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Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISIONS
Multiple Choice
3-1 A firm will maximize profit by producing that level of output at which
a. the additional revenue from the last unit sold exceeds the additional cost of the last unit
by the largest amount.
b. the additional revenue from the last unit sold equals the additional cost of the last unit.
c. total revenue exceeds total cost by the largest amount.
d. total revenue equals total cost.
e. both b and c
3-2 The function a decision maker seeks to maximize or minimize is the ________ function.
a. optimal
b. decision-making
c. objective
d. marginal
e. none of the above
3-3 Choice variables
a. determine the value of the objective function
b. determine the constraint
c. can only take on integer values
d. cannot be continuous
e. both c and d
3-4 For an unconstrained maximization problem
a. the decision maker seeks to maximize net benefits.
b. the decision maker seeks to maximize total benefits.
c. the decision maker does not take cost into account because there is no constraint.
d. the decision maker does not take the objective function into account because there is no
constraint.
e. none of the above
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-5 When marginal cost is greater than marginal benefit at the current activity level, the decision
maker can increase net benefit by decreasing the activity because
a. total benefit will rise by more than total cost will rise.
b. marginal cost is rising faster than marginal benefit is falling.
c. net benefit is upward sloping at this point.
d. total cost will fall by more than total benefit will fall.
3-6 For a constrained minimization problem, the decision maker
a. is constrained by the specific amount of total benefits.
b. is constrained by the choice set of values for the activities.
c. seeks to minimize the cost of achieving a specific goal.
d. all of the above
e. none of the above
3-7 A continuous choice variable
a. must be continuously varied to attain the goal.
b. can take on only special values between two end points.
c. is in unconstrained but not constrained problems.
d. all of the above
e. none of the above
3-8 An agency is having problems with personal phone calls made during working hours. Each
minute of a personal call costs the agency $0.50 in wasted wages. The agency hires operators to
monitor calls in order to attain the optimal number of personal calls (minimize total cost of
personal calls).
Total minutes of
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
Number of
Operators
personal calls (per
hour)
0
600
1
480
2
410
3
370
4
350
Based on the above information, if operators receive $25 an hour, how many operators should the
agency hire?
a. 0
b. 1
c. 2
d. 3
e. 4
3-9 An agency is having problems with personal phone calls made during working hours. Each
minute of a personal call costs the agency $0.50 in wasted wages. The agency hires operators to
monitor calls in order to attain the optimal number of personal calls (minimize total cost of
personal calls).
Number of
Operators
Total minutes of
personal calls (per
hour)
0
600
1
480
2
410
3
370
4
350
Based on the above information, if operators receive $25 an hour, what is the minimum possible
total cost of personal calls (per hour)?
a. $460
b. $255
c. $120
d. $ 85
e. none of the above
3-10 An agency is having problems with personal phone calls made during working hours. Each
minute of a personal call costs the agency $0.50 in wasted wages. The agency hires operators to
monitor calls in order to attain the optimal number of personal calls (minimize total cost of
personal calls).
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
Number of
Operators
Total minutes of
personal calls (per
hour)
0
600
1
480
2
410
3
370
4
350
Based on the above information, what is the most the agency would be willing to pay the first
operator?
a. $480
b. $300
c. $240
d. $120
e. none of the above
3-11 Refer to the figure below, which shows marginal benefits (MB) and marginal cost (MC) of
activity A:
100 200 300 400 500
0
10
20
30
40
Marginal benefit and cost (dollars)
Activity A
A
$
MC
MB
If the decision maker is choosing 200 units of activity A,
a. this level maximizes net benefits.
b. the activity could be reduced by one unit and net benefits will increase by $10.
c. the activity could be increased by one unit and net benefits will increase by $10.
d. the activity could be increased by one unit and net benefits will increase by $25.
e. the activity could be reduced by one unit and net benefits will increase by $15.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-12 Refer to the figure below, which shows marginal benefits (MB) and marginal cost (MC) of
activity A:
100 200 300 400 500
0
10
20
30
40
Marginal benefit and cost (dollars)
Activity A
A
$
MC
MB
If the decision maker is choosing 400 units of activity A,
a. this level maximizes net benefits.
b. the activity could be reduced by one unit and net benefits will increase by $10.
c. the activity could be reduced by one unit and net benefits will rise by $25.
d. the activity could be increased by one unit and net benefits will increase by $15.
e. the activity could be reduced by one unit and net benefits would decrease by $10.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-13 Refer to the figure below, which shows marginal benefits (MB) and marginal cost (MC) of
activity A:
100 200 300 400 500
0
10
20
30
40
Marginal benefit and cost (dollars)
Activity A
A
$
MC
MB
If the decision maker is choosing 300 units of activity A,
a. this level maximizes net benefits.
b. if the activity is increased by one unit, net benefits will increase by $20.
c. if the activity is decreased by one unit, net benefits will decrease by $20.
d. both b and c
e. all of the above
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-14 A manager in charge of new product development can hire engineers and market researchers.
The annual salary of an engineer is $40,000 while a market researcher receives $20,000. The
marginal contribution of engineers and market researchers are:
Engineers (E)
Market Researchers (R)
Worker
Additional
New Products
Worker
Additional
New Products
1st
240
1st
80
2nd
200
2nd
70
3rd
160
3rd
60
4th
100
4th
50
5th
40
5th
40
Based on the above information, how should a manager with an annual budget of $140,000,
allocate this budget in order to maximize the number of new products developed?
a. Hire one engineer and five market researchers
b. Hire two engineers and three market researchers
c. Hire three engineers and one market researcher
d. Hire four engineers and four market researchers
3-15 A manager in charge of new product development can hire engineers and market researchers.
The annual salary of an engineer is $40,000 while a market researcher receives $20,000. The
marginal contribution of engineers and market researchers are:
Engineers (E)
Market Researchers (R)
Worker
Additional
New Products
Worker
Additional
New Products
1st
240
1st
80
2nd
200
2nd
70
3rd
160
3rd
60
4th
100
4th
50
5th
40
5th
40
Based on the above information, if the manager has an annual budget of $140,000 and currently is
hiring two engineers and three market researchers, then
a. the last dollar spent on an engineer yielded more new products than the last dollar spent
on a market researcher.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
b. the last dollar spent on a market researcher yielded more new products than the last dollar
spent on an engineer.
c. he is making the correct decision because engineers make more than market researchers.
d. he is making the correct decision because the last market researcher hired was more
productive than the last engineer hired.
3-16 A manager in charge of new product development can hire engineers and market researchers.
The annual salary of an engineer is $40,000 while a market researcher receives $20,000. The
marginal contribution of engineers and market researchers are:
Engineers (E)
Market Researchers (R)
Worker
Additional
New Products
Worker
Additional
New Products
1st
240
1st
80
2nd
200
2nd
70
3rd
160
3rd
60
4th
100
4th
50
5th
40
5th
40
Based on the above information, how should a manager with an annual budget of $240,000,
allocate this budget in order to maximize the number of new products developed?
a. Hire three engineers and four market researchers.
b. Hire three engineers and five market researchers.
c. Hire five engineers and two market researchers.
d. Hire four engineers and four market researchers.
3-17 The decision rule for constrained optimization is to select the level for each activity at which
a. marginal benefit equals marginal cost for each activity.
b. total benefit equals total cost for each activity.
c. marginal benefit per dollar of marginal cost is equal across all activities.
d. total benefit per dollar of total cost is equal across all activities.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-18 A student taking economics, statistics, and finance has decided to spend 9 hours per week
studying. The objective is to maximize the average grade, which means maximizing the total
grade in the three courses. The table shows the student's estimate of the relation between time
spent studying each course and the grade for each course.
Grade In
Hours of Study
Economics
Statistics
Finance
0
50
42
56
1
62
54
68
2
71
64
76
3
79
72
82
4
85
80
87
5
88
84
90
6
90
87
93
7
92
89
95
Based on the above information, how should the student allocate her time?
a. 3 hours economics, 4 hours statistics, 2 hours finance
b. 3 hours economics, 3 hours statistics, 3 hours finance
c. 4 hours economics, 3 hours statistics, 2 hours finance
d. 3 hours economics, 2 hours statistics, 4 hours finance
3-19 A student taking economics, statistics, and finance has decided to spend 9 hours per week
studying. The objective is to maximize the average grade, which means maximizing the total
grade in the three courses. The table shows the student's estimate of the relation between time
spent studying each course and the grade for each course.
