On returns to scale and input substitutability in slave agriculture

Abstract

The presence or absence of economies of scale in slave agriculture has long been debated. Since certain characteristics of slave cotton production support (see Fogel and Engerman, 1974; Metzer, 1975) and others deny (Russell, 1966) its existence, conclusive evidence on returns to scale has been difficult to establish. At issue is not merely the technical parameters of slave agriculture, but characteristics bearing on the larger questions of slave versus free farm efficiency and the viability of the institution, itself. If there were economies of scale in agriculture, the larger slave farms would have at least one advantage over the smaller free farms. Moreover, if slavery were subject to economies, observed increases in slaves per farm would appear to be rational adjustments in farm size, not conspicuous consumption which was helping to lead the institution of slavery down the path of self-destruction. In Time on the Cross, Fogel and Engerman (1974) have used cliometric techniques to generate detailed evidence on returns to scale and the relative efficiency of slave agriculture. In concluding that slave agriculture was more efficient, they have placed major emphasis upon finding quantitative support for economies of scale. But their estimates of returns to scale and differences in farm efficiencies depend crucially upon the unverified assumption of unitary elasticity of substitution between considered inputs-an assumption quite different from that made by traditional scholars of slavery. Though some econometric historians (e.g., Fogel and Engerman, 1971: Passe11 and Wright, 1972) have also taken the elasticity of substitution between slaves and other inputs to have been 1, most works indicate slaves and other inputs were poor substitutes. Several have implied slaves and other inputs were prefectly inelastic substitutes, the elasticity of substitution was zero. Hawk reported slaves and mules as well as slaves and land were combined in fixed proportions (1934, pp. 236, 239). More recently, Ransom and Sutch (1975) have taken fixed input proportions as a key assumption for their arguments on the causes of slow economic recovery in the postbellum South. Other historians (North, 1974, p. 87; Cairnes, 1909, pp. 752-757: Conrad and Meyer, 1958; Saraydar, 1964) have taken