A.7 Choosing Inputs
Review Questions
Lesson Topics
Profit Maximization (3) through choosing each
input into production balances the value of the
marginal product of each input with the marginal cost
of each input.
Cost Minimization (7) balances the marginal
product per dollar invested into an input across all
inputs. Cost minimization makes the most of the
resources devoted to charity.
Cost Measures including total cost and marginal
cost are alternatives to productivity measures to help
firms chose output to maximize profit. They also
determine when it is best to shut down production.
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A.7 Choosing Inputs
Review Questions
Profit Maximization
Question. You are a manager of a firm that sells
cotton at a price of $0.50 per pound. Renting one
more cotton gin machine (see picture) will increase
your firm's output by 200 units per day. Employing one
more full-time worker will increase your firm's output by 100 units per day.
a. What is the most you should be willing to pay to rent one more cotton gin
machine for one day?
b. What determines whether or not you actually have to offer that much to
the owner of the machine to induce him to rent his machine to your firm?
Explain your answers.
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A.7 Choosing Inputs
Review Questions
Answer to Question:
a. The extra revenue you will earn by renting the machine is 200 × $0.50 =
$100 per day. The most you should pay for the machine is $100 per day.
b. How much you have to offer the owner of the machine to induce him to
rent his machine to your firm depends on how much that owner can get
from other firms (his opportunity cost), and depends on the rules for
bargaining. For instance, if his opportunity cost is $60 per day and if you
can make him a take-it-or-leave-it offer, then you will only have to pay
$60.01 to get him to rent to you because he faces the choice between
$60.01 renting to you versus $60 renting to some other firm.
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A.7 Choosing Inputs
Review Questions
Profit Maximization
Question. The A-1 Corporation supplies airplane
manufacturers with preformed sheet metal panels that
are used on the exterior of aircraft. Manufacturing
these panels requires only five sheet metal-forming
machines, which cost $300 each, and workers. These workers can be
hired on an as-needed basis in the labor market at $7,000 each. Given the
simplicity of the manufacturing process, the preformed sheet metal panel
market is perfectly competitive. Therefore, the market price for one of A-1’s
panels is a constant, $50. Based on the production data in the following
table, how many workers should A-1 hire to maximize its profits?
Workers
Output
0
0
5
1
600
5
2
1,000
5
3
1,290
5
4
1,480
5
5
1,600
5
6
1,680
Machines
5
4
A.7 Choosing Inputs
Review Questions
Answer to Question: To maximize profits the firm should continue
adding workers so long as the value marginal product of labor exceeds the
wage. The value marginal product of labor is defined as the marginal
product of labor times the price of output. Here, output sells for $50 per
panel, so the value marginal product of the third worker is $50(290) =
$14,500. The table below summarizes the VMPL for each choice of labor.
Since the wage is $7,000, the profit maximizing number of workers is 4.
Workers
Output
MPL
VMPL
Wage
0
0
–
–
–
5
1
600
600
$30,000
$7,000
5
2
1,000
400
$20,000
$7,000
5
3
1,290
290
$14,500
$7,000
5
4
1,480
190
$9,500
$7,000
5
5
1,600
120
$6,000
$7,000
5
6
1,680
80
$4,000
$7,000
Machines
5
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A.7 Choosing Inputs
Review Questions
Profit Maximization
Question. You are a manager of a firm that sells
output at a price of $40 per unit. Renting one more
unit of capital will increase your firm's output by 4,000
units per year. Employing one more full-time worker
will increase your firm's output by 2,000 units per year. Several other firms
also are interested in hiring this worker.
a. What is the most you should be willing to pay this full-time worker to
come to your firm?
b. What determines whether or not you actually have to offer this much to
the worker to induce him to join your firm?
Explain your answers.