Grade In
Hours of Study
Economics
Statistics
Finance
0
50
42
56
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
1
62
54
68
2
71
64
76
3
79
72
82
4
85
80
87
5
88
84
90
6
90
87
93
7
92
89
95
Based on the above information, what is the maximum AVERAGE grade the student can earn if
she studies 9 hours per week?
a. 80
b. 80.3
c. 82
d. 78.3
3-20 Use the following marginal benefit and marginal cost functions for activity A:
MB = 100 − 5A
MC = 20 + 3A
The optimal level of A is
a. 40
b. 30
c. 20
d. 10
e. 0
3-21 Use the following marginal benefit and marginal cost functions for activity A:
MB = 100 − 5A
MC = 20 + 3A
The fifth unit of activity A will
a. increase net benefits by 75.
b. reduce net benefits by 35.
c. increase net benefits by 40.
d. decrease net benefits by 40.
e. reduce net benefits by 75.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-22 In order to minimize the net cost of pollution reduction, the level of pollution reduction (the
amount of a pollutant not released into the environment) should be the level at which
a. the marginal benefit of reducing pollution exceeds the marginal cost of reducing pollution
by the greatest possible amount.
b. the total benefit of reducing pollution equals the total cost of reducing pollution.
c. the marginal benefit of reducing pollution equals the marginal cost of reducing pollution.
d. the total cost of reducing pollution is minimized and the total benefits of reducing
pollution are maximized.
3-23 When the choice variable is a continuous variable, the decision rule for an unconstrained
maximization problem is:
a. If MB > MC, increase the activity.
b. If MB < MC, decrease the activity.
c. Choose the activity so that MB = MC.
d. all of the above
e. none of the above
3-24 If profits depend on both how much is produced (output) and on the level of advertising, then a
profit-maximizing firm should choose the levels of output and advertising at which
a. the marginal revenue of output equals the marginal cost of output.
b. the addition to total revenue of the last unit of advertising equals the addition to total cost
of the last unit of advertising.
c. total revenue equals total cost for both output and advertising.
d. both a and b
e. both b and c
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-25 Gigi consumes only Perrier and cheese. In order to maximize her happiness subject to limited
income, Gigi should purchase the amounts of Perrier and cheese at which
a. the addition to happiness of the last bottle of Perrier is the same as the addition to
happiness of the last pound of cheese.
b. the addition to happiness per dollar spent on Perrier is the same as the addition to
happiness per dollar spent on cheese.
c. she spends all her income.
d. both b and c
e. both a and c
3-26 A firm is deciding whether or not to close down its plant and modernize by installing new
technology. Which of the following should management ignore when making the decision?
a. How much the present plant cost
b. Cost of lost sales while the plant is closed
c. Added cost of the labor needed for the new plant
d. All of the above
3-27 In making a decision about whether to increase its advertising budget the firm management
should not consider
a. the added revenue from increased sales.
b. the added cost of producing more goods for sale.
c. interest payments on the firm’s loan.
d. the cost of the increased advertising.
e. none of the above
3-28 Which of the following statements represents bad decision making?
a. I’ve already spent 3 years in the college so I can’t drop out and go to work now.
b. I’ve already paid for the ticket so I might as well stay to the end.
c. I’ve put in so much time on this paper, I can’t quit now.
d. My stock has dropped $10 a share so I can’t afford to sell it now.
e. all of the above.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-29 A firm can maximize profit (net benefit) by choosing to produce that level of output at which
a. the difference between the additional revenue from the last unit sold and the additional
cost of that unit is maximized.
b. the additional revenue from the last unit sold equals the additional cost of that unit.
c. the additional revenue from the last unit sold is just a little more than the additional cost
of that unit.
d. total revenue equals total cost.
3-30 A clinic uses doctors and nurses optimally and is servicing the maximum number of patients
given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while
the last nurse hired treated 1,000 extra patients in a year. If doctors make $40,000 a year, what do
nurses make?
a. $25,000 a year
b. $20,000 a year
c. $15,000 a year
d. $10,000 a year
3-31 A clinic uses doctors and nurses optimally and is servicing the maximum number of patients
given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while
the last nurse hired treated 1,000 extra patients in a year. If doctors make $80,000 a year and
nurses make $40,000 a year, then
a. the clinic could serve more patients by hiring more doctors and fewer nurses.
b. the clinic could serve more patients by hiring fewer doctors and more nurses.
c. the clinic is making the correct decision because doctors are more productive than nurses.
d. the clinic is not making the correct decision because the additional patients per dollar
spent on doctors is greater than the additional patients per dollar spent on nurses.
e. both a and d.
