¹ Helper, Hinton Rowan, The Impending Crisis of the South: How to Meet It (New York, 1857)Google Scholar, reprinted in part in Woodman, Harold D., ed., Slavery and the Southern Economy (New York, 1966), p. 201Google Scholar.

² For example, see Russel, Robert R., “General Effects of Slavery Upon Southern Economic Progress,” Journal of Southern History, 6 (February 1938), 46–48Google Scholar. See also Fogel, Robert William and Engerman, Stanley L., eds., The Reinterpretation of American Economic History (New York, 1971), p. 337Google Scholar; Starobin, Robert S., Industrial Slavery in the Old South (New York, 1970), p. 186Google Scholar; Conrad, Alfred H. and Meyer, John R., “The Economics of Slavery in the Ante Bellum South,” The Journal of Political Economy, 66 (April 1958), 120Google Scholar.

³ Gates, Paul W., The Farmer's Age (New York, 1968Google Scholar; first published in 1960), pp. 40, 165, 277; Gates, Paul W., “Frontier Estate Builders and Farm Laborers,” in Wyman, W. D. and Kroeber, C. B., The Frontier in Perspective (Madison, 1957), p. 155Google Scholar; Bidwell, Percy W. and Falconer, John I., History of Agriculture in the Northern United States, 1620–1860 (Washington, D.C., 1925), pp. 163–164, 204–205, 274–276Google Scholar.

⁴ Benson, Lee, Toward the. Scientific Study of History (Philadelphia, 1972), pp. 258, 260Google Scholar.

⁵ Ogg, Frederic Austin, ed., Fordham's Personal Narrative, 1817–1818 (Cleveland, 1906), pp. 192, 209–211Google Scholar.

⁶ Ibid., p. 212.

⁷ Thwaites, R. G., ed., Bradbury's Travels in the Interior of America in the Years 1809–1811, Vol. 5 of Early Western Travels, 1748–1846 (Cleveland, 1904), pp. 282–283Google Scholar; see also pp. 285–286.

⁸ Burkett, Charles W., History of Ohio Agriculture (Concord, N.H., 1900), p. 49Google Scholar; Fletcher, Stevenson W., Pennsylvania Agriculture and Country Life, 1640–1840 (Harrisburg, Penn., 1950), pp. 107, 110, 306, 308Google Scholar; Hedrick, U. P., A History of Agriculture in the State of New York (Albany, 1933), p. 51Google Scholar.

⁹ P. W. Gates, “Frontier Estate Builders,” pp. 155, 157; F. A. Ogg, Fordham's Narrative, p. 211; State of Massachusetts, Report of the Bureau of Statistics of Labor, 1871 (Boston, 1871), p. 161Google Scholar.

¹⁰ Bradbury claimed that “the accumulation of property by the regular and rapid advance in the value of his land, forms more than an equivalent to the savings of the labourer or mechanic.” R. G. Thwaites, ed, Bradbury's Travels, pp. 285–286.

¹¹ Easterlin estimated agricultural income per worker at $182 in New England and $225 in the Middle Atlantic region, compared to $147 in the East North Central and $140 in the West North Central. In contrast, per capita agricultural income was lower in the old South than it was in the frontier South, the area of southern net immigration. In constructing his estimates of output, Easterlin properly excluded changes in land values, but such changes might explain regional migration patterns; Richard A. Easterlin, “Interregional Differences in Per Capita Income, Population, and Total Income, 1840–1950,” in Trends in the American Economy in the Nineteenth Century (“National Bureau of Economic Research, Studies in Income and Wealth,” Vol. 24 [Princeton, 1960]), pp. 97–98Google Scholar.

Using data collected for 1818, 1826, 1830, 1850, and 1860, Lebergott found that the average monthly earnings of farm laborers, including board, were higher in New England than in the Middle Atlantic, East North Central, or West North Central regions. That finding is reversed for the South, where wages in the South Atlantic were persistently below wages in the East or West South Central regions; Lebergott, Stanley, Manpower and Economic Growth (New York, 1964), p. 539Google Scholar.

¹² I am particularly indebted to Stephen Salant for his assistance in writing this section.

