Managerial Economics

1517 Words Nov 14th, 2012 7 Pages
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?

o No, 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:
**Marginal Product measures additional output from one more unit of the variable input.**

o MPA = MS/MA

= ∂Sales (units) / ∂Advertising (OR ∂Q/∂A) = 100 - A

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.

o The rule for determining the optimal amount of a resource to employ is:

MRPA = PA (see slide 17)

MPA * MRQ = PA (see slide 9)

The above equation turns to:

∂Q/∂A * ∂TR/∂Q = ∂TC/∂A

 Q’s cancel each other out and the equation turns to:

∂TR/∂A = ∂TC/∂A

This leads to Marginal Total Revenue (MTR) = Marginal Total Cost (MTC), which means the inflow = outflow.

C. Using the rule for optimal resource employment, determine the profit-maximizing number of radio ads.

o Using the above equation MPA * MRQ = PA

 (100-A )* \$2 = \$100

\$200-2A = \$100 \$100= 2A  A=\$50

P7.9 Net Marginal Revenue. Crane, Poole & Schmidt, LLC, is a successful Boston-based law firm. Worker productivity at the firm is measured in billable hours, which vary between partners and associates. Partner time is billed to clients at a rate of \$250 per hour, whereas associate time is billed at a rate of \$125 per hour. On average, each partner generates 25 billable hours per 40-hour workweek, with 15 hours spent on promotion, administrative, and supervisory responsibilities. Associates generate an average of 35 billable hours per 40-hour