SECTION VIII: THE LABOR MARKET

Up to now we have been dealing almost exclusively with the product market. Equally important are the factor markets, where firms become the buyers and households the sellers. In this section we concentrate upon the labor market, but address the capital market as well.

PROnT MAXIMIZATION IN LABOR MARKETS

Like the theory of product supply, the theory of labor demand is based upon the presumption that firms seek to maximize total profit. Consequently, any firm - whether competitive in the labor market or not - should continue to hire labor so long as the increase in revenue obtained from selling one more workers product exceeds the increase in labor cost caused by hiring him. The increase in revenue thereby obtained is termed the marginal revenue product of labor (MRPj) and the increase in tolal cost caused by hiring one more laborer is termed the marginal factor cost of labor (MFC]). For example, suppose that hiring another worker and selling the resulting increase in output brings in revenue of $10; if hiring him increases cost by say, $4, then the firm will earn a profit of $6 ($10 - $4) on hiring this one particular worker and will do so. In this case, the marginal revenue product of labor is $10 and the marginal factor cost is only $4. If hiring the next worker and selling the output increase

brings m, say, $6 (MRP] = $6) but costs the firm $4 (MFCi = $4), then the firm will hire that worker too. Only when the marginal revenue product of labor equals the marginal factor cost does the profit maximizing firm cease hiring. Although this basic profit maximization rule applies to all buyers of labor, we will first consider its implications in competidve labor markets.

COMPETITIVE LABOR MARKETS

As with compedtive product markets, all transactors are price-takers in competitive labor markets, i.e., both buyers and sellers take the price of labor services as essendally given. In other words, an indi\idual firm can hire any number of workers it wishes at the going wage rate, W, and a worker can sell all the labor he wishes at that rate. As a result, both the supply curve of labor to competitive firms and the demand curve of labor to households are perfectly elasdc at the going wage. (Recall Figure XIII in Section III if you need to refresh your memory on this point). We illustrate profit maximizadon under these conditions in the following example.

Suppose that a competitive firm producing widgets has in place fixed quantities of non-labor factors of production, that is, land and capital equipment. Then by the analysis in Section V, we know we are dealing with a short run situation characterized ultimately

Table I Derivation of the Marginal Revenue Product (Demand Curve) of Labor

(1) Number of

Workers

0 1 2 3 4 5

(2) Total Ptiysical Product (TPPi = q)

(3) IViarginal Physical Product (MPPi)

Product Price

(5) Marginal Revenue Product (MRPi)

by diminishing returns to the variable factor, labor. Colunm two of Table I shows the total physical product of labor (TPP] ) obtained when vfarious numbers of workers are hired; it isjust the same thing as output, q. For example, a total output of five widgets will be produced if the firm hires just one worker; a total of nine will be produced with two workers and so forth. The marginal physical product of labor (MPPi ) measures the change in total physical product ( or Aq where " ", as always, means "the change in") brought about by hiring an added worker. For example, increasing the number of workers hired from 2 to 3 means that output rises from 9 to 12 units. Therefore, the MPP of the third worker is 3 units (12 - 9). Similarly, increasing employment from three workers to four means that output (total physical product) rises by two units (14-12). As such, the MPP] associated with four workers is two units. We recommend that you verify the other entries in the table.

As Table I indicates, hiring each additional worker causes output to rise by less than the previous one, wluch is to say, the MPPi diminishes as employment is increased. These diminishing returns set in because each addidonal worker has a smaller amount of the fixed factor, capital, to work with and because the exisdng workers start to crowd and interfere with each other.

