9781118041581

Summary 223

c. Suppose the input price of labor falls to $18. Determine the new least-

cost input amounts in the long run. Provide an intuitive explanation

for the change in inputs caused by the lower labor price.

S3. The accompanying spreadsheet captures the profit-maximizing decisions

of a carmaker facing stricter fuel-efficiency standards as discussed earlier

in the chapter. The carmaker in question must decide how much

aluminum to use in its trucks and sedans so as to lower their weight and

improve their fuel efficiency. Cells C8 and C10 list these decision variables

(expressed as percentages in decimal form, so that a value such as .10

means that the proportion of aluminum has increased by 10 percentage

points). The company also must determine its mix of trucks and sedans

by setting the proportion of trucks (again as a decimal) in cell D8 with

cell D10 computed as:  1 D8.

Because of aluminum’s extra cost, each vehicle’s contribution per

unit declines as more aluminum is used. Truck contribution (cell E8) is

given by the Excel formula:  10 80*H8*C8^2. The cost impact of

using aluminum depends on the relative cost of aluminum (cell H8)

and increases quadratically as more and more aluminum is used. In

turn, sedan contribution is given by the Excel formula:  6 80*H8*C10^2.

These formulas imply that current contribution margins for trucks and

sedans (with cells C8 and C10 set to zero) are $10 thousand and

$6 thousand, respectively. Each vehicle’s fuel efficiency increases

directly with its aluminum content. For trucks (cell F8), the Excel

formula is:  18 60*C8, while for sedans (cell F10), the formula

is: 38 80*C10. These formulas imply that current fuel efficiency

A B C D E F G H I

1

2 IMPROVING FUEL ECONOMY

3

4

5 AluminumFleet ShareContrib/unitFuel Eff. A’s relative

6 (%) (%) ($ 000) (MPG) Cost

7

8 Truck 0 .30 10.0 18.0 1.3

9

10 Sedan 0 .70 6.0 38.0

11

12 Fleet Average: 7.2 32.0

13

14 Requirement: 32

15

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