleet, all the vehicles of which are rented for $100 per day.
Assume that the additional vehicle would be capable of delivering 1500 packages per day
and that each package that is delivered brings in ten cents ($.10) in revenue.
Part a:
To find the Marginal Revenue Product (MRP) of an additional truck, calculate the
additional revenue this truck will generate for the company. Since the truck delivers 1500
packages and each package generates $0.10 in revenue, the truck generates $150.00 (=
$0.10 x 1500) in total revenue. Thus, the MRP of the truck is $150.00. The Marginal
Resource Cost is the cost of renting the truck for the day, which is $100.00.
Given that the MRP = $150.00 and the MRC = $100.00 (MRP>MRC) you should add
this delivery vehicle.
Part b:
Since the cost of renting the vehicle has doubled, the MRC = $200. The MRP has not
changed and equals $150.00. The company should not add the vehicle (MRP<MRC).
Part c:
Since the cost of renting the vehicle is $100.00 again, the MRC = $100.00. However, the
truck only delivers 750 packages per day now and each package delivered still brings in
ten cents ($.10) in revenue. Thus, the truck generates $75.00 (= $0.10 x 750) in total
revenue. Here the MRP = $75.00. This is less than the MRC so adding the truck would
reduce profits.
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Chapter 12 - The Demand for Resources
2. Suppose that marginal product tripled while product price fell by one half in Table 12.1. What
would be the new MRP values in Table 12.1? What would be the net impact on the location of the
resource demand curve in Figure 12.1? LO2
Answer: MRP values equal: $21, $18, $15, $12, $9, $6, $3; resource demand schedule to
shift to the right.
Feedback: Consider the following scenario: Suppose that marginal product tripled while
product price fell by onehalf in Table 12.1.
New Table:
Units of
Resource
Total Product
(Output)
Marginal
Product (MP)
0
1
2
3
4
5
6
7
0
21
39
54
66
75
81
84
Product Price
Total
Revenue
21
18
15
12
9
6
3
$1
$1
$1
$1
$1
$1
$1
$1
0
$21
$39
$54
$66
$75
$81
$84
Marginal
Revenue
Product
(MRP)
$21
$18
$15
$12
$9
$6
$3
Relative to the original resource demand schedule the new demand schedule will lie to
the right. That is, the scenario above will cause the resource demand schedule to shift to
the right because the Marginal Revenue Product is higher for each unit of the resource.
3. Suppose that a monopoly firm finds that its MR is $50 for the first unit sold each day, $49 for
the second unit sold each day, $48 for the third unit sold each day, and so on. Further suppose that
the first worker hired produces 5 units per day, the second 4 units per day, the third 3 units per
day, and so on. LO3
a. What is the firms MRP for each of the first five workers?
b. Suppose that the monopolist is subjected to rate regulation and the regulator stipulates that it
must charge exactly $40 per unit for all units sold. At that price, what is the firms MRP for each
of the first five workers?
c. If the daily wage paid to workers is $170 per day, how many workers will the unregulated
monopoly demand? How many will the regulated monopoly demand? Looking at those figures,
will the regulated or the unregulated monopoly demand more workers at that wage?
d. If the daily wage paid to workers falls to $77 per day, how many workers will the unregulated
monopoly demand? How many will the regulated monopoly demand? Looking at those figures,
will the regulated or the unregulated monopoly demand more workers at that wage?
e. Comparing your answers to parts c and d, does regulating a monopolys output price always
increase its demand for resources?
Answers: The answers for parts (a) and (b) are included in the following table.
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Chapter 12 - The Demand for Resources
(c) At a daily wage of $170, the unregulated firm will demand 2 workers while the regulated
firm will demand 1 workers. So at that wage, the unregulated firm will demand more
workers.
(d) At a daily wage of $77, the unregulated firm would demand 3 workers while the
regulated firm would demands 4 workers. So at that wage, the regulated firm will demand
more workers
(e) No; the effect depends on resource prices
Feedback: Consider the following example. Suppose that a monopoly firm finds that its
MR is $50 for the first unit sold each day, $49 for the second unit sold each day, $48 for
the third unit sold each day, and so on. Further suppose that the first worker hired
produces 5 units per day, the second 4 units per day, the third 3 units per day, and so on.
Parts a and b:
To find the Marginal Revenue Product for the first unit of labor in the unregulated
economy we need to add up the marginal revenue for each sequential worker given that
the first unit can be sold for $50, the second for $49, and so on.