As a profit maximizer, the firm is interested in how its revenues respond when it hires addidonal labor. The marginal revenue product of labor (MRPj) measures the change in revenue obtained by hiring another worker and selling the resulting increase in output For example, in Table 1 hiring the second worker means that output rises by 4 widgets

(MPP] = 4), which can be sold for $10 each (MR = P = $10), so that the marginal revenue product of labor associated with two workers is $40 (4 x $10). As the example illustrates, the marginal revenue product of labor (MRP]) is simply the marginal physical product of labor (MPP]) multiplied by the price P at which the product sells. (Since we are dealing with a competitive firm, this price is assumed constant at $10 in the table.) Continuing to the third worker, we see that the MPP is three units; hence the MRP associated with the third worker is $30 (3 x $10). Similarly, $20 is the increase in revenue which the firm could gain by hiring a fourth worker Because the marginal physical product of labor (MPPj) is declining due to diminishing returns, it follows that the marginal revenue product (MRP] = MPP] X P) must also decline as employment rises. We emphasize that diminishing returns are the sole reason for dechning MPPj : The model presumes labor to be homogenous, so that decreases in the quality of the work force are ruled out.

Now consider a particular going wage rate VA. say, $20 per day. Should the firm hire the first worker? Of course it should; the first worker adds $50 to the firms revenue (MRP = $50), but only $20 to its cost (MFC = W = $20). Similarly, hiring die second worker adds revenue of $40, but increases the firms cost by only $20. A similar analysis applies to the third worker; but the fourth worker adds $20 to the firms revenue (MRP now equals $20) and also adds $20 to its cost (MFC also equals $20). Hence the firm just breaks even on hiring him. Thus, at four workers W = MFC], = MRPi, which is our profit maximizing, condition. Note that its unprofitable to hire a fifdi worker if the wage is $20; doing so adds only $10 to die 1

firms revenues, but $20 to its costs. Hence W = $20 and n = 4, where n = the number of workers, is one point on the firms labor demand curve in Figure I. On the other hand, the firm would be willing to hire the fifth worker if the wage rate were $10 per day. Therefore W = $10 and n = 5 is another point on the labor demand curve. Similarly, at the higher wage rate of $40 per day employment will only be two workers. This is sdll another point. Since for any given wage rate we know the amount of labor the firm will hire, we have derived the compeddve demand for labor: it is the marginal revenue product of labor Connecdng all the points together yields the demand curve portrayed in Figure I.

As with the product demand curve, it is important to emphasize what is being held constant in deriv-ing labor demand. Here the product price, the technology, and the quandties of other factors of producdon are held fixed. A change in any of these will cause a shift in the labor demand curve. Suppose, for example, that the product price P were to rise due to a change in tastes in favor of the final product, then the MRPi = [P x (MPPj)] will rise, shifting die labor demand curve up as in Figure II. Of course, a decrease in product price would reverse these effects. Since the demand for labor depends upon the product price, it is often called a derived demand. That is to say, the demand for labor is derived from the demand for the final product If the produa was valueless, the demand for labor to make the product would be non-existent.

Changes in the quandties of other factors of producdon or the technology will also change the MPPi relation in Table 1 and therefore the labor demand. Normally we would expect an increase in

capital or technological progress to raise the MPPi, thereby increasing the labor demand as in Figure II.

Just as we obtained the market demand .schedule as the horizontal summation of the individual household demands, so also can we approximate the industry demand for labor schedule by horizontally summing the firms labor demands. However, this can only serve as an approximation: in deriving tlie firms labor demand as MRP we held product price constant. But because an industrys output expands as employment rises, product price normally falls, thereby affecting the price component in the marginal revenue product of labor (MRPj) curve. This point is further addressed in intermediate price theory courses and completely ignored hereafter in this treaunent. In an\ event, be assured that the demand for labor does indeed slope dowii.

Given the industry or market demand for labor, we can find the equilibrium level of employment and wages if we have the labor supply curve. The supply curve of labor is customarily assumed to slope upward, but this is by no means necessarily true at all wages. For example, at high wage rates, people may feel wealthy enough to work less and play tennis more. If so, the supply of labor begins to bend backward, so that eventually, less, rather than more labor is supplied. We will also completely ignore this possibili tv-hereafter. Figure III-displays-die typical oipvard sloping industry supply curve with the familiar equilibrium illustrated at N* and W*. Note that the supply curve faced by the individual competitive firm is perfectly elastic at the going wage W*. The firm can buy all the labor it wants at the going wage because, under compedtion, the firm is too small to affect the market wage on its own accord. In other words, the competitive