Deck 7: Production Analysis and Compensation Policy

Question 1

The marginal product concept is:

A) used to describe the relation between output and variation in all inputs in a production function.
B) the change in output associated with a one-unit change in an individual factor.
C) total product divided by the number input units employed.
D) the complete output from a production system.

Answer 1

B

Question 2

Marginal product is the change in output associated with a unit change in:

A) all inputs.
B) technology.
C) scale.
D) one input factor.

Answer 2

D

Question 3

Returns to a factor denotes the relation between the quantity of an individual input employed and the:

A) optimal scale of a firm.
B) optimal size of production facilities.
C) optimal length of production runs.
D) level of output produced.

Answer 3

D

Question 4

When P_X = $100, MP_X = 10 and MR_Q = $5, the marginal revenue product of X equals:

A) $100.
B) $50.
C) $10.
D) $5.

Question 5

When P_X = $60, MP_X = 5 and MP_Y = 2, relative employment levels are optimal provided:

A) P_Y = 16.7¢.
B) P_Y = $24.
C) P_Y = $60.
D) P_Y = $150.

Question 6

Total product divided by the number of units of variable input employed equals:

A) average product.
B) marginal revenue product.
C) returns to scale.
D) marginal product.

Question 7

The production function Q = 0.25X^0.5Y exhibits:

A) constant returns to scale.
B) increasing returns to scale.
C) increasing and then diminishing returns to scale.
D) diminishing returns to scale.

Question 8

A production function describes the relation between output and:

A) technical progress.
B) one input.
C) total cost.
D) all inputs.

Question 9

When the slope of the average product curve equals zero:

A) total product is maximized.
B) returns to the variable input are increasing.
C) marginal product equals average product.
D) marginal product equals zero.

Question 10

Total output is maximized when:

A) average product equals zero.
B) marginal product is maximized.
C) average product is maximized.
D) marginal product equals zero.

Question 11

The returns to scale characteristic of a production system:

A) is measured by the way in which inputs can be varied in an unbroken marginal fashion rather than incrementally.
B) illustrates the distinct, or "lumpy," pattern of input combination.
C) shows the relation between output and the variation in all inputs.
D) is the relation between output and variation in only one of the inputs employed.

Question 12

The law of diminishing returns:

A) deals specifically with the diminishing marginal product of fixed input factors.
B) states that the marginal product of a variable factor must eventually decline as increasingly more is employed.
C) can be derived deductively.
D) states that as the quantity of a variable input increases, with the quantities of all other factors being held constant, the resulting output must eventually diminish.

Question 13

Right-angle shaped isoquants reflect inputs that are:

A) perfect complements.
B) perfect substitutes.
C) imperfect substitutes.
D) inefficient.

Question 14

A firm will maximize profits by employing the quantity of each input where the marginal:

A) revenue product of each input equals its price.
B) revenue equals the price of each input.
C) product of each input is equal.
D) product of each input equals its price.

Question 15

A new production function results following:

A) a new wage agreement following collective bargaining.
B) a surge in product demand.
C) a decrease in the availability of needed inputs.
D) the successful completion of a training program that enhances worker productivity.

Question 16

The marginal rate of technical substitution is:

A) the slope of the marginal revenue product curve.
B) the marginal product of either input.
C) minus one times the ratio of marginal products for each input.
D) the slope of an isocost curve.

Question 17

Marginal revenue product equals:

A) marginal revenue multiplied by marginal product.
B) marginal product multiplied by total revenue.
C) total revenue multiplied by total product.
D) marginal revenue multiplied by total product.

Question 18

An isoquant represents:

A) input combinations that can be employed at the same cost.
B) input combinations that can efficiently produce the same output.
C) output combinations that can be efficiently produced using the same input combination.
D) output combinations that can be produced for the same cost.

Question 19

The relation between output and the variation in all inputs taken together is the:

A) factor productivity of a production system.
B) law of diminishing returns.
C) returns to scale characteristic of a production system.
D) returns to factor characteristic of a production system.