¹³ Qualitative evidence of imperfect wage adjustment may be found in P. W. Gates, The Farmer's Age, pp. 40, 165, 277; Lebergott's data show little net change in agricultural wages over extended periods, consistent with but not uniquely supporting the notion of an institutional wage; S. Lebergott, Manpower, pp. 257–258.

¹⁴ We might also envision a situation in which the wage is constant until the demand for labor reaches , after which the wage might rise with the increase in the demand for labor. This case may be demonstrated independently, but the reader can see that it follows as a limiting case of the assumption discussed in the Appendix.

¹⁵ With respect to the conclusions reached here, note first that all linear homogeneous functions are homothetic. Moreover, if f(K, L) is linear homogeneous, then f = f_k(K + f_lL and f_kl. = − (IVK)f_LL but if f_LL, < 0, then f_KL > 0.

¹⁶ There seems to be general agreement that entrepreneurial skills, however defined, are not distributed homogeneously among the population at large; see, for example, McClelland, David D., The Achieving Society (New York, 1961), chs. vi, viiCrossRefGoogle Scholar; Bruton, H. J., Principles of Development Economics (Englewood Cliffs, N.J., 1965), pp. 94, 254–255Google Scholar; Lewis, W. Arthur, The Theory of Economic Development (Homewood, Ill., 1955), p. 99Google Scholar; Buchanan, Norman S. and Ellis, Howard S., Approaches to Economic Development (New York, 1955), p. 50Google Scholar; Schumpeter, Joseph A., Tlie Theory of Economic Development (New York, 1961; orig. pub. 1934), p. 81Google Scholar. McClelland states that entrepreneurs are not motivated strictly by profit but rather seek profit because it gives the entrepreneur “definite” knowledge of his competence; D. D. McClelland, Achieving Society, p. 234.

¹⁷ It is the need for slavery to maximize the absolute return to the landowner, or equivalently, to maximize the rate of return on the constraining fector, that Domar places at the core of his model which seeks to explain the origin of slavery in a high land/labor ratio. Engerman has discussed Domar's position extensively; Domar, Evsey, “The Causes of Slavery or Serfdom: A Hypothesis,” The Journal of Economic History, 30 (March 1970), pp. 18–32CrossRefGoogle Scholar; Engerman, Stanley, “Some Considerations Relating to Property Rights in Man,” The Journal of Economic History, 33 (March 1973), pp. 56–65CrossRefGoogle Scholar.

¹⁸ David has stressed the link between agricultural mechanization and industrialization in his study of northern reaping machines. Genovese and North emphasize the absence of strong local markets in retarding southern industrialization; Parker has revised and restated this argument. Fogel and Engerman discuss the position critically; Paul David, “The Mechanization of Reaping in the Ante-Bellum Midwest,” reprinted in R. Fogel and S. Engerman, eds., Reinterpretation, p. 215; E. Genovese, The Political Economy of Slavery, ch. viii, esp. p. 181; D. North, Economic Growth, pp. 131–133; Parker, William N., “Slavery and Southern Economic Development: An Hypothesis and Some Evidence,” Agricultural History, 44 (January 1970), pp. 116–117Google Scholar); R. Fogel and S. Engerman, eds., Reinterpretation, p. 337.

¹⁹ Whether the capital-output ratio will be greater for the constrained farm if only concavity and homotheticity are assumed depends essentially on whether the constraint produces an equilibrium output close or far from the equilibrium output of the unconstrained farm. The proof of this has been omitted.

²⁰ We have not shown that the totat size of the agricultural sector is independent of the condition of labor, but have confined ourselves to discussing whether there will be entrepreneurs in the agricultural sector. The question would be interesting to investigate, but a different, lengthy apparatus is required. Let it suffice that the ingredients of such a story would at least weigh the increase in total output that might be attributed to slavery's permitting scale economies, against the possible effects of slavery in retarding movement to new lands (slavery reduces the number of people who can decide to move west).

²¹ We have not treated the effects of slavery on the composition of demand for farm capital. Clearly, as the constrained farmer substitutes capital for labor he must be buying some labor-saving machines; however, other forms of capital, such as better buildings and fences, also substitute for labor but have a smaller direct effect on the farm-machinery industry.