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A.7 Choosing Inputs
Review Questions
Answer to Question:
a. The extra revenue you will earn by hiring the worker is 2,000 × $40 =
$80,000 per year. The most you should pay the worker is an annual salary
of $80,000.
b. How much you have to offer this worker to induce him to join your firm
depends on how much the worker can get from other firms (his opportunity
cost) and the rules for bargaining. For instance, if his opportunity cost is
$60,000 and if you can make him a take-it-or-leave-it offer, then you will
only have to pay $60,000.01 to get him because he faces the choice
between $60,000.01 working for you versus $60,000 working for some
other firm.
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Each of the following review questions apply the
theory of Cost Minimization to the managerial decision
of how best to select labor and capital inputs for given
input costs.
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Question. Fourteen McDonalds in Oregon and
southeastern Washington have been linked to the
call center operated by SEI-CCS Inc., a Fargo,
N.D.-based company that works closely with
McDonald's. The call taker in Grand Forks enters your order into a
computer and relays it back to the home restaurant, where it pops up on a
screen in the kitchen. Meanwhile, a digital camera photographs your car as
you drive through. The photo pops up on a separate screen next to the
order at the drive-through cashier's window to match the order with the car.
The reason for outsourcing is that Oregon and Washington state have
minimum wages of $8.55 per hour, which is higher than Federal minimum
wages, but North Dakota has minimum wages of $7.25 per hour, which
equals Federal minimum wages
Let’s see how decreasing the cost of hiring handicapped and unskilled
workers would affect the McDonald’s Corporation.
McDonald’s currently uses 290,000 handicapped and unskilled workers
and 140,000 semiskilled workers to produce fast food in the United States.
McDonald’s pays the unskilled workers state minimum wages of $7.25 per
hour, down from $8.55 per hour, but the semiskilled workers $14.50 per
hour.
Predict the implications of decreasing the wage of handicapped and
unskilled workers from $8.55 to $7.25 on your company’s optimal mix of
inputs in the short run (when you cannot adjust your capital) and in the long
run (when you can adjust your capital).
Hint: Remember to state any assumptions needed to make your
predictions.
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A.7 Choosing Inputs
Review Questions
Answer to Question: In the short run, a lower wage paid to handicapped
and unskilled labor makes
MPU/wU > MPS/wS (since wU decreases),
which implies that to minimize costs the firm should decrease its use of
semi-skilled worker (S) and increase its use of handicapped and unskilled
workers (U) to produce the same fixed level of output. In the longer run, to
produce the same fixed level of output, the company will also substitute
labor for capital (invest in fewer machines to replace labor) assuming
capital is a substitute with handicapped and unskilled labor.
This answer assumes you keep the level of output fixed. (We also assume
that the optimal mix of unskilled and semi-skilled labor was being used at
the time of the decrease in the wage, but that is what we assume in every
problem unless we are given explicit data to the contrary.)
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Question. Minimum Wage Stuck in the 1950s
Op-ed by Holly Sklar
Distributed by McClatchy Tribune News Service, July
23, 2009
Are you better off than you were 40 years ago? Not if you're a minimum
wage worker. It would take $9.92 today to match the buying power of the
minimum wage at its peak in 1968, the year Martin Luther King died fighting
for living wages for sanitation workers. Let’s see how increasing the
national minimum wage from $7.25 to $9.92 would affect the Coca-Cola
Company.
The Coca-Cola Company’s currently uses 1,689 unskilled workers and
6,832 semiskilled workers to produce and ship Coke Zero worldwide. The
Coca-Cola Company pays the unskilled workers minimum wages, but the
semiskilled workers $15.87 per hour.
Predict the implications of increasing the national minimum wage from
$7.25 to $9.92 on your company’s optimal mix of inputs in the short run
(when you cannot adjust your capital) and in the long run (when you can
adjust your capital).
Tip: State any assumptions needed to make your predictions.
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A.7 Choosing Inputs
Review Questions
Answer to Question: In the short run, a higher minimum wage paid to
unskilled labor makes
MPU/wU < MPS/wS,
which implies that to minimize costs the retailer should increase its use of
semi-skilled worker (S) and decrease its use or unskilled workers (U) to
produce the same fixed level of output. In the longer run, to produce the
same fixed level of output, the company will also substitute capital for labor
(invest in some machines to automate a portion of your boxing needs)
assuming unskilled labor and capital are substitutes.
