marize all this by saying:

MPPi,

is the amount by whicb output rises (or falls) from spending a dollar more (or less) on capital. In our example, given that MPP;,, equals 12 and Pi equals 4, output rises by 3 units per dollar spent on capital. Using standard economic jargon, the expression in (1) is termed the marginal physical product per dollar spent on capital.

Similarly, the marginal physical product per dollar spent on labor is:

MPPi W

For example, if the marginal physical product of labor is 10 units of output and the going wage rate W is $2 per unit of labor, then by substitution in (2), the marginal physical product per dollar spent on labor is 5 units per dollar Again, the interpretation is that spending a dollar more (or less) on labor will cause output to rise (or fall) by 5 units.

Clearly, if the last dollar spent on labor is to cause output to rise by the same amount as the last dollar spent on capital, then in equilibrium we must have:

MPPi MPPk W Pk

Hence, if the left hand side in (3) exceeds the right hand side, the firm could increase its total output while keeping costs the same by spending $1 less on capital and $1 more on labor. Doing so will decrease total output from capital by the amount MPP / but will increase that from labor by MPPi / W. For exam-

ple, suppose tbe MPPj per dollar spent is 8 unil per dollar and the MPP per dollar spent is 2 units per dollar, then spending $1 more on labor and $] le.ss on capital will cause output (total physical product) rise by 6 units (8 - 2), while keeping total cost the same. If after this adjustment, the left hand side still exceeds the right" the firm can continue to increa.se output by shifting into labor and out of capital. But by diminishing returns, hiring more labor and less capital means that MPPj falls and the MPPj rises. Thus, eventually, equation (3) will be established. Consequently, in the long run, a firm will adjust its factor mix so that die marginal physical product per dollar spent is equal for all factors.

Equation (3) can also be cross-multiplied and rearranged to yield

MPPk MPPi

This says that in equilibrium the ratio of marginal physical products of labor and capital equals that of their prices. For example, if capital is twice as expensive as labor, then we know the firm will not be in equilibrium unless the MPPk is twice that of labor. Moreover, if we have any three of the terms in (3) or (4) we can algebraically solve for the other provided -and this is crucial-rthe firmis ui.eqiulibrium.

A litde care needs to be exercised when considering the price of factors. Clearly, the firm does not buy the worker, only the temporary use of his time. Similarly, with capital the relevant price is not that of the machine itself, but rather the price of the services rendered by the machine per unit of dme. In other words, the relevant price of capital, P, is the rental price of machines, i.e., a machine-hour, month, or year, etc., not the purchase price. Finally, since the wage rale W is the price of Labor, Pj formulas (2)

through (4) often appear with P] in place of W. ALGEBRAIC RELATIONS

We close this section with an algebraic restatement of the principle new relations introduced here.

Marginal Physical Product of Labor (MPPj) = (Aq/An). Measures the change in output (Aq) or total physical product (ATPP) resulting from a small change in labor (An), one more worker.

Marginal Physical Product of Capital (MPPk) = (Aq/Ak). Measures the chzmge in output (Aq) or total physical product (ATPP) resulting from the employment of an added unit of capital, where the change in capital (Ak) is small, usually just one unit.

Marginal Revenue Product of Labor (MRPj) -j (MR) (MPPi) = P(MPPi) when die firm sells as a price-taker in the product market. The concept measures the change in revenue to the firm resulting from selling the output obtained from hiring another worker

MarginalFactorCostof Labor (MFC]) = (ATFC/An). This concept measures the change in the lotal factor cost of labor (ATFC) when one more laborer is employed. MFC = W when the firm is a price-taker in the labor market and MFC] exceeds W when the firm is a monopsonist facing an upward sloping supply curve.

1. Sown. Thomas. Markeis and Minorides (.NW Vort: Basic Books. ) 981) p. 47

2. Firing Line transcripi of program broadcasi November 3, 1983

3. Crouch. Robert, Human Behavior Ari E-nnomir Approach (Belmont: Duxbury. 1979) p.

4. Slat;sUcal Abstract of th Sutes various issues

5. Ibid.

6. To-well. Thomas, The Economirs and Folilics of Race (New York Morrow, 1983) p. 200

7. Ibid. p. 2011817)

Warm-Up Questions for Section VTII

A. In the equilibrium of competitive firms: (a) W = MPP, (b) W = MC (c) W = MRP (d) W = MFC] (e) MFC, = MRP, (f) all of the above except (e) and (b).

Reanswer for a monopsony.

C. Marginal revenue product of labor is: (a) MR X MPP] (b) another name for MFC(c) output of the firm (d) added output obtained from employing another worker.

D. Marginal factor cost of labor is: (a) the wage if the firm is compedtive (b) less than the wage if the firm is a monopoly (c) greater than the wage if the firm is a monopsony (d) the change in total cost resulting from hiring one more worker (e) all of the above but (b).

E. Marginal physical product of labor represents: (a) the change in the firms revenues from selling one more unit (b) the dollar value of the additional output obtained from selling the product of an additional laborer (c) the change in output from hiring another unit of labor (d) another name for marginal factor cost (e) the same thing as the marginal physical product of capital in equilibrium.

F. The firm is not in long run equilibrium unless: (a) MPPi/Pk = MPPu/P], (b)MPPk/MPP, = Pi/Pk (c) [(MPPi)/(MPPk)] =Pi/Pk (d) MPPu = MPP] (e) none of these.

G. The marginal physical product of labor is defined as: (a) the marginal factor cost of labor (b) the marginal revenue product of labor (c) the change output resulting from employing one more worker (d) output per man-hour (e) maiginal revenue times the marginal physical product of labor

H. The demand for labor by a competitive firm is best described as which of the following curves? (a) the marginal phj-sical product of labor (b) die marginal factor cost of labor (c) the marginal revenue product of labor (d) the supply of labor (e) the marginal factor cost of capital.

demand for labor by a competitive industry? (a) a decrease in the price of labor (b) a decrease in the amount of capital available for labor to use (c) a change in technology (d) an increase in the number of firms demanding labor (e) a decrease in the price of substitutes for labor

J. Professional basketball players receive much

higher rates of pay than lemon pickers because: (a) the demand for players is very high in relation to the supply (b) lemon pickers are often members of minority groups (c) professional basketball pla\ers are often members of minority groups (d) the supply of lemon pickers is relatively low in relation to the demand for them (e) lemon pickers are exploited.

K. When we look at the occupational history of ethnic groups that have met with litde or no discrimination in the United States, we fmd that they are:

(a) about proportionally represented in various occupations (b) about equally prosperous today (c) usually among the most prosperous ethnic groups

(d) strongly involved m politics (e) none of the above.

L. If a union restricts the supply of labor through a discrimination scheme of one type or another, then we would expect to find in the unionized sector relative to competition: (a) wages higher and employment higher (b) wages higher and some unemployment (c) wages higher, employment lower, and no unemployment (d) wages lower, employment higher, and some unemployment (e) none of the above.

M. A union using collective bargaining techniques to increase wages would present employers with a supply curve of labor with an elasticity of: (a) zero

(b) infinity (c) one (d) between one and infinity

(e) between zero and one.

N. As used by economists, the term exploitation refers to a situation in which: (a) some people receive pitifully small wages (b) some employers pay their workers more than their marginal revenue product

(c) the difference between the marginal revenue productof labor and the wage rate is zero (d) the dif ference between the marginal revenue product of labor and the wage rate is greater than zero (e) none of the above.

Which of the following will not shift the