Calculating Slave Reparations in Dollars

✑ PAUL COCKSHOTT` ╱ ± 10 minutes
The only effective ‘reparation’ that can be made for past exploitation is to socialise all of the economy.

Yes, we can estimate how much surplus labour was plausibly extracted from slaves in the USA; around ten trillion dollars. But the demand for reparations is by its very nature a bourgeois reform, which presupposes the continuation of private ownership and the continued private exploitation of wage labour.

From: Paul Cockshott's Blog, Sep 9, 2019. ╱ About the author
Paul Cockshott (1952) is a computer scientist and Marxist political economist. In political economy, he has published several books on value theory, socialist planning theory and the econophysics models of production and money. He is now an honourary research fellow at the University of Glasgow, having retired from teaching. On twitter: @PCockshott.

Last week I discussed the issue of slave reparations in the USA in the abstract. I now want to look at it more concretely, to put figures to it. I will be analysing just how much surplus labour was plausibly extracted from slaves in the USA from shortly after independence to just before the Civil War, what this would be worth in present money, whether this ‘debt’ could be met out of the current capital stock of the US economy and what the implications would be for pursuing a claim just for the proceeds of exploitation before 1860 whilst neglecting almost 160 years of subsequent exploitation. Along the way, I will address certain criticisms that were raised against last week’s paper.

So how do we set about working out how much surplus was extracted from the slaves?

We need several distinct bits of information, some of which are readily obtainable, others of which I can at the moment only give plausible estimates for. The point about my calculations will be to give rough estimates, with error bounds of perhaps 30% or so for the quantity of surplus labour. This is enough to form judgements on the economic and political implications of the reparations claims. Historical research could later provide more accurate bounds on the figures.

We need to know the number of working slaves in each year that we are considering, the length of their working year, and the typical exploitation rate for unfree labour.

Numbers of slaves are known very precisely at 10-year intervals from US census data.

Year Slaves
1790 697,214
1800 893,602
1810 1,191,363
1820 1,538,022
1830 2,009,043
1840 2,487,355
1850 3,204,287
1860 3,953,731

But totals of slaves include children not just working slaves. Whilst child slaves had to work, as in most precapitalists societies where children make up a significant part of the labour force [Minge-Klevana et al., 1980], but it is not until they are teenagers that the food they produce is sufficient not only to feed themselves but to produce a surplus. I assume a hard cutoff at 12 years of age – before that child slaves produce no surplus, above that they produce the full surplus of an adult. This decision tends to increase the estimate of surplus because in practice the teenage slaves would be producing less than an adult. Given the age at which we count slaves as part of the workforce, we then need to know what fraction of the total slave population this makes up. We know that the average life expectancy of slaves was only 36, so I am assuming that one-third of the slaves were children below 12 years old. For the years when there was a large import of slaves, this estimate of the number of children will be too high, but these were the earlier period when the slave population was low, so this approximation produces an offsetting error to the one induced by assuming slaves of age 12 were fully productive. So we now have a new table showing the working slave population.

Year slaves Slaves of working age
1790 697214 464,809
1800 893602 595,735
1810 1191363 794,242
1820 1538022 1,025,348
1830 2009043 1,339,362
1840 2487355 1,658,237
1850 3204287 2,136,191
1860 3953731 2,635,821

How many hours did each slave work per year?

Field slaves worked from dawn to dusk. Averaged over the seasons the average number hours of sunlight is 12, so I take that to be the working day. I am also assuming all slaves to be field slaves. This is obviously wrong since a portion were house slaves. According to classical and Marxian political economy, domestic servants do not produce an economic surplus. So assuming all slaves were working in the fields will tend to overestimate the surplus. Further research could provide compensatory figures for this.

I am assuming that slaves only had Sundays off work and not other holidays. So that they worked on 312 days for a total of 3744 hours a year.

Marx was of the view that the rate of exploitation under forced labour systems tended to be lower than under capitalist production:

"Capital has not invented surplus labour. Wherever a part of society possesses the monopoly of the means of production, the labourer, free or not free, must add to the working-time necessary for his own maintenance an extra working-time in order to produce the means of subsistence for the owners of the means of production7 , whether this proprietor be the Athenian χαλος γαχαθος [well-to-do man], Etruscan theocrat, civis Romanus [Roman citizen], Norman baron, American slave-owner, Wallachian Boyard, modern landlord or capitalist.8 It is, however, clear that in any given economic formation of society, where not the exchange-value but the use-value of the product predominates, surplus labour will be limited by a given set of wants which may be greater or less, and that here no boundless thirst for surplus labour arises from the nature of the production itself. Hence in antiquity over-work becomes horrible only when the object is to obtain exchange-value in its specific independent money-form; in the production of gold and silver. Compulsory working to death is here the recognised form of over-work. Only read Diodorus Siculus.9 Still these are exceptions in antiquity. But as soon as people, whose production still moves within the lower forms of slave-labour, corvée-labour, &c., are drawn into the whirlpool of an international market dominated by the capitalistic mode of production, the sale of their products for export becoming their principal interest, the civilised horrors of overwork are grafted on the barbaric horrors of slavery, serfdom, &c. Hence the negro labour in the Southern States of the American Union preserved something of a patriarchal character, so long as production was chiefly directed to immediate local consumption. But in proportion, as the export of cotton became of vital interest to these states, the over-working of the negro and sometimes the using up of his life in 7 years of labour became a factor in a calculated and calculating system. It was no longer a question of obtaining from him a certain quantity of useful products. It was now a question of production of surplus labour itself: So was it also with the corvée, e.g., in the Danubian Principalities (now Roumania)." [Capital I, chap 10, sec 2]