This answer assumes you keep the level of output fixed. (We also assume
that the optimal mix of unskilled and semi-skilled labor was being used at
the time of the increase in the minimum wage, but that is what we assume
in every problem unless we are given explicit data to the contrary.)
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Question. You are the manager of a firm that
currently uses 17 unskilled workers and 6 semiskilled
workers to ship products that you sell online. Your
company pays the unskilled workers minimum wages,
but the semiskilled workers $15 per hour. You read an article in The Wall
Street Journal that the House of Representatives passed legislation that
would increase minimum wages.
Discuss the implications of this legislation on your company’s optimal mix
of inputs in the short run (when you cannot adjust your capital) and in the
long run (when you can adjust your capital).
Tip: State any assumptions needed to make your predictions.
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A.7 Choosing Inputs
Review Questions
Answer to Question: In the short run, a higher minimum wage paid to
unskilled labor makes
MPU/wU < MPS/wS,
which implies that to minimize costs the retailer should increase its use of
semi-skilled worker (S) and decrease its use or unskilled workers (U) to
produce the same fixed level of output. In the longer run, to produce the
same fixed level of output, the company will also substitute capital for labor
(invest in some machines to automate a portion of your boxing needs)
assuming unskilled labor and capital are substitutes.
This answer assumes you keep the level of output fixed. (We also assume
that the optimal mix of unskilled and semi-skilled labor was being used at
the time of the increase in the minimum wage, but that is what we assume
in every problem unless we are given explicit data to the contrary.)
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Each of the following review questions apply the
theory of Cost Minimization to the public policy
decision of how best to help the disabled or
unemployed.
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Question. Consider a handicapped person that
values his own time at $9 per hour. Suppose In-NOut Burger and McDonalds and Burger King each
value employing the handicapped person at $7 per
hour, for 40 hours per week. Discuss the implications of the government
subsidizing the handicapped worker’s employment by giving any employer
$3 per hour.
In particular, does the subsidy increase the employment of the
handicapped person? Does the subsidy increase the happiness of the
handicapped person? Is the subsidy a good idea?
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A.7 Choosing Inputs
Review Questions
Answer to Question: Without the subsidy, the handicapped person is not
working since he values his time more than potential employers.
With the subsidy of $3 per hour, competition among multiple employers
means the handicapped person will be offered work at the highest wage
that is profitable for the employer. That is the wage of $10 per hour since
$10 minus the subsidy of $3 means the employer pays a net wage of $7,
which is the value of employing the handicapped person. So, the subsidy
increases the employment of the handicapped person, from 0 to the new
level of 40 hours per week.
Does the subsidy increase the happiness of the handicapped person?
Yes, he sells his time for $10 per hour and he values it at $9 per hour, and
so gains $1 per hour, which amounts to $40 per week of gain.
Is the subsidy a good idea? No. The subsidy benefits the handicapped
person $40 per week, but it costs taxpayers $3x40 = $120 per week. Both
the handicapped person and taxpayers would be better off (and the
potential employers would not care) if the handicapped person did not
receive the wage subsidy but, instead, received $80 per week (or any
amount between $40 and $120) in welfare.
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Each of the following review questions apply the
theory of Cost Minimization to the managerial decision
of how best to run a charity.
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Question. You have been hired to replace the
manager of the Toys for Tots charity that uses only
two inputs, labor and capital, to produce and distribute
toys to poor children. The charity can hire as much
labor as it wants at a wage of $5 per hour and can rent as much capital as
it wants at a price of $5 per hour. After you look at the company books, you
learn that the charity has been using labor and capital in amounts that
imply a marginal product of labor of 50 and a marginal product of capital of
100.
a. Is the charity running right? Explain. b. How can the charity be
improved? Explain. c. What do Microeconomic assumptions imply about
the effectiveness of giving toys to poor children? Explain.