Question 20

If tripling the quantities of all inputs employed doubles the quantity of output produced, the output elasticity:

A) equals one.
B) is greater than one.
C) cannot be determined without further information.
D) is less than one.

Question 21

As the quantity of a variable input increases, the resulting rate of output increase eventually:

A) falls.
B) rises.
C) becomes constant.
D) none of these.

Question 22

Returns to Scale. Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale.

Question 23

Optimal Input Mix. Boch, Ltd., has designed a fuel injector for oil fired generators that provides a throughput of 3 gallons of oil per minute. If the diameter of the industrial injector nozzle were increased by 1 centimeter, throughput would increase 1 gallon per minute. Alternatively, throughput could be increased by 2 gallons per minute using the original injector diameter with fuel pumps that had 50 more pounds of pressure (psi).
A. Estimate the marginal rate of technical substitution between pump psi and injector diameter.
B. Assuming the cost of additional fuel pump size is $10 per psi (due to changing of the pump and fuel supply peripheral), and the cost of larger diameter fuel injector is $400 per centimeter (due to machining of combustion units), does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?

Question 24

Optimal Input Mix. Hydraulics Ltd. has designed a pipeline that provides a throughput of 70,000 gallons of water per 24-hour period. If the diameter of the pipeline were increased by 1 inch, throughput would increase by 4,000 gallons per day. Alternatively, throughput could be increased by 6,000 gallons per day using the original pipe diameter with pumps that had 100 more horsepower.
A. Estimate the marginal rate of technical substitution between pump horsepower and pipe diameter.
B. Assuming the cost of additional pump size is $600 per horsepower and the cost of larger diameter pipe is $200,000 per inch, does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?

Question 25

Optimal Input Mix. Salem-based Horton & Brady, Inc., is a small firm offering a wide variety of stock brokerage and financial services to high net worth individuals. Mickey Horton, president of Horton & Brady is reviewing the company's compensation plan. Currently, the company pays its three experienced financial advisors a salary based on the number of years of service. Nicole Walker, a new sales trainee, is paid a more modest salary. Sales and salary data for each employee are as follows:

Walker in particular has shown great promise during the past year, and Horton believes a substantial raise is clearly justified. At the same time, some adjustment to the compensation paid other sales personnel would also seem appropriate. Horton is considering changing from the current compensation plan to one based on a 5% commission. Horton sees such a plan as fairer to the parties involved and believes it would also provide strong incentives for needed market expansion.
A. Calculate Horton & Brady's salary expense for each employee expressed as a percentage of the commissions and fees generated by that individual.
B. Calculate income for each employee under a 5% commission-based system.
C. Will a commission-based plan result in efficient relative salaries, efficient salary levels, or both?

Question 26

Production Relations. Indicate whether each of the following statements is true or false.

Question 27

Economic efficiency is achieved when all firms equate the marginal:

A) product and price for all inputs.
B) cost of all inputs.
C) revenue product and price for all inputs.
D) product of all inputs.

Question 28

Optimal Input Mix. Rachel Green, owner-manager of the Manhattan-based Central Perk Coffee Shop, is reviewing the company's compensation plan. Currently, the company pays its three experienced management staff members salaries based on the number of years of service. Chandler Bing, a new management trainee, is paid a more modest salary. Monthly sales and salary data for each employee are as follows:
Bing in particular has shown great promise during the past year, and Green believes a substantial raise is clearly justified. At the same time, some adjustment to the compensation paid other sales personnel would also seem appropriate. Green is considering changing from the current compensation plan to one based on a 9% commission. Green sees such a plan as fairer to the parties involved and believes it would also provide strong incentives for needed market expansion.
A. Calculate Central Perk's salary expense for each employee expressed as a percentage of sales generated by that individual.
B. Calculate monthly income for each employee under a 9% commission-based system.
C. Will a commission-based plan result in efficient relative salaries, efficient salary levels, or both?

Question 29

Returns to Scale. Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale.

Question 30

Returns to Scale. Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale.

