Question

1. 2. 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:

Sales (units) = 5,200 + 50A - 0.5A²

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.

Answer 1

A. Marginal product of advertising can be found by calculating the first derivative of value with respect to advertising units. Value (at $10 per guest) is as per the following function (pls note that the function representing the number of guests in the question has been multiplied by 10 to get value)

Value: V = 52000 + 500A - 5A^2

dV / dA = 500 - 10A

B. The optimal amount of resource to be employed is where the marginal product is equal to marginal cost. Since the production function slopes downward showing that marginal production falls as more units of resource are deployed, profit would be maximized when the falling productivity (marginal product) becomes equal to the cost of the resource employed.

C. Using this rule the profit-maximizing number for 10-minute ads would be obtained when dV / dA is equal to marginal cost, which is $300 per unit of A

Solving for the above

300 = 500 - 10A

A = 20

20 instances of 10-minutes ads would maximize the profit.