Optimal max of newspaper and magazine ads

Question

Problem 1: 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 max of newspaper and magazine ads? Why or why not?

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

Problem 2: Production Function Estimation. Consider the following Cobb-Douglas production function for bus service in a typical metropolitan area:

Q = b₀L^b1K^b2F^b3

Where

Q = output in millions of passenger miles
L = labor input in worker hours
K = capital input in bus transit hours
F = fuel input in gallons

Each of the parameters of this model was estimated by regression analysis using monthly data over a recent 3-year period. Results obtained were as follows (standard errors in parentheses):

b_o =  1.2; b₁ = 0.28; b₂ = 0.63; b₃ = 0.12    (note: all the bs or bo b1 b2 and b3 should have the ^ mark above them but I could not get the computer program to complete these marks.)

The standard error estimates for each coefficient are

o b0 = 0.4; o b1 = 0.15; o b2= 0.12; o b3 = 0.07

A. Estimate the effect on output of a 4% decline in worker hours (holding K and F constant).

B. Estimate the effect on output of a 3% reduction in fuel availability accompanied by a 4% decline in bus transit hours (holding L constant.)

C. Estimate the returns to scale for this production system.

Problem 3: Cost Curves. Indicate whether each of the following involves an upward or downward shift in the long-run average cost curve or, instead, involves a leftward or rightward movement along a given curve. Also indicate whether each will have an increasing, decreasing, or uncertain effect on the level of average cost.

A. rise in wage rates
B. A decline in output
C. An energy-saving technical change
D. A fall in interest rates
E. An increase in learning or experience.