Exam 7: Production Analysis and Compensation Policy

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?

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?

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?

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

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.

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

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

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

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?

A production function describes the relation between output and: