Deck 3: Marginal Analysis for Optimal Decision Making

Question 1

The next questions refer to the following:
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

Answer 1

$25,000 a year

Question 2

The next questions refer to the following:
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.

Answer 2

the clinic could serve more patients by hiring fewer doctors and more nurses.

Question 3

refer to the following:
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


-If the manager currently has two engineers and one market researcher, what must be true?

A) He is making the correct decision because


B) He is not making the correct decision because


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.

Answer 3

More new products will be developed if he hires fewer engineers and more market researchers.

Question 4

refer to the following:
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:


-If the manager currently hires four engineers and one market researcher, what must be true?

A) She is making the correct decision because


B) More new products would be developed if she hires more engineers and fewer market researchers.
C) More new products would be developed if she hires fewer engineers and more market researchers.
D) She is not making the correct decision because .

Question 5

refer to the following:
The manager of the customer service department at a bank can hire employees with a high school degree (HS) who earn $10,000 annually or employees with a bachelor's degree (B) who earn $20,000. The manager wants to maximize the number of customers served given a fixed payroll.


-If the manager currently has three HS and three B, what must be true?

A) More customers could be served if the manager hires fewer HS and more B.
B) More customers could be served if the manager hires more HS and fewer B.
C) The manager is making the correct decision because the marginal contributions are proportionate.
D) The manager is not making the correct decision because

Question 6

A publishing house is using 400 printers and 200 printing presses to produce books. The printers' wage rate is $20 and the price of a printing press is $100. The last printer added 20 books to total output, while the last press added 50 books to total output. In order to maximize the number of books published with a budget of $28,000, the publishing house

A) should continue to use 400 printers and 200 presses.
B) should use more printers and fewer presses because printers cost less than presses.
C) should use more printers and fewer presses because the last dollar spent on a printer yielded more output than the last dollar spent on a press.
D) should use more presses and fewer printers because the marginal output of the last press was more than the marginal output of the last printer.
E) should use more presses and fewer printers because the last dollar spent on a press yielded more output than the last dollar spent on a printer.

Question 7

In a constrained maximization problem with two activities, A and B, the highest level of benefits obtainable at a given level of cost is achieved when _______________ equals ____________ and the constraint is met.

Question 8

The marginal benefit and marginal cost functions for activity A are
MB = 100 - 0.04A
MC = 28 + 0.02A

-The optimal level of A is _________ units at which MB = _________ and MC = ____________.

Question 9

The marginal benefit and marginal cost functions for activity A are
MB = 100 - 0.04A
MC = 28 + 0.02A

-The 800^th unit of A increases total benefit by $_________ and total cost by $_________ thereby _____________________ net benefit by $__________.

Question 10

The marginal benefit and marginal cost functions for activity A are
MB = 100 - 0.04A
MC = 28 + 0.02A

-The 1,400^th unit of A increases total benefit by $______ and total cost by $______ thereby _____________________ net benefit by $__________.

Question 11

Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions.

-Net benefit is maximized when _________ units of A are chosen; marginal benefit is $_________ and marginal cost is $_________.

Question 12

Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions.

-If 300 units of A are chosen, net benefit will increase by $_________ if one _________ unit of A is used.

Question 13

Use the following graph showing the marginal benefit and marginal cost curves for activity A to answer the following questions.

-If 100 units of A are chosen, net benefit will increase by $_________ if one _________ unit of A is chosen.

Question 14

Fill in the blanks in the following table. Then use the table to answer the questions:X

-If activity X is increased from 3 to 4 units, total benefit ___________ by $_________.

Question 15

Fill in the blanks in the following table. Then use the table to answer the questions:X

-If X is increased from 3 to 4 units, total cost ___________ by $_________.

Question 16

Fill in the blanks in the following table. Then use the table to answer the questions:X

-If X is decreased from 6 to 5 units, total benefit ___________ by $_________, and total cost ___________ by $_________. Thus, net benefit _____________.

Question 17

Fill in the blanks in the following table. Then use the table to answer the questions:X

-The optimal level of activity is ___ units of activity X, and net benefit at the optimal level of X is $____________.

Question 18

Activity A has the following marginal (MB) and marginal cost (MC) functions:
MB = 2,500 - 20A
MC = 500 + 30A
where MB and MC are measured in dollars.

-The 10^th unit of the activity increases total benefit by $_________ and increases total cost by $_________. Since marginal benefit is _________ (greater, less) than marginal cost, adding the 10^th unit of activity _________ (increases, decreases) net benefit by $_________.

Question 19

Activity A has the following marginal (MB) and marginal cost (MC) functions:
MB = 2,500 - 20A
MC = 500 + 30A
where MB and MC are measured in dollars.

-The 50^th unit of the activity increases total benefit by $_________ and increases total cost by $_________. Since marginal benefit is _________ (greater, less) than marginal cost, subtracting the 50^th unit of activity _________ (increases, decreases) net benefit by $_________.

Question 20

Activity A has the following marginal (MB) and marginal cost (MC) functions:
MB = 2,500 - 20A
MC = 500 + 30A
where MB and MC are measured in dollars.

-The optimal level of the activity is ________ units. At the optimal level of activity, marginal benefit is $_________ and marginal cost is $__________.
The total benefit (TB) and total cost (TC) functions for the activity are:
TB = 2,500A -10A²
TC = 500A + 15A²
where TB and TC are measured in dollars.

Question 21

Activity A has the following marginal (MB) and marginal cost (MC) functions:
MB = 2,500 - 20A
MC = 500 + 30A
where MB and MC are measured in dollars.

-For the optimal level of the activity in part c, the total benefit is $_________, the total cost is $_________, and the net benefit is $__________.

Question 22

A decision maker can choose the levels of two activities, A and B, so as to maximize net benefits. The marginal benefit functions of A and B are
Activity A costs $160 per unit and activity B Costs $540 per unit.
-The optimal level of activity A is _________ units.

Question 23

A decision maker can choose the levels of two activities, A and B, so as to maximize net benefits. The marginal benefit functions of A and B are
Activity A costs $160 per unit and activity B Costs $540 per unit.
-The optimal level of activity B is _________ units.

Question 24

Your firm sells club soda in both grocery stores and convenience stores. You have a budget of $550 for store displays, and must decide how to allocate this budget between grocery stores and convenience stores to maximize the total number of sales. The following table shows the total number of units that can be sold in grocery stores and convenience stores, according to the number of displays in each type of store. Displays in grocery stores cost $150 each and displays in convenience stores cost $100 each.

-With $550 to spend, the total number of units sold will be maximized by choosing ______ displays in grocery stores and ______ displays in convenience stores. With $550 to spend, the maximum number of units that can be sold is ________.

Question 25

Your firm sells club soda in both grocery stores and convenience stores. You have a budget of $550 for store displays, and must decide how to allocate this budget between grocery stores and convenience stores to maximize the total number of sales. The following table shows the total number of units that can be sold in grocery stores and convenience stores, according to the number of displays in each type of store. Displays in grocery stores cost $150 each and displays in convenience stores cost $100 each.

-Suppose your firm can spend $1,200 on store displays. The total number of units sold will be maximized by choosing ______ displays in grocery stores and ______ displays in convenience stores. The maximum number of units that can be sold is ________.