Question 31

Optimal Input Mix. Brisco, Van Buren & Associates is a New York City based law firm. Anita van Buren, managing partner of Brisco, Van Buren is reviewing the firm's compensation plan. Currently, the firm pays its staff attorneys salaries based upon the number of years of service. The value of billable hours generated by each staff attorney during the past year are as follows:

Van Buren believes some adjustment to the compensation paid all staff members would be appropriate. Van Buren is considering changing from the current compensation plan to one whereby each staff member would be paid a salary equal to 10% of client billings (gross revenue generated). Van Buren sees such a plan as fairer to the parties involved and believes it would also provide strong incentives for needed client development.
A. Calculate Brisco, Van Buren's salary expense for each employee expressed as a percentage of the client billings generated by that individual.
B. Calculate income for each employee under a 10% commission-based system.
C. Will a commission-based plan result in efficient relative salaries, efficient salary levels, or both?

Question 32

Input Combination. The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. (Assume that these are just illustrative points on a spectrum of continuous input combinations.)

Question 33

The output effect of a proportional increase in all inputs is called:

A) returns to scale.
B) returns to a factor.
C) total product.
D) marginal product.

Question 34

The maximum output that can be produced for a given amount of input is called a:

A) discrete production function.
B) production function.
C) continuous production function.
D) discontinuous production function.

Question 35

Returns to Scale. Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale.

Question 36

Input Combination. The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. (Assume that these are just illustrative points on a spectrum of continuous input combinations.)

Question 37

Optimal Input Mix. Puerto Rico-based Chocolate Products, Inc., manufactures and distributes a distinctive line of hand-packed candies. Lucy Ricardo president of Chocolate is reviewing the company's sales-force compensation plan. Currently, the company pays its three experienced sales staff members salaries based on the number of years of service. Matty Trumbull, a new sales trainee, is paid a more modest salary. Monthly sales and salary data for each employee are as follows:
Trumbull in particular has shown great promise during the past year, and Ricardo believes a substantial raise is clearly justified. At the same time, some adjustment to the compensation paid other sales personnel would also seem appropriate. Ricardo is considering changing from the current compensation plan to one based on a 3.5% commission. Ricardo sees such a plan as fairer to the parties involved and believes it would also provide strong incentives for needed market expansion.
A. Calculate Chocolate's salary expense for each employee expressed as a percentage of the sales generated by that individual.
B. Calculate monthly income for each employee under a 3.5% commission-based system.
C. Will a commission-based plan result in efficient relative salaries, efficient salary levels, or both?

Question 38

Optimal Input Mix. Electron Specialties, Inc. has designed an electric feeder cable that provides a throughput of 2,000 ampere hours (aH) per 24-hour period. If the diameter of the cable were increased by 1/2 inch, throughput would increase by 500 aH per day. Alternatively, throughput could be increased by 1,000 aH per day using the original cable diameter with an additional 100 mf of capacitance electronics designed by the firm.
A. Estimate the marginal rate of technical substitution between capacitance electronics and cable diameter.
B. Assuming the cost of additional capacitance electronics is $50 per mf and the cost of larger diameter cable is $20,000 per 1/2 inch, does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?

Question 39

When MR_Q = $25, P_X = $200, and MP_X = 8, employment of X:

A) is optimal.
B) should expand.
C) should contract.
D) none of these.

Question 40

Production Relations. Indicate whether each of the following statements is true or false.

Question 41

Optimal Input Mix. Third World Solutions, Inc., has designed a manual water pump that attains a flow rate of 5 gallons per minute using 1 manpower. If the diameter of the pump were increased by 1 inch, throughput would increase 4 gallons per minute. Alternatively, throughput could be increased by an additional 8 gallons per minute using the original pump diameter with one hydraulic chamber.
A. Estimate the marginal rate of technical substitution between hydraulic chambers and pump diameter.
B. Assuming the cost of additional hydraulic chamber size is $5 per chamber and the cost of a larger pump diameter is $2.50 per inch, does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?

