Let’s make the discussion of labor demand more concrete by looking at The Clip Joint, a small business that grooms dogs. The Clip Joint uses both capital, such as clippers, tubs, and brushes, and labor to produce its output of groomed dogs.
The production function that applies to The Clip Joint appears in Table 3.2. For given levels of productivity and the capital stock, it shows how The Clip Joint’s daily output of groomed dogs, column (2), depends on the number of workers employed, column (1). The more workers The Clip Joint has, the greater its daily output is.
The MPN of each worker at The Clip Joint is shown in column (3). Employing the first worker raises The Clip Joint’s output from 0 to 11, so the MPN of the first worker is 11. Employing the second worker raises The Clip Joint’s output from 11 to 20, an increase of 9, so the MPN of the second worker is 9; and so on. Column (3) also shows that, as the number of workers at The Clip Joint increases, the MPN falls so that labor at The Clip Joint has diminishing marginal productivity. The more workers there are on the job, the more they must share the fixed amount of capital (tubs, clippers, brushes), and the less benefit there is to adding yet another worker.
The marginal product of labor measures the benefit of employing an addi- tional worker in terms of the extra output produced. A related concept, the mar-
ginal revenue product of labor, or MRPN, measures the benefit of employing an additional worker in terms of the extra revenue produced. To calculate the MRPN, we need to know the price of the firm’s output. If The Clip Joint receives $30 for each dog it grooms, the MRPN of the first worker is $330 per day (11 additional dogs groomed per day at $30 per grooming). More generally, the marginal reve- nue product of an additional worker equals the price of the firm’s output, P, times the extra output gained by adding the worker, MPN:
MRPN = P * MPN. (3.3)
tabLe 3.2
the Clip Joint’s production Function
(1) (2) (3) (4) number of workers, N number of dogs groomed, Y Marginal product of labor, MPN Marginal revenue product of labor, MRPN = MPN : P (when P= $30 per grooming) 0 0 11 $330 1 11 9 $270 2 20 7 $210 3 27 5 $150 4 32 3 $90 5 35 1 $30 6 36
72 part 2 | Long-Run Economic Performance
At The Clip Joint the price of output, P, is $30 per grooming, so the MRPN of each worker, column (4), equals the MPN of the worker, column (3), multiplied by $30.
Now suppose that the wage, W, that The Clip Joint must pay to attract quali- fied workers is $240 per day. (We refer to the wage, W, when measured in the conventional way in terms of today’s dollars, as the nominal wage.) How many workers should The Clip Joint employ to maximize its profits? To answer this question, The Clip Joint compares the benefits and costs of employing each additional worker. The benefit of employing an additional worker, in dollars per day, is the worker’s marginal revenue product, MRPN. The cost of an additional worker, in dollars per day, is the nominal daily wage, W.
Table 3.2 shows that the MRPN of the first worker is $330 per day, which exceeds the daily wage of $240, so employing the first worker is profitable for The Clip Joint. Adding a second worker increases The Clip Joint’s profit as well because the MRPN of the second worker ($270 per day) also exceeds the daily wage. However, employing a third worker reduces The Clip Joint’s profit be- cause the third worker’s MRPN of $210 per day is less than the $240 daily wage. Therefore, The Clip Joint’s profit-maximizing level of employment at $240/day— equivalently, the quantity of labor demanded by The Clip Joint—is two workers.
In finding the quantity of labor demanded by The Clip Joint, we measured the benefits and costs of an extra worker in nominal, or dollar, terms. If we mea- sure the benefits and costs of an extra worker in real terms, the results would be the same. In real terms the benefit to The Clip Joint of an extra worker is the number of extra groomings that the extra worker provides, which is the mar- ginal product of labor, MPN. The real cost of adding another worker is the real
wage, which is the wage measured in terms of units of output. Algebraically,
the real wage, w, equals the nominal wage, W, divided by the price of output, P. In this example the nominal wage, W, is $240 per day and the price of out- put, P, is $30 per grooming, so the real wage, w, equals ($240 per day)/($30 per grooming), or 8 groomings per day. To find the profit-maximizing level of employment, The Clip Joint compares this real cost of an additional worker with the real benefit of an additional worker, the MPN. The MPN of the first worker is 11 groomings per day, which exceeds the real wage of 8 groomings per day, so employing this worker is profitable. The second worker also should be hired, as the second worker’s MPN of 9 groomings per day also exceeds the real wage of 8 groomings per day. However, a third worker should not be hired, as the third worker’s MPN of 7 groomings per day is less than the real wage. The quantity of labor demanded by The Clip Joint is therefore two work- ers, which is the same result we got when we compared costs and benefits in nominal terms.
This example shows that, when the benefit of an additional worker exceeds the cost of an additional worker, the firm should increase employment so as to maximize profits. Similarly, if at the firm’s current employment level the benefit of the last worker employed is less than the cost of the worker, the firm should reduce employment. For example, if The Clip Joint currently employed three workers, the MRPN of the third worker is $210, which is less than the nominal wage of $240, so the firm should fire one worker. Summary table 2 compares ben- efits and costs of additional labor in both real and nominal terms. In the choice of the profit-maximizing level of employment, a comparison of benefits and costs in either real or nominal terms is equally valid.
Chapter 3 | Productivity, Output, and Employment 73