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Slave labor as labor hoarding - input use inside the economic region of production.

If bound to daily labor while he lives, His is the daily bread that labor gives; Guarded from want, from beggary secure, He never feels what hireling crowds endure, Nor knows like them in hopeless want to crave, For wife and child, the comforts of the slave, Or the sad thought that, when about to die, He leaves them to the cold world's charity, And sees them slowly seek the poor-house door - The last, vile, hated refuge of the poor.

This paper is a nontechnical note on the analysis of the use of slave labor as production inside the economic region of production and the consequent reallocation of the fixed slave input to other plantation activities. The planter of the antebellum South's primary staples - sugar, rice, tobacco, and king cotton - would from time-to-time experience a downturn in market demand as a result of European wars or economic stagnation. Supply-side factors, such as unfavorable climate condition, also would affect production, but not necessarily employment, decisions. If the planter were hiring free labor, he would experience no compunction to release from hire labor which he considered, for the most part, unskilled. This attitude would be reinforced by the by the knowledge that such adverse conditions would also affect his neighbors. They were not going to hire "his" laborers. When conditions changed to again make employment of his released labor economically feasible, he would have a ready supply of labor available from which to hire save for the diminution of this reserve due to migration or morbidity.

Since the value of the slave's labor was capitalized over his lifetime, the planter was not in a position to discharge his services as conditions deemed feasible. To my knowledge, U. B. Phillips was the first to allude to this phenomenon. "With large amounts of capital invested in slaves, the system would be maintained even in time of depression, when the plantations were running at something of a loss; for, just as in a factory, the capital was fixed, and operations could not be stopped without still greater loss." [13, p. 259] Earle and Hoffman [4] and Anderson and Gallman [1] also touch on these points. When viewed in the conventional, static, short-run analysis of microeconomic theory, slave labor would be as fixed as the land and capital to which it was applied, i.e., the planter was a labor hoarder.

In fact, this rigidity is one reason given why slave labor did not often find favor in Southern factories.(1) Oscillations in demand frequently necessitate layoffs of industrial workers. When the workers are owned, layoffs are impossible. If the slave is sold, he is sold at a discount. When demand conditions recover so that the slave again may be employed profitably, repurchase is at a premium. Insofar as manufacturing and agricultural production positively correlate, slaves belonging to the plantation could not be hired out to factories when agricultural demand fell.

Human capital theory is helpful in explaining some important aspects of the plantation's reluctance to part with slaves.(2) This literature helps explain the observed pecuniary preference of the purchaser for the domestic over the African slave [9]. The concept of firm-specific training is useful in understanding a planter's reluctance to part with a lifelong household servant. The approach, however, is more limited when production is viewed in the static short run. The planter was forced by economic and legal considerations to maintain even his most unskilled and superannuated slave. Thus, slavery from this perspective takes on the characteristics of pure capital theory as well as a social relationship.

One approach to deal with the planter's problem of the depressed short run is to analyze the production function of the primary staple he grows and secondary products arising from the plantation system. Isoquant theory is so often understood in its two-dimensional form instead of its three-dimensional origin. But, one must look at under what circumstances production occurs inside the economic region of production. Slave labor as used in the "peculiar institution" provides an excellent example of this phenomenon.

If the planter reduces production of his staple commodity because of slack demand, he must leave part of his labor force (expressed in man hours of work) idle or shift them to auxiliary plantation activities. These included clearing woods, cutting firewood, draining ditches (production activities) and serving as household servants, coachmen, etc. (consumption activities). These uses are clearly economically and engineering inefficient when viewed from efficiency prevailing before the reduction in staple production. It is doubtful that during such periods the planter was able to reduce significantly the outlay necessary to maintain his slave force since the slave was likely kept at the subsistence level of medical care and provision for shelter.(3)

Assume the outlay for land and equipment used by slaves and their input prices remain unchanged during depressed periods. If we combine land equipment used by the slaves into one variable, K, and let slave labor be denoted by L, we can construct isoquants showing all possible combinations of inputs which produce a given output. Labor hoarding however cannot be adequately expressed by isoquants. Figure 1 shows the dilemma faced by a plantation owner with fixed land and labor. Given the planter's production function, engineering efficiently implies that he will produce a level of output [Q.sub.o] i.e., uu'. The planter would be producing the maximum output from the given quantities of capital and slave labor, [K.sub.1] and [L.sub.1], respectively. Classical theory would regard labor as perfectly mobile, or nearly so, so that a reduction in production to, say, [Q.sub.1], would be marked by a concomitant decrease in the use of labor. The slave system would require the planter to continue to employ all, or nearly all, of his slave labor force at [L.sub.1] in spite of his reduction of output inside the economic region of production at point F.

The outcome does not imply that the planter was irrational. Indeed, the peculiar feature of purchasing the discounted income stream of slave labor requires the planter treat his slave as the manufacturer treats his physical capital. In another context, Pasour [12, p. 74] suggests that labor hoarding is probably most often a behavior which reflects the entrepreneur's understanding of long term economic conditions. The planter practicing labor hoarding was not irrational or ignorant but "maximizing wealth over time instead of maximizing profits for a single period."

Suppose that the planter in question is the owner of a cotton plantation with production function

C = C([L.sup.c], [K.sup.c]). (1)

Where, [L.sup.c], [K.sup.c] are the inputs of his slave labor and capital and land devoted to cotton. And for simplicity assume that the production of all other plantation goods is expressible as output Z; where Z might be production of corn, poultry, the clearing of woods, or the drainage of swamps. Let the production function of Z be represented as

[Mathematical Expression Omitted]

Where, L = [L.sup.c] + [L.sup.z] or his fixed supply of slave labor, and K = [K.sup.c.] [K.sup.z] or his fixed supply of capital and land in the short run. The planter may have motives other than maximizing profits such as the use of slave labor for consumption purposes or just conspicuous consumption but assume that the planter maximizes profits given by

[Mathematical Expression Omitted]

Where, [p.sub.c] is the market price of cotton, [p.sub.z] is the imputed price of other plantation production and w is the imputed wage per unit slave input, i.e., the price of output times the marginal product of labor, and r is the rental rate of land. The first-order conditions which arise from (3) are given as
 [pi]L = [p.sub.c][C.sub.L] - [p.sub.z][Z.sub.L] = O, (4)
 [pi]K = [p.sub.c][C.sub.K] - [p.sub.z][Z.sub.K] = O. (5)

Equation (4) implies that the value of the marginal product of labor in the production of cotton must equal the value of the marginal product of labor in the production of alternative plantation goods

[p.sub.c][C.sub.L] = [p.sub.z][Z.sub.L] or

[VMP.sup.c.sub.L] = [VMP.sup.z.sub.L], (6) and likewise for K. Equation (6) implies that if the price of cotton falls the marginal product of labor in cotton production must rise and the marginal product of labor in alternative production must fall in order to maintain the equality. That is, less labor should be devoted to the production of cotton and more to the production of other plantation goods. At the same time, less of K is likely to be used in cotton production. If Genovese [6, p. 46] is right when he says that "Slavery requires all hands to be occupied at all times" it must be understood as a reallocation between primary and secondary production. However, it is not necessarily the case that production effort continue at the same level.

Slave laborers were not usually compensated explicitly for their efforts but instead received food, clothing, shelter, and other basic necessities. Sutch [14, p. 266] notes that the "caloric requirements of the human body depend upon the total energy expanded as well as body weight and stature. Since we have reason to believe that the slave was required to exert more work effort than the free workers, the question of the caloric requirements for slaves will depend upon how hard they were forced to work." If cotton prices fell sufficiently, it may very well have been more economical to leave labor idle and save the extra expenditures on sustenance. The optimal solution might indeed be point F in Figure 1.

I no other production occurs on the plantation (Z = O) and no slave rental market exists, then as long as the price of cotton is high enough to warrant the additional caloric intake by the slave, the plantation owner would never reduce production in the short run. If the price of maintaining the slave is invariant with respect to the level of effort, the owner's marginal cost of producing cotton with its fixed inputs is zero. In this case, production will be at [Q.sub.o] in Figure 1 regardless of the (positive) price of cotton.

Ideally, one would like to know precisely how many labor units were diverted to non-cotton production activities as a consequence of unexpected falls in cotton prices. Limitations on historical data make this extremely difficult. As a second-best solution one might wish to know how the production of non-cotton activities changed in response to cotton price fluctuations. This too entails measurement problems.