Question 42

Optimal Input Level. Communications Consultant Services, Inc., advises small to medium-sized businesses on telephone equipment and network configurations. The primary resources CCS employs are skilled network consultants and computers. Currently, CCS employs 16 consultants at a cost of $70 per hour (wage plus fringes and variable overhead), and purchases 160 hours of computer time each week at a time-sharing cost of $280 per hour. Each consultant works a 40-hour week. This level of employment allows CCS to complete 213 communications analyses per week for which the firm receives $300 each.
A. Assuming that both returns to factors and returns to scale are constant, what are the marginal products for: (1) communication consultants and, (2) computer time (up to the full capacity level)?
B. Is CCS employing labor and computers in an optimal ratio, assuming that substitution of the resources is possible? Explain.
C. Determine the marginal revenue products for consultants and for the computer services employed by CCS. (Assume constant returns to factors in part A.)
D. Is CCS employing an optimal (profit-maximizing) quantity of labor and computer time? Explain.

Question 43

Nonprice Competition. Top Gun Marketing, Inc., offers overhead banner fly-by promotion services using their Cessna aircraft and banner creation facilities. The Padres Island firm specializes in restaurant promotion via fly-bys at outdoor events and other high traffic centers, where each 10 minute increment of advertising costs $300. Over the past year, the following relation between fly-by advertising and incremental restaurant guests per month has been observed:
and

Here A represents a 10-minute fly-by advertisement, and sales are measured in numbers of restaurant guests.
Pete Mitchel, manager for the Padres Island firm, has been asked to recommend an appropriate level of advertising. In thinking about this problem, Mitchel noted its resemblance to the optimal resource employment problem he had studied in a managerial economics course that was part of his MBA program. The advertising-sales relation could be thought of as a production function with advertising as an input and sales as the output. The problem is to determine the profit-maximizing level of employment for the input, advertising, in this "production" system. Mitchel recognized that to solve the problem he needed a measure of output value. After consultation with the restaurant, he determined that the value of output is $10 per guest, the net marginal revenue earned by the client (price minus all marginal costs except fly-by advertising).
A. Continuing with Mitchel's production analogy, what is the "marginal product" of advertising?
B. What is the rule for determining the optimal amount of a resource to employ in a production system? Explain the logic underlying this rule.
C. Using the rule for optimal resource employment, determine the profit-maximizing number of 10-minute ads.

Question 44

Optimal Input Level. Laboratory Testing, Inc., provides routine drug tests for employers in the Los Angeles metropolitan area. Tests are supervised by skilled technicians using equipment produced by two leading competitors in the medical equipment industry. Records for the current year show an average of 24 tests per hour performed on the A-1, and 51 tests per hour on a new machine, the Caltec. The A-1 is leased for $16,000 per month, and the Caltec is leased at a rate of $34,000 per month. On average, each machine is operated 25 eight-hour days per month. Labor and all other costs are fixed.
A. Does company usage reflect an optimal mix of testing equipment?
B. At a price of $5 per test should the company lease more machines?

Question 45

Optimal Input Level. Sunshine Pest Control, Inc., provides exterminator services to residences in the Miami area. The primary resources SPC employs are skilled exterminators and large dome/air pumps used to cover the homes, pump in insecticide, and minimize leakage to the environment. Currently, SPC employs 10 exterminators at a cost of $15 per hour, employs 2,000 hours of pump time each week at a cost of $3 per hour. Each exterminator works a 40-hour week. This level of employment allows SPC to complete 100 treatments per week for which the firm receives $100 each.
A. Assuming that both returns to factors and returns to scale are constant, what are the marginal products for (1) exterminators and (2) gallons of chemicals?
B. Is SPC employing labor and domes in an optimal ratio, assuming that substitution of the resources is possible? Explain.
C. Determine the marginal revenue products for exterminators and for the domes/pumps employed by SPC. (Assume constant returns to factors in part A.)
D. Is SPC employing an optimal (profit-maximizing) quantity of labor and computer time? Explain.

Question 46

Optimal Input Level. Just Bikes, Inc., sells tricycles, in partially-assembled and fully assembled forms. Parents who assemble their own tricycles benefit from the lower price of $40 per tricycle. "Full-service" customers enjoy the luxury of an assembled tricycle, but pay a higher price of $60 per tricycle. Both partially and fully assembled tricycle prices are stable. The company has observed the following relation between the number of assembly workers employed per day and assembled tricycle output:

A. Construct a table showing the net marginal revenue product derived from assembly worker employment.
B. How many assemblers would Just Bikes employ at a daily wage rate of $100?
C. What is the highest daily wage rate Just Bikes would pay to hire three assemblers per day?

Question 47

Optimal Input Level. U-Do-It Furniture, Inc., sells hardwood chairs, in both kits and fully assembled forms. Customers who assemble their own chairs benefit from the lower kit price of $35 per chair. "Full-service" customers enjoy the luxury of an assembled chair, but pay a higher price of $60 per chair. Both kit and fully assembled chair prices are stable. The company has observed the following relation between the number of assembly workers employed per day and assembled chair output:

A. Construct a table showing the net marginal revenue product derived from assembly worker employment.
B. How many assemblers would U-Do-It Furniture employ at a daily wage rate of $75?
C. What is the highest daily wage rate U-Do-It Furniture would pay to hire four assemblers per day?

Question 48

Nonprice Competition. Tickets, Inc., uses mall intercept promotion services to promote concerts and sporting events. The St. Louis firm uses a team of ten students to hand-deliver flyers at shopping malls and other high traffic centers, where every hour increment of flyer advertising costs $130. Over the past year, the following relation between advertising and ticket sales per event has been observed:
and
Here A represents one hour of flyer distribution, and sales are measured in numbers of tickets. Niki Martin, manager for the St. Louis firm, has been asked to recommend an appropriate level of advertising. In thinking about this problem, Martin noted its resemblance to the optimal resource employment problem she had studied in a managerial economics course that was part of her MBA program. The advertising-sales relation could be thought of as a production function with advertising as an input and sales as the output. The problem is to determine the profit-maximizing level of employment for the input, advertising, in this "production" system. Martin recognized that to solve the problem she needed a measure of output value. After consultation with associates, she determined that the value of output is $2 per ticket, the net marginal revenue earned (price minus all marginal costs except flyer advertising).
A. Continuing with Martin's production analogy, what is the "marginal product" of advertising?
B. What is the rule for determining the optimal amount of a resource to employ in a production system? Explain the logic underlying this rule.
C. Using the rule for optimal resource employment, determine the profit-maximizing number of flyer distribution hours.

Question 49

Optimal Input Level. Do-It-Yourself, Inc., sells budget-priced stereo receivers, in both kit and fully-assembled forms. Customers who assemble their own receivers benefit from the lower kit price of $100 per receiver. "Full-service" customers enjoy the luxury of an assembled receiver, but pay a higher price of $150 per receiver. Both kit and fully assembled receiver prices are stable. The company has observed the following relation between the numbers of assembly workers employed per day and assembled receiver output:

A. Construct a table showing the net marginal revenue product derived from assembly worker employment.
B. How many assemblers would Do-It-Yourself employ at a daily wage rate of $120?
C. What is the highest daily wage rate Do-It-Yourself would pay to hire four assemblers per day?

Question 50

Optimal Input Level. Smokey's Garage, Inc., provides routine auto diagnostics for customers in the Atlanta, Georgia, metropolitan area. Tests are supervised by skilled mechanics using equipment produced by two leading competitors in the auto test equipment industry. Records for the current year show an average of 4 tests per hour performed on the Sunny Tune System (STS), and 6 tests per hour on a new machine, the Car Care Tower (CCT). The STS is leased for $8,000 per month, and the CCT is leased at a rate of $12,000 per month. On average, each machine is operated 25 eight-hour days per month. Labor and all other costs are fixed.
A. Does company usage reflect an optimal mix of testing equipment?
B. At a price of $15 per test should the company lease more machines?