Elsewhere, I’ve been involved in a discussion on the economics of slavery. I mentioned Robert Fogel’s and Stanley Engerman’s Time on the Cross, which argues — and this is a very simplified paraphrase — that slavery is not everywhere and always unprofitable. In fact, Engerman co-authored a paper with Kenneth Sokoloff, “Institutions, Factor Endowments, and Paths of Development in the New World,” where they use a similar argument to explain institutional divergence in different parts of the Americas. The argument is that industries affected by economies of scale, where fixed costs are relatively high, are better suited for slave labor (or, otherwise, low-paid wage labor).

The intuition is that, given economies of scale, comparatively large quantities of output are necessary to push down average costs, thereby requiring relatively large labor inputs. This is especially true where the industry is relatively labor intensive, which was the case during the early colonization of the Americas (relatively capital intensive industry began to appear around the 1840s, and then took off in the United States following the U.S. Civil War). Engerman and Sokoloff posit that the geographic distribution of these different industries is decided by geographic factor endowments. Further, producers in these geographic areas will tend to specialize in industries that are intensive in the good that is locally abundant. This follows from the Heckscher–Ohlin trade model (the idea is that local abundance drives the opportunity cost of these resources down, giving that area a comparative advantage).

I suggest that Fogel and Engerman’s book is the definitive study on American slavery. Not everyone agrees, I guess; I was pointed to a crical review of the book by Mark Thornton, “Slavery, Profitability, and the Market Process.”

In any case, I made a number of points as to why it’s not probable that slavery is a profitable means of employment, for the employer, in an advance economies,

There is the classic incentives argument, which says that differences in payment will alter incentives, implying that low wage (or, in our case, unpaid) labor has less of an incentive to maximize productivity; Influenced by George Reisman’s argument, elucidated in his book Capitalism, on the fundamental scarcity of labor, I suggest that as the division of labor grows, and the competition for labor rises, the option of enslavement — unless slavery is institutionalized through law — disappears. As the marginal productivity of labor rises, and therefore so do wages, workers will simply opt to move to industries where wages are highest.

These are the typical, superficial arguments as to why slavery eventually peters out as a viable means of employment. But, inspired by an excerpt from Don Lavoie’s Rivalry and Central Planning, I wonder if Mises’ calculation argument offers a different path to explaining the downfall of slavery’s viability (in relatively advanced divisions of labor). Mises’ case against socialism boils down to a knowledge problem, but one that specifically deals with the problem of imputation. In a nutshell, Carl Menger, in Principles of Economics, develops a subjective theory of value, where factor of productions’ value is determined by means of imputation, which means that they’re derived from the values attached to the final consumer goods, whose values are directly determined by their (subjective) benefits. The problem was that there was no convincing price theory which explains how exactly these values come to be known. Friedrich von Wieser thereafter developed his own theory of “natural value,” where, as I understand it, these values are exogenous to the market process. Unconvinced by this theory, Mises (Boris Brutzkus, Nicolas Pierson, and Max Weber developed similar theories independently — see Hayek’s Collectivist Economic Planning and Individualism and Economic Order) advanced a novel alternative hypothesis, which argues that only a competitive market process, based on the institution of private property, can allow for price formation. And, only through price formation can the values of factors of production be known to firms, who can use these prices to choose between alternative means, and also rely on profit and loss accounting to track their efficiency.

Labor is a factor of production, so its value must be imputed from the final product. Specifically, following Böhm-Bawerk’s law of costs, since labor — to an imperfect extent — is a relatively mobile factor, the value of the marginal worker will be imputed from the least valuable alternative end (because, if this worker were drop out of the labor market, the firm would sacrifice the least valuable attainable end, rather than the most — in other words, the opportunity cost is the alternative end with the lowest value). The price of labor gives firms added information regarding the value of the labor they employ, allowing firms (and labor itself) to allocate its employees in a relatively efficient way. Where the marginal productivity of labor is very low, this issue loses some relevance. But, as the marginal productivity of labor rises, if slavery is institutionalized in such a way that it sacrifices the bidding process allowed by a frequent movement of labor, it suffers from the fact that the lack of market prices (apart from the initial cost of acquisition) will make it much more difficult, if not impossible, for firms to efficiently allocate their labor. The result is that slave-employing firms will be at a competitive disadvantage relative to wage-paying firms producing the same goods.

Does this sound like a plausible thesis? Skimming over the above-linked Thornton article, he advances a similar argument. Has anybody else made the same argument? I think this theory fits nicely with the work done by Engerman and Fogel. Their theory, as aforementioned, relies on the assumption of economies of scale and labor-intensive industries. Imagine labor intensity as a ratio between the quantity of labor employed to the quantity of capital employed (L/K). With capital accumulation, this ratio should become smaller (L/K↑), meaning the capital intensity of the industry is increasing. Capital is what raises the productivity of labor, and therefore raises wages. With capital accumulation, and therefore economic growth, slavery becomes gradually more uncompetitive. As argued in, for example, Acemoglu’s and Robinson’s Why Nations Fail, southern production remained relatively labor intensive, even as northern industry became more-and-more capital intensive. This is probably why the profitability of slavery, in the south, was not drastically challenged during the first half of the 19th century.

Finally, in passing, what this all suggests is that, in the context of perfect markets, slavery should become nonviable with industrialization and mechanization. The problem is institutional. Not only was slavery institutionalized in the South, but Southern institutions were generally more extractive than those of the North. The South, relative to their Northern brethren, were less innovative, and the economy was less competitive. This is related to the factor endowments argument, but that slavery didn’t fade on its own is also a product of the effort that entrenched interests put in to make sure that their way of doing business isn’t forced into irrelevancy through competition. In other words, there’s also a political dimension to the problem of slavery. I don’t think we can divorce markets from politics (or, institutions more broadly), but this is a point consider.