Optimal Input Level

Ticket Services, Inc., offers ticket promotion and handling services for concerts and sporting events. The Sherman Oaks, California, branch office makes heavy use of spot radio advertising on WHAM-AM, with each 30-second ad costing $100. During the past year, the following relation between advertising and ticket sales per event has been observed:

Sales (units)  =  5,000  +  100A  - 0.5A2

DSales (units)/DAdvertising   =  100  -  A

Here, A represents a 30-second radio spot ad, and sales are measured in numbers of tickets. Rachel Green, manager for the Sherman Oaks office, has been asked to recommend an appropriate level of advertising. In thinking about this problem, Green noted its resem- blance to the optimal resource employment problem she had studied in a managerial eco- nomics course that was part of her M.B.A. 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. Green recognized that to solve the problem, she needed a measure of output value. After reflection, she determined that the value of output is $2 per ticket, the net marginal revenue earned by Ticket Services (price minus all marginal costs except advertising).

A. Continuing with Green'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 radio ads.