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Chapter 5
Production
Extra workers are assigned to less productive tasks. These workers generate additional output but at a diminishing rate.
Optimal Use of an Input The law of diminishing returns means that the firm faces a basic trade-off in determining its level of production. By using more of a variable input, the firm obtains a direct benefit—increased output—in return for incurring an additional input cost. What level of the input maximizes profits? As before, we look at the firm’s marginal profit, but this time we look at marginal profit per unit of input. We increase the input until the marginal profit per unit of input is zero. In analyzing this input decision, a definition is helpful. Marginal revenue product is the formal name for the marginal revenue associated with increased use of an input. An input’s marginal revenue product is the extra revenue that results from a unit increase in the input. To illustrate, suppose the auto parts supplier is considering increasing labor from 20 to 30 workers. According to Table 5.2, the resulting marginal product is 4.5 parts per worker. Suppose further that the supplier’s marginal revenue per part is constant. It can sell as many parts as it wants at a going market price of $40 per part. Therefore, labor’s marginal revenue product (MRPL) is ($40)(4.5) $180 per worker. Similarly, the MRPL for a move from 30 to 40 workers is ($40)(5.0) $200 per worker. More generally, labor’s marginal revenue product can be expressed as MRPL (MR)(MPL),
[5.2]
where MR denotes marginal revenue per unit of output.3 Now consider the marginal cost of using additional labor. The marginal cost of an input is simply the amount an additional unit of the input adds to the firm’s total cost.4 If the firm can hire as many additional workers as it wishes at a constant wage (say, $160 per day), then the marginal cost of labor is MCL $160. (In some cases, however, the firm may have to bid up the price of labor to obtain additional workers.) Now note that the additional profit from adding one more worker is the revenue generated by adding the worker less the worker’s marginal cost. M L MRPL MCL. In calculus terms, MRPL dR/dL (dR/dQ)(dQ/dL) (MR)(MPL). It is important to distinguish between the marginal cost of an input and the marginal cost of an additional unit of output. Taking labor as an example, MCL is defined as C/ L, the cost of hiring an extra worker. In contrast, the added cost of producing an extra unit of output is MC C/ Q. 3 4
