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How many hours of labor should the firm hire, and how much output should

it produce?

To answer these questions, we apply the fundamental rule

First, observe that labor’s marginal product is MPLdQ/dL  60 2L. In

turn, labor’s marginal revenue product is MRPL($2)(60 2L)  120 

4L. Setting this equal to $16, we obtain 120 4L 16. The optimal amount

of labor is L 26 hours. From the production function, the resulting output

is 884 units. Finally, the firm’s operating profit (net of its labor cost) is

($2)(884) ($16)(26) $1,352.

PRODUCTION IN THE LONG RUN

In the long run, a firm has the freedom to vary all of its inputs. Two aspects of

this flexibility are important. First, a firm must choose the proportion of inputs

to use. For instance, a law firm may vary the proportion of its inputs to econo-

mize on the size of its clerical staff by investing in computers and software specif-

ically designed for the legal profession. In effect, it is substituting capital for

labor. Steeply rising fuel prices have caused many of the major airlines to mod-

ify their fleets, shifting from larger aircraft to smaller, fuel-efficient aircraft.

Second, a firm must determine the scale of its operations. Would building

and operating a new facility twice the size of the firm’s existing plants achieve

a doubling (or more than doubling) of output? Are there limits to the size of

the firm beyond which efficiency drastically declines? These are all important

questions that can be addressed using the concept of returns to scale.

Returns to Scale

The scale of a firm’s operations denotes the levels of all the firm’s inputs. A

change in scale refers to a given percentage change in allinputs. At a 15 percent

scale increase, the firm would use 15 percent more of each of its inputs. A key

question for the manager is how the change in scale affects the firm’s output.

Returns to scalemeasure the percentage change in output resulting from a

given percentage change in inputs. There are three important cases.

Constant returns to scaleoccur if a given percentage change in all inputs

results in an equal percentage change in output. For instance, if all inputs are

doubled, output also doubles; a 10 percent increase in inputs results in a 10 per-

cent increase in output; and so on. A common example of constant returns to

scale occurs when a firm can easily replicate its production process. For instance,

a manufacturer of electrical components might find that it can double its

MRPLMCL.

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