The Profitability of Slave Labor and the "Time" Effect
- The Profitability of Slave Labor and the "Time" Effect
For over fifty years, the profitability of slave labor - an issue almost wholly identified with investments in slavery in the southern United States - has been assessed using econometric models. From the scores of influential articles and the hundreds of others that share a methodology which was in fact developed for this purpose, two observations can be made.
First, that the discussion has focused less on econometric models and more on the research and critique of the data used for the 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 the selection and interpretation of primary sources.1
The second observation, which follows from the first, is that there is a consensus regarding the basic equation of the discussion, the rate of profit. How many units of profit are produced by one unit of capital: nothing simpler than this ratio. Following the article by Conrad and Meyer in 1957, the problem became one of comparing the 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 the same nominal value.
The definitions used in neoclassical theory express the comparison in a very simple manner. If the rate of profit (i) of an investment - for example in slaves - is defined as
where
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b = gross earnings (output)
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a = production expenditure for the gross earnings (input) [End Page 1]
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C = capital required to generate the flow (b-a)
and gross earnings, ignoring the capitalization of profits, are defined as
where t is the unit of time considered,
we can deduce, from (1) and (2):
and to compare profitability, use the NPV (Net Present Value) calculation:
where i is the alternative earning rate to compare.
In this sequence of equations, which follows the 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 the composition of the 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 the denominator in (1), the variable a includes "the value of all services consumed in producing whatever is regarded as the output stream of that particular resource."3 At least one of those "services" - the 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 the cash flow period.4 Slaves represent capital advanced during more than one yearly rotation and in all cases where the NPV is greater than or [End Page 2] equal to 0, the variable b should therefore cover the maintenance/amortisation quota included in each yearly rotation. Even if one considers the distinction between these two types of expenditure (maintenance expenditure and the actual amortisation) irrelevant, gross earnings must include a fraction of value corresponding to the renewal of the capital invested in slaves advanced for the whole of the cash flow period. The assumption that the 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, the period t should not always be defined: otherwise the NPV equation could also not be used to compare profitability.5
In order for the flow b to include the amortisation quota, the asset must be used during a minimum period in each unit of time of its rotation. The less labor time coincides with total possible labor time, the lower the gross earnings will be; below a certain limit, these may actually not cover the amortisation quota and below this level capital is no longer being reproduced. Therefore, all equations above assume two dimensions of the time factor, though this...