²² Appendix Table A-l, column 16. Table A-l contains tabulations of each statistic by region, definitions of regions, and data sources.

²³ Table A-l, column 1.

²⁴ Table A-l, column 18.

²⁵ Table A-l, column 3.

²⁶ Table A-l, column 4.

²⁷ Table A-l, column 5.

²⁸ Table A-l, column 6.

²⁹ Table A-l, column 17.

³⁰ Table A-l, column 10.

³¹ Table A-l, column 11.

³² Table A-l, column 20.

³³ Table A-l, column 12.

³⁴ See notes to Table A-l, cols. 18 and 4.

³⁵ The data come from the Census tabulations, not from a Census sample, and thereby provide conclusive proof that the true population means are different; statistical confirmation of this would be inappropriate. At a different level, however, one might conceive of a statistical test, of the proposition that the observed variance in the cited ratios among states could be successfully explained with a single dummy variable for the presence of slavery. Equivalently, one might consider a thought-experiment whereby one drew states, with associated data, at random, arbitrarily labeled them “slave” or “free,” and then asked what would be the chance of drawing two samples with the differences actually observed between the slave and free states. To examine that possibility, the data were analyzed with a one-way weighted analysis of variance. In one case, intra-state variance was assumed to be zero; in the other case, intra-state variance was estimated with the mean-variance ratio of the distribution of farm sizes within each state. In all cases the presence or absence of slavery was statistically highly significant, although in most cases it did not explain a great deal of the variance. The paper does not report these findings at greater length because they are not surprising and they lend a spurious air of authority to the findings. The key issue is whether we should attach much economic importance to the statistically significant differences we observe, a question that cannot be resolved by such a test.

³⁶ We have not examined the question of whether observed differences in factor proportions might be explained by regional differences in relative factor prices, a useful but difficult exercise.

³⁷ The argument presented here is independent of, though consistent with, the assumption of economies of scale in plantation agriculture. Benson has argued that economies of scale realized by slave-owning planters retarded industrialization; L. Benson, Scientific Study, pp. 258, 262. Wright did not detect such economies of scale in plantation agriculture, but Fogel and Engerman suggest in their preliminary study of northern and southern agriculture that they may have existed; Wright, Gavin, “The Economics of Cotton in the Antebellum South” (Ph. D. dissertation, Yale University, 1969), ch. ivGoogle Scholar; Fogel, Robert W. and Engerman, Stanley L., “The Relative Efficiency of Slavery: A Comparison of Northern and Southern Agriculture in 1860,” Explorations in Economic History, 8 (Spring 1971), pp. 364–365CrossRefGoogle Scholar.

³⁸ Schmookler suggests that “inventiveness,” measured by the number of patents issued, is related to changes in the demand for the output of the industry. While the structure of the process envisaged by Schmookler is quite different from the analysis above, it does provide oblique support for the notion that, other things being equal, there will be greater “inventiveness” when the profit from the invention appears to be great; Schmookler, Jacob, “Economic Sources of Inventive Activity,” The Journal of Economic History, 22 (March 1962), pp. 1–19CrossRefGoogle Scholar. Parker relates the lack of southern mechanization to the lack of invention by the reasonable observation that “nothing so much helps in the solving of an industrial technological problem as the proximity of craftsmen and inventors to areas where the problem exists”; W. N. Parker, “Slavery and Southern Economic Development,” p. 117. The relation of agricultural invention to certain structural characteristics of the South is set forth briefly in Fleisig, Heywood, “Mechanizing the Cotton Harvest in the Nineteenth-Century South,” The Journal of Economic History, 25 (December 1965), pp. 704–706CrossRefGoogle Scholar, and in Fleisig, H., “Comment on the Paper by Aufhauser,” The Journal of Economic History, 34 (March 1974), pp. 79–83CrossRefGoogle Scholar. See also E. D. Genovese, Slavery, p. 60, and Gray, Lewis Cecil, History of Agriculture in the Southern United States to 1860 (Washington, 1933), Vol. II, pp. 792–794Google Scholar. More generally, see Habakkuk, H. J., American and British Technology in the Nineteenth Century (London, 1967), pp. 65–69Google Scholar, 91–111.

³⁹ H. Fleisig, “Comment,” p. 82.