The solution to (4) and (5) implies that the plantation's slave labor demand function for cotton production is of the form

[L.sup.D.sub.c] = f(w,r,[p.sub.c],[p.sub.z] (7)

The market demand for slave labor in cotton production is then just the summation of individual plantation demands. At an instant in time, the supply of slave labor for all intents and purposes was fixed with increases occurring at the natural rate. The problem with estimating (7) while assuming that slave labor on cotton plantations is slave labor used in cotton production is to introduce a bias resulting from mismeasurement. Naive estimation would lead us to assume [p.sub.z] is not an argument in (7). An assumption that all labor or a constant proportion of slave labor goes into cotton production each period would lead us to believe that slave labor's marginal product is falling when the price of cotton is falling, whereas, in fact, it is rising due to the movement of plantation slave use to other areas of production activity.

Equation (7) offers at least a partial solution to the estimation problem. By including prices, [p.sub.z], of other goods slave labor was used to produce, e.g., grains and livestock, it is possible to remove some of the bias in estimating the slave labor demand function. Since variations from the trend use of slave labor in cotton production would be highly correlated with the price of cotton, it is impossible to argue that measurement errors of [L.sub.c] would be random. The most realistic solution would be to better measure the output of secondary plantation production and infer the use of slave labor in these activities.


(1.) In 1863, J. E. Cairnes [3] cited slave ignorance as preventing them from operating factory machinery. He also believed that educated slaves grouped in cities as industrial workers increased the probability of rebellion. (2.) See Becker [2], Mincer [10] and Parsons [11]. (3.) The amount of food provided to the slave has been the subject of an ongoing debate. Fogel and Engerman [5, p. 112] claim that the average slave caloric intake in 1860 exceeded that of the entire population. Sutch [14] counters that when adjusted for work effort, slaves were not well fed. Genovese [7, p. 308] believed that "Slaves received clothing and food designed to provide at least minimum comfort." He goes on to say that slaves normally did not work outdoors in the rain or extreme cold; usually, they were deliberately ordered to stay indoors."


Anderson, R. V., and R. E. Gallman, "Slaves as Fixed Capital: Slave Labor and Southern Economic Development," The Journal of American History, 63 (1977), 4-26. Becker, G. S., Human Capital (2nd ed., New York: Columbia University Press, 1975) chps. 1-3. Cairnes, J. E., The Slave Power: It's Character, Career, and Probable Designs (London: A. M. Kelley, 1968). Earle, C., and R. Hoffman, "The Foundation of the Modern Economy: Agriculture and the Costs of Labor in the United States and England, 1800-60," American Historical Review, 85 (1980), 1055-94. Fogel, R., and S. Engerman, Time on the Cross: The Economics of American Negro Slavery, (Boston: Little, Brown and Co., 1974). Genovese, E. D., The Political Economy of Slavery: Studies in the Economy and Society of the Slave South, (New York: Pantheon Books, 1965). Genovese, E. D., "Rebelliousness and Docility in the Negro Slave," in Civil War History, v. 13, (Iowa City: Kent State University Press, 1967). Grayson, W. J., The Hireling and the Slave, (Charleston: Mnemosyne Pub. Co., 1969). Littlefield, D. C., Rice and Slaves, (Baton Rouge, La. Louisiana State University Press, 1981), chps. 1-3. Mincer, J., "On-the-Job Training: Costs, Returns, and Some Implications," Journal of Political Economy, 70 (1962), 50-79. Parsons, D. O., "Specific Human Capital: An Application to Quit Rates and Layoff Rates," Journal of Political Economy, 80 (1972), 1120-1143. Pasour, E. C., "A Further Note on the Production Outside the |Economic' Region of Production," The American Economist, 24 (1980), 71-75. Phillips, U. B., "The Economic Cost of Slaveholding in the Cotton Belt," Political Science Quarterly, 20 (1905), 257-75. Sutch, r., "The Care and Feeding of Slaves," in P. A. David, et al., Reckoning with Slavery, (New York: Oxford University Press, 1976).
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Author:Smith, Bruce Henry
Publication:American Economist
Date:Mar 22, 1992
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