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A.7 Choosing Inputs
Review Questions
Answer to Question:
a. Is the charity running right?
Answer: Currently,
(marginal rate of labor / wage) = 50 / 5 = 10
(marginal rate of capital / rental rate) = 100 / 5 = 20
Since those numbers are different, the firm is not minimizing the cost of
producing its current level (call it Q) of toys.
b. How can the charity be improved?
Answer: Since the marginal product per dollar is lower for labor, the firm
should use less labor and more capital in order to minimize costs of
producing Q toys. There is not enough information to figure out how many
toys Q to produce and distribute.
c. What do Microeconomic assumptions imply about the effectiveness
of giving toys to poor children?
Answer:
1. If “poor” children are in families lead by rational people, then giving
away toys probably makes the poor family less happy than giving
away the cash value of the toys. Toys for Tots is thus not as
effective as “Cash” for Tots.
2. If children are treated as commodities to be chosen like cars, then
having a lot of children does not make a family poor. Calling a family
with a $12,000 yearly income poor if there are 5 kids and not poor if
there are no kids makes as much sense as calling a family poor if
they bought nice cars. Cash for Tots is thus not as effective as Cash
for “Poor People”.
3. Sometimes having a low income is a choice of leisure over other
commodities. So when giving Cash to Poor People you should make
sure you are not including people that have little income but a lot of
leisure time (like Huckleberry Finn wearing rags but happy to float
down the Mississippi river).
Comment: Using too much labor is a common mistake for charities that get
volunteer labor. They could produce more output if they asked some of
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A.7 Choosing Inputs
Review Questions
their volunteers to work extra hours at their day jobs and donate their extra
income, which the charity can then use to rent extra capital.
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A.7 Choosing Inputs
Review Questions
Cost Minimization
Question. Operation Christmas Child was created in
1990 by Dave and Jill Cooke for children in Romania.
Each November thousands of churches, groups and
individual donors prepare and collect shoeboxes filled
with toys to send to poor children in East Asia.
You have been hired to the current manager of Operation Christmas Child
charity that uses only two inputs, labor and capital, to produce and
distribute toys to poor children in East Asia. The charity can hire as much
labor as it wants at a wage of $8 per hour and can rent as much capital as
it wants at a price of $15 per hour. After you look at the company books,
you learn that the charity has been using labor and capital in amounts that
imply a marginal product of labor of 40 and a marginal product of capital of
60.
a. Is the charity running right? Explain.
b. How can the charity be improved? Explain.
c. What do Microeconomic assumptions imply about the effectiveness of
giving toys to poor children? Explain.
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A.7 Choosing Inputs
Review Questions
Answer to Question:
a. Is the charity running right?
Answer: Currently,
(marginal rate of labor / wage) = 40 / 8 = 5
(marginal rate of capital / rental rate) = 60 / 15 = 4
Since those numbers are different, the firm is not minimizing the cost of
producing its current level (call it Q) of toys.
b. How can the charity be improved?
Answer: Since the marginal product per dollar is higher for labor, the firm
should use more labor and less capital in order to minimize costs of
producing Q toys. There is not enough information to figure out how many
toys Q to produce and distribute.
c. What do Microeconomic assumptions imply about the effectiveness
of giving toys to poor children?
Answer:
1. If “poor” children are in families lead by rational people, then giving
away toys probably makes the poor family less happy than giving
away the cash value of the toys. Toys for Children is thus not as
effective as “Cash” for Children.
2. If children are treated as commodities to be chosen like cars, then
having a lot of children does not make a family poor. Calling a family
with a $12,000 yearly income poor if there are 5 kids and not poor if
there are no kids makes as much sense as calling a family poor if
they bought nice cars. Cash for Children is thus not as effective as
Cash for “Poor People”.
3. Sometimes having a low income is a choice of leisure over other
commodities. So when giving Cash to Poor People you should make
sure you are not including people that have little income but a lot of
leisure time (like Huckleberry Finn wearing rags but happy to float
down the Mississippi river).
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