9781118041581

ratings for trucks and sedans (with cells C8 and C10 set to zero) are

18 miles per gallon and 38 miles per gallon, respectively. Finally, the

fleet averages in row 12 are computed by weighting the vehicle values by

the fleet shares in column D.

a. The company seeks to maintain a fleetwide average of 32 miles per

gallon. To maximize its fleetwide average contribution (cell E12), how

much aluminum should the maker add to each vehicle, and what mix

of vehicles should it produce?

b. Re-answer the questions in part (a) if price cuts mean that aluminum

is only 10 percent more costly than steel, that is, cell H8 takes the

value 1.1.

c. Finally, what is the company’s optimal production response if the fuel-

efficiency standard is raised to 36 miles per gallon?

Suggested References

The following reading surveys the use and estimation of production functions.

Gold, B. “Changing Perspectives on Size, Scale, and Returns: An Interpretative Survey.” Journal of

Economic Literature (March 1981): 5–33.

The following references offer case studies of production and economies of scale.

Basu, S., and J. G. Fernald. “Returns to Scale in U.S. Production: Estimates and Implications.” Jour-

nal of Political Economy105 (April 1997): 249–283.

Boyd, G. A. “Factor Intensity and Site Geology as Determinants of Returns to Scale in Coal Min-

ing.” Review of Economics and Statistics (1987): 18–23.

Cookenboo, L. “Production Functions and Cost Functions: A Case Study.” In E. Mansfield (Ed.),

Managerial Economics and Operations Research. New York: Norton, 1993.

Noulas, A. G., S. C. Ray, and S. M. Miller. “Returns to Scale and Input Substitution for Large U. S.

Banks.” Journal of Money, Credit and Banking22 (February 1990): 94–108.

Managers’ production strategies are discussed in:

Womack, J. P. “From Lean Production to Lean Enterprise.” Harvard Business Review (March–April

1994): 93–103.

224 Chapter 5 Production

CHECK STATION

ANSWERS

1. Labor’s marginal product is uniformly greater (i.e., greater for any size of
   labor force) at a 30,000-square-foot plant than at a 10,000-square-foot
   plant.


2. At a 20,000-square-foot plant, the optimal labor force is 50 workers. (Here
   the MRPLchanges from $180 to $140.) At a 40,000-square-foot plant, the
   optimal labor force is 90 workers. (The MRPLchanges from $180 to
   $140.)


3. Doubling scale (starting from 10 workers and a 10,000-square-foot plant)
   more than doubles output. The same is true starting from 20 workers and
   a 20,000-square-foot plant. In contrast, doubling scale (starting from
   50 workers and a 20,000-square-foot plant) produces less than double the

c05Production.qxd 9/5/11 5:49 PM Page 224