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Other Production Decisions 211

employing different degrees of automation), what is the effect on output of

expanding the labor force (for instance, adding extra shifts)? Does the

industry exhibit economies of scale and, if so, over what range of outputs?

(That is, will a 40 percent increase in plant scale deliver more than a 40 per-

cent increase in output?)

Production data—though subject to measurement errors—are very useful

to managers. Based on these data, the manager (often with the help of an oper-

ations research specialist) can estimate the mathematical relationship between

levels of inputs and quantity of output. The principal statistical method for car-

rying out this task is regression analysis (the most important elements of which

were discussed in Chapter 4). The end product of this analysis is a tangible rep-

resentation of the firm’s production function.

OTHER PRODUCTION DECISIONS

Within the limits of its production technology, the firm’s managers face a num-

ber of important decisions. We have already discussed finding the optimal use

of single input in the short run and choosing the best mix of inputs in the long

run. We now consider two other decisions: (1) the allocation of a single input

among multiple production facilities and (2) the use of an input across multi-

ple products.

Multiple Plants

Consider an oil company that buys crude oil and transforms it into gasoline at

two of its refineries. Currently it has 10 thousand barrels of oil under long-term

contract and must decide how to allocate it between its two refineries. The com-

pany’s goal is to allocate supplies to maximize total output from the refineries.

Let MAand MBrepresent the crude input at each refinery and QAand QBthe

gasoline outputs. The firm’s problem is:

The key to maximizing total output is to compare marginal products at the two

refineries. Barrels of crude first should be allocated to the refinery at which the

marginal product is greater. Let’s say this is refinery A. As additional barrels are

allocated to this refinery, its marginal product diminishes, and it becomes

worthwhile to allocate oil to refinery B as well.

In the final allocation of all 10 thousand barrels, output is maximized if

and only if the marginal products of both refineries are equal, that is, when

MPAMPB.

Maximize QQAQB, subject to MAMB 10 thousand.

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