Managerial Economics

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P7.6 Optimal Input Mix. The First National Bank received 3,000 inquiries following the latest advertisement describing its 30-month IRA accounts in the Boston World, a local newspaper. The most recent ad in a similar advertising campaign in Massachusetts Business, a regional business magazine, generated 1,000 inquiries. Each newspaper ad costs $500, whereas each magazine ad costs $125.

A.Assuming that additional ads would generate similar response rates, is the bank running an optimal mix of newspaper and magazine ads? Why or why not?

oNo, the bank is not running an optimal mix of newspaper and magazine ads because the optimal combination would occur when MPn / Pn = MPm / Pm  newspaper output: 3,000 / 500 = 6 and magazine output: 1,000 / 125 = 8.

Therefore, amount spent on newspaper ads attracted 6 inquiries while amount spent on magazine ad attracted 8 inquiries. So to run an optimal mix of newspaper and magazine ads, the bank has to run more magazine ads and/ or fewer newspaper ads.

B.Holding all else equal, how many inquiries must a newspaper ad attract for the current advertising mix to be optimal?

oFor the current advertising mix to be optimal, MPn / Pn = MPm / Pm therefore, to increase the newspaper output from 6 to 8,

Find: MPn / 500 = 8 *500  MPn = 4,000
*500

So inquiries generated by newspaper ads would have to increase from 3,000 to 4,000.

P7.7 Marginal Revenue Product of Labor. To better serve customers interested in buying cars over the Internet, Smart Motors, Inc., hired Nora Jones to respond to customer inquiries, offer price quotes, and write orders for leads generated by the company’s Web site. During last year, Jones averaged 1.5 vehicle sales per week. On average, these vehicles sold for a retail price of $25,000 and brought the dealership a profit contribution of $1,000 each.

A.Estimate Jones’ annual (50 workweek) marginal revenue product.

oJones’ marginal revenue product can be found by the number of cars sold and the profit of each sale.

MRPL = MPL * MRQ  MRPL = (1.5 * 50) * ($1,000) = $75,000
(Vehicles sales p/week * workweek) * (profit contribution)

B.Jones earns a base salary of $60,000 per year, and Smart Motors pays an additional 28 percent of this base salary in taxes and various fringe benefits. Is Jones a profitable employee?

oNo, Jones is not a profitable employee because her cost to be employed is $76,800 ($60,000 base salary + 28% of taxes and fringe benefits) and her marginal revenue product is only $75,000. Therefore, MRPL ($75,000) < PL ($76,800).

This means that even though Jones brings in $75,000 additional profit it costs Smart Motors $76,800 to have her which means she brings $1,800 of marginal loss to Smart Motors.

P7.8 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

∂Sales (units) / ∂Advertising = 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 resemblance to the optimal resource employment problem studied in a managerial economics course. 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 a measure of output value was needed to solve the problem. After reflection, Green determined that the value of output is $2...
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