9781118041581

Production with One Variable Input 197

The firm should continue to increase its labor force as long as the amount of

additional profit from doing so is positive, that is, as long as the additional rev-

enue (MRPL) is greater than the additional cost (MCL). Due to diminishing

marginal returns, labor’s marginal revenue product eventually will fall. When

MRPLexactly matches MCL(that is, when ML 0), increasing the labor force

any further will be unprofitable, which leads to the following principle:

To maximize profit, the firm should increase the amount of a variable input up to

the point at which the input’s marginal revenue product equals its marginal cost,

that is, until:

[5.3]

After this point, the marginal cost of labor will exceed the marginal revenue

product of labor and profits will decline.

EXAMPLE 1 The human resources manager of the auto parts firm with a

10,000-square-foot plant estimates that the marginal cost of hiring an extra

worker is PL$160 per day. Earlier we noted that a move from 20 to 30 workers

implies an MRPLof $180 per worker (per day). Since this exceeds the daily cost

per worker, $160, this move is profitable. So, too, is a move from 30 to 40

workers (MRPL$200). But an increase from 40 to 50 workers is unprofitable.

The resulting MRPLis ($40)(3.3) $132, which falls well short of the marginal

labor cost. After this, MRPLcontinues to decline due to diminishing returns.

Thus, the optimal size of the firm’s labor force is 40 workers.

What would be the firm’s optimal labor force if it had in place a 30,000-

square-foot plant? From Table 5.1, we see that a move from 50 to 60 workers

results in an MRPLof $212, a move from 60 to 70 workers an MRPLof $168, and

a move from 70 to 80 workers an MRPLof $128. Given a labor price of $160 per

day, the firm profits by increasing its labor force up to a total of 70 workers

(since MRPLMCLin this range). But an increase beyond this level reduces

profitability (MRPLMCL). The firm would best utilize the 30,000-square-foot

plant by using 70 workers and producing 520 parts per day.

MRPLMCL.

CHECK

STATION 2

Let MR $40 and MCL$160 per day. Using the relevant information from Table 5.1,

determine the firm’s optimal number of workers for a 20,000-square-foot plant. Repeat

the calculation for a 40,000-square-foot plant.

EXAMPLE 2 Suppose that a firm’s production function is described by

where Q measures units of output and L is the number of labor hours. Suppose

that output sells for $2 per unit and the cost of labor is MCL$16 per hour.

Q60LL^2 ,

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