Exam 7: Production Analysis and Compensation Policy

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

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?

The marginal product concept is:

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

A new production function results following:

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

Economic efficiency is achieved when all firms equate the marginal:

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

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.

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

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?

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

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

Total output is maximized when:

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

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.

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.)

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.)

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

The law of diminishing returns: