The Profitability of Slave Labor and the "Time" Effect

(ProQuest: ... denotes formulae omitted.)For over fifty years, profitability of slave labor - an issue almost wholly identified with investments in slavery in southern United States - has been assessed using econometric models. From scores of influential articles and hundreds of others that share a methodology which was in fact developed for this purpose, two observations can be made.First, that discussion has focused less on econometric models and more on research and critique of data used for variables in those models. Although various production functions have been perfected, it is still interesting to see how so many important contributions differed merely on matters of historical methodology, that is on selection and interpretation of primary sources.The second observation, which follows from first, is that there is a consensus regarding basic equation of discussion, rate of profit. How many units of profit are produced by one unit of capital: nothing simpler than this ratio. Following article by Conrad and Meyer in 1957, problem became one of comparing returns obtained from investments in slave labor and those obtained from available alternative uses.2 With this goal in sight, profitability was reduced to its financial expression: two rates of return for bonds with same nominal value.The definitions used in neoclassical theory express comparison in a very simple manner. If rate of profit (/) of an investment - for example in slaves - is defined as(1)...whereb = gross earnings (output)a = production expenditure for gross earnings (input)C = capital required to generate flow (b-a)and gross earnings, ignoring capitalization of profits, are defined as(2)a + [a(( + i) - a]t = bwhere t is unit of time considered,we can deduce, from (1) and (2):(3)...and to compare profitability, use NPV (Net Present Value) calculation:(4)...where i is alternative earning rate to compare.In this sequence of equations, which follows apparent movement of profit and where slaves now seem remote, no distinction is made between constant and variable capital. Such a distinction would mean that composition of product would include a surplus-value - a capital gain - which is not justified if, as neoclassical theory assumes, all factors of production receive their marginal remuneration.However, a distinction is made between fixed and circulating capital: in denominator in (1), variable a includes the value of all consumed in producing whatever is regarded as output stream of that particular resource.3 At least one of those services - one which follows from slave labor - comes from a capital account (C) which has a rotation time greater than each unit of time used to measure cash flow period.4 Slaves represent capital advanced during more than one yearly rotation and in all cases where NPV is greater than or equal to 0, variable b should therefore cover maintenance/amortisation quota included in each yearly rotation. Even if one considers distinction between these two types of expenditure (maintenance expenditure and actual amortisation) irrelevant, gross earnings must include a fraction of value corresponding to renewal of capital invested in slaves advanced for whole of cash flow period. The assumption that slave population grows through natural reproduction, which would give rise to a perpetual flow of earnings, does not mean that maintenance/amortisation costs do not take place and that, in order to make comparisons, period t should not always be defined: otherwise NPV equation could also not be used to compare profitability.5In order for flow b to include amortisation quota, asset must be used during a minimum period in each unit of time of its rotation. …