Exam 7: Production Analysis and Compensation Policy

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?

When the slope of the average product curve equals zero:

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?

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?

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

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

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

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?

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?

Right-angle shaped isoquants reflect inputs that are:

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

Marginal revenue product equals:

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?

The marginal rate of technical substitution is:

The returns to scale characteristic of a production system:

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.

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

An isoquant represents:

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?

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