3-32 A clinic uses doctors and nurses optimally and is servicing the maximum number of patients
given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
the last nurse hired treated 1,000 extra patients in a year. If doctors make $50,000 a year and
nurses make $40,000 a year, then
a. the clinic could serve more patients by hiring more doctors and fewer nurses.
b. the clinic could serve more patients by hiring fewer doctors and more nurses.
c. the clinic is making the correct decision.
d. the clinic is not making the correct decision because the additional patients per dollar
spent on doctors is greater than the additional patients per dollar spent on nurses.
e. a and d
3-33 A clinic uses doctors and nurses optimally and is servicing the maximum number of patients
given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while
the last nurse hired treated 1,000 extra patients in a year. If doctors make $64,000 a year and
nurses make $40,000 a year, then
a. the clinic could serve more patients by hiring more doctors and fewer nurses.
b. the clinic could serve more patients by hiring fewer doctors and more nurses.
c. the clinic is making the correct decision.
d. the clinic is not making the correct decision because the additional patients per dollar
spent on doctors is greater than the additional patients per dollar spent on nurses.
e. a and d
3-34 In order to minimize the NET costs associated with crime,
a. steps must be taken to eliminate all crime.
b. crime should be reduced to the level at which the total benefit from crime equals the total
cost of crime prevention.
c. crime should be reduced to the level at which the marginal cost from crime equals the
marginal cost of crime prevention.
d. no crime should be eliminated.
3-35 The optimization rule for unconstrained optimization is to select that level of activity at which
a. marginal benefit equals marginal cost.
b. total benefit is less than total cost.
c. total benefit is equal to total cost.
d. marginal benefit exceeds marginal cost.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-36 Whenever the additional revenue from the last unit of output exceeds the additional cost of that
unit, a profit-maximizing firm should
a. do nothing, the firm is making profits.
b. produce less in order to increase profits.
c. produce more in order to increase profits.
d. think about investing in another industry.
3-37 A toy manufacturer is experiencing quality problems on its assembly line. Every defective toy
that leaves the factory costs the firm $20. The firm has decided to hire quality inspectors to catch
defective toys before they leave the factory.
Number of
Inspectors
Number of Defective
Toys (per day)
0
40
1
24
2
16
3
10
4
6
5
2
6
0
Given the above information, if each inspector is paid $100 a day, how many inspectors should
the firm hire to minimize the total cost of defective toys?
a. 3
b. 4
c. 5
d. 6
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-38 A toy manufacturer is experiencing quality problems on its assembly line. Every defective toy
that leaves the factory costs the firm $20. The firm has decided to hire quality inspectors to catch
defective toys before they leave the factory.
Number of
Inspectors
Number of Defective
Toys (per day)
0
40
1
24
2
16
3
10
4
6
5
2
6
0
Given the above information, if the cost of each defective toy rises to $50, while inspectors are
paid $150 a day, how many inspectors should the firm hire?
a. 3
b. 4
c. 5
d. 6
3-39 Gonzo consumes only two things--coke and hot dogs. We can define the addition to "happiness"
of consuming an additional coke as the marginal utility of coke and that for hot dogs as the
marginal utility of hot dogs. The prices of coke and hot dogs are fixed and Gonzo has a limited
budget. To maximize "happiness" subject to his limited budget, Gonzo should purchase coke and
hot dogs so that
a. the marginal utility of coke is the same as the marginal utility of hot dogs.
b. he spends the same amount on coke as on hot dogs.
c. the addition to happiness of the last coke is the same as the addition to happiness of the
last hot dog.
d. the addition to happiness per dollar spent on coke is the same as the addition to happiness
per dollar spent on hot dogs.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-40 A manager in charge of new product development can hire engineers and market researchers.
The annual salary of an engineer is $30,000 and that of a market researcher is $20,000. The
marginal contribution of engineers and market researchers are
Engineers (E)
Market Researchers (R)
Worker
Additional
New Products
Worker
Additional
New Products
1st
50
1st
30
2nd
30
2nd
25
3rd
15
3rd
20
4th
10
4th
15
5th
8
5th
10
Given the above information, if the manager has an annual budget of $120,000, how should this
budget be allocated in order to maximize the number of new products developed?
a. Hire two engineers and one market researcher.
b. Hire two engineers and three market researchers.
c. Hire three engineers and two market researchers.
d. Hire three engineers and four market researchers.