Since the first worker can produce 5 units and each of these sequential units sell for $50,
$49, $48, $47, and $46, the MRP for the first worker is $240 (=$50+$49+$48+$47+$46).
The second worker can produce 4 units and each of these sequential units sell for $45,
$44, $43, and $42, the MRP for the first worker is $174 (=$45+$44+$43+$42).
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Chapter 12 - The Demand for Resources
The same procedure is applied to the next 3 workers, where the third worker produces 3
units, the fourth 2 units, and the fifth 1 unit. Be sure to reduce the price by $1 for each
additional unit sold.
To find the Marginal Revenue Product for the first unit of labor in the regulated economy
we just multiply the regulated wage, $40, by the number of units this worker produces,
which is 5. Thus, the MRP for this worker is $200.00 (=$40 x 5).
The second worker has an MRP=$160 (=$40 x 4), the third's MRP=$120 (=$40 x 3), and
so on.
All of the values are in the table above for the unregulated and regulated economy.
Part c:
Now assume the daily wage rate is $170.00. The firm will employ additional workers as
long as the Marginal Revenue Product (MPL) is greater than or equal to the Marginal
Resource Cost (MRC). The MRC in this case is $170.00, the wage rate.
Based on this MRC, the unregulated firm will employ the first worker where the
MRP=$240 and the second worker where MRP = $174. This unregulated firm will not
employ the third worker because the MRP = $120. The unregulated firm will demand 2
workers.
We can apply the same process to the regulated firm (price regulated at $40). The
regulated firm will employ the first worker where MRP=$200.00, but will not employ the
second worker because MRP = $160.00. The regulated firm will demand 1 worker.
Thus, the unregulated firm will demand more workers.
Parts d and e:
Now assume the daily wage rate is $77. Using the same logic applied in part c we see that
the unregulated firm will employ the first 3 workers where MRP>MRC=$77. The
regulated firm will employ the first 4 workers where MRP>MRC=$77. In this case the
regulated firm will employ more workers. So we can conclude that regulating a
monopoly does NOT always increase the demand for resources. The direction will
depend on the resource price.
4. Consider a small landscaping company run by Mr. Viemeister. He is considering increasing his
firms capacity. If he adds one more worker, the firms total monthly revenue will increase from
$50,000 to $58,000. If he adds one more tractor, monthly revenue will increase from $50,000 to
$62,000. Additional workers each cost $4000 per month while an additional tractor would also
cost $4000 per month. LO5
a. What is the marginal product of labor? The marginal product of capital?
b. What is the ratio of the marginal product of labor to the price of labor (MP L/PL)?
What is the ratio of the marginal product of capital to the price of capital (MP K/PK)?
c. Is the firm using the leastcostly combination of inputs?
d. Does adding an additional worker or adding an additional tractor yield a larger increase in total
revenue for each dollar spent?
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Chapter 12 - The Demand for Resources
Answers: (a) The MPL = $8,000. The MPK = $12,000. (b) MPL/PL = $8,000/$4,000 = 2.
MPK/PK = $12,000/$4,000 = 3. (c) No because MPK/PK > MPL/PL. (d) Because 3 > 2, total
revenue is increased more by spending money on an additional tractor rather than an
additional worker.
Feedback: Consider the following example: If Mr. Viemeister adds one more worker, the
firms total monthly revenue will increase from $50,000 to $58,000. If he adds one more
tractor, monthly revenue will increase from $50,000 to $62,000. Additional workers
would cost $4000 per month while an additional tractor would cost $4000 per month.
Part a:
The marginal (revenue) product of labor is $8,000. This is the increase in total revenue
generated by the additional worker (=$58,000-$50,000).
The marginal product of capital can be found the same way. The change in total revenue
generated by the additional tractor is $12,000 (=$62,000-$50,000), which equals the
Marginal Product of Capital.
So we have:
MPL=$8,000 and MPK=$12,000
Part b:
The ratio of the Marginal Product of Labor to the price of labor is:
MPL/PL = $8,000/$4,000 = 2
The ratio of the Marginal Product of Capital to the price of labor is:
MPK/PK = $12,000/$4,000 = 3
Part c:
Since MPK/PK = 3 > MPL/PL = 2, this is not the least-cost combination of inputs.
Part d:
The landscaping firm should invest in an additional tractor. This will generate more
revenue per dollar (compared to labor).
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