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Chapter 5
Production
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 MRPL MCL. First, observe that labor’s marginal product is MPL dQ/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 economize on the size of its clerical staff by investing in computers and software specifically 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 modify 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 all inputs. 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 scale measure the percentage change in output resulting from a given percentage change in inputs. There are three important cases. Constant returns to scale occur 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 percent 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