3-41 A manager in charge of new product development can hire engineers and market researchers.
The annual salary of an engineer is $30,000 and that of a market researcher is $20,000. The
marginal contribution of engineers and market researchers are
Engineers (E)
Market Researchers (R)
Worker
Additional
New Products
Worker
Additional
New Products
1st
50
1st
30
2nd
30
2nd
25
3rd
15
3rd
20
4th
10
4th
15
5th
8
5th
10
Given the above information, if the manager currently has two engineers and one market
researcher, what must be true?
a. He is making the correct decision because
E R
MP MP=
.
b. He is not making the correct decision because
E E R R
/ /MP P MP P>
.
c. Fewer new products will be developed if he hires fewer engineers and more market
researchers.
d. More new products will be developed if he hires fewer engineers and more market
researchers.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-42 A clinic uses doctors and nurses to serve the maximum number of patients given a limited annual
payroll. The clinic currently has 10 doctors and 30 nurses. The last doctor hired can serve 300
additional patients, while the last nurse hired can serve 200 additional patients. If doctors make
$60,000 a year and nurses make $20,000 a year, the clinic
a. is making the correct hiring decision because doctors are more productive than nurses.
b. is making the correct hiring decision because doctors are paid more than nurses.
c. could serve more patients with the same payroll by hiring more doctors and fewer nurses.
d. could serve more patients with the same payroll by hiring more nurses and fewer doctors.
3-43 The optimal level of pollution reduction is that level at which
a. the total benefits of pollution reduction exceeds the total cost of pollution reduction by
the largest amount.
b. the total benefits of pollution reduction equal the total cost of pollution reduction.
c. the marginal benefit of pollution reduction exceeds the marginal cost of pollution
reduction by the largest amount.
d. the additional benefit of the last unit of pollution reduction equals the additional cost of
the last unit of pollution reduction.
e. both a and d
3-44 A Blue Ribbon Committee has decided that acid rain should be reduced and is trying to determine
the optimal level of reduction. There are benefits from reducing acid rain (more wildlife and
forests, better health, etc.), but there are also costs. The committee estimates that the marginal
benefit of each unit of reduction is $1,400 − 5R, where R is units of reduction, and the marginal
cost is 2R. If the committee wants to maximize the net benefit from reducing acid rain, what is
marginal cost at the optimal level of reduction?
a. $ 10
b. $ 20
c. $100
d. $200
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-45 A Blue Ribbon Committee has decided that acid rain should be reduced and is trying to determine
the optimal level of reduction. There are benefits from reducing acid rain (more wildlife and
forests, better health, etc.), but there are also costs. The committee estimates that the marginal
benefit of each unit of reduction is $700 − 5R, where R is units of reduction, and the marginal
cost is 2R. If the committee wants to maximize the net benefit from reducing acid rain, what is the
optimal level of pollution reduction?
a. 10
b. 20
c. 100
d. 200
3-46 If profits depend on both how much is produced (output) and the level of quality, then a profit-
maximizing firm should choose the levels of output and quality at which
a. The marginal revenue of output exceeds the marginal cost of output by the largest
amount.
b. The marginal revenue of quality exceeds the marginal cost of quality by the largest
amount.
c. The difference between the addition to total revenue and the addition to total cost of the
last units of output and quality is the greatest.
d. both a and b
e. none of the above
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-47 A manager in charge of new product development can hire engineers and market researchers.
The annual salary of an engineer is $40,000, while a market researcher receives $20,000. The
marginal contributions of engineers and market researchers are:
Engineers (E)
Market Researchers (R)
Worker
Additional
New Products
Worker
Additional
New Products
1st
50
1st
20
2nd
40
2nd
15
3rd
30
3rd
10
4th
20
4th
5
5th
10
5th
2
Based on the above information, how should the manager with an annual budget of $160,000,
allocate this budget in order to maximize the number of new products developed?
a. Hire 2 engineers and 1 market researcher.
b. Hire 3 engineers and 2 market researchers.
c. Hire 4 engineers and 3 market researchers.
d. Hire 4 engineers and 1 market researcher.