He then gives detailed calculations showing that the most extreme example of forced labour he had available to him corvée had an exploitation rate of 66%. Instead of this rate however, I am going to assume that slaves were subject to what, in capitalist terms, would be a 100% rate of surplus value. Whilst higher than the rate Marx calculated for forced labour, it corresponds to the estimates he used for wage labourers in the English cotton industry of the 19th century. A surplus of 100% means half the working day is for the exploiting class.

We are now in a position to estimate how many surplus hours slaves had extracted from them over the period 1790 to 1860. For each decade I have used the mean slave population between the start and finish of the decade.

Year Surplus hours per decade
1790 9,926,691,840
1800 13,010,181,600
1810 17,031,362,400
1820 22,133,685,600
1830 28,057,523,520
1840 35,515,846,080
1850 44,666,032,320
total 125,675,291,040 hours

In words that is one hundred and twenty five billion hours of surplus labour.

To turn this into more comprehensible figures, what does that mean in money terms, and what would it equate to in reparations to each slave descendant could it be pursued?

In the calculations that follow I will use 2011 US dollars because I will be using the Penn World Tables online economic database and they use 2011 US dollars at Purchaing Power Parity as the basis for their calculations. The value of the dollar has fallen slightly since then but 2011 is sufficiently recent that calculations in 2011 terms are still meaningful.

This shows that in 2011 US employees worked 247,814,266,738 hours to produce a GDP of $15,542,582,000,000 which amounts to the creation of about $62 of GDP for each hour of work. Since this is GDP, it includes what in Marxist terms are Sector I industries producing capital goods so it is not all available for direct consumption, but lets go with this figure for now. It means that the 125 billion hours of slave surplus labour has a money value of about $10,561,162 million, or ten trillion dollars.
That is a vast sum of money. Divided through the 47 million black population of the USA who are likely descended from slaves it amounts to some $220 thousand dollars each.
That is a vast sum of money. Divided through the 47 million black population of the USA who are likely descended from slaves it amounts to some $220 thousand dollars each. The World Inequality database shows that the average per-adult national wealth in the USA that year was around $200 thousand, so that were black Americans to get this sum it would put them around the average level of wealth. But, were it paid out it would put black Americans well above the median wealth. The bottom 50% of the US population in 2011 had negative wealth, that is to say they owed more than they owned. If we look at the middle 40% of the wealth distribution they had on average $133K per adult, so the hypothetical reparations would put black Americans well into the top ⅓ of the wealth distribution.

Is there enough capital to cover this?

Yes. The 2017 capital stock of the USA was $60,923,964 million valued at 2011 prices. So the reparation claims would amount to to a claim of 18% of the total capital stock.

But did 18% of the value of total capital stock now existing arise from the exploitation of less than 4 million slaves prior to 1860?

According to Marx, capital is accumulated surplus labour. It is the unpaid labour of the past that is now used to dominate the living, making sure that a small minority capture the greatest part of the wealth created by labour each year. Suppose we look at the potential claims on capital that other victims of exploitation have, what about exploitation of wage labourers?

The Penn World Tables allow us to calculate how many hours of work were performed by US employees for the years they cover 1950 to 2017. They also give the labour share of national income from which we can work out the rate of surplus labour. Using this I calculate that 5,365,735,086,566 hours of surplus labour were performed over that period. We can disregard all but the leading figures since this is an approximation like the slave estimate, though a more accurate one. We find that the historic slave exploitation from 1790 to 1860 pans out at about 3% of the exploitation of wage labourers since 1950 ( a period of roughly the same length ). And this ignores all capitalist exploitation prior to 1950.

In fact whilst slave exploitation amounts to a claim of the order of 18% of the total US capital stock, capitalist exploitation since 1950 amounts to 546% of the capital stock. If you attempted to get ‘reparations’ in the form of share certificates for the entire ‘debt’ to the exploited classes of the USA then there would not be nearly enough capital stock to go round. And this ignores all capitalist exploitation prior to 1950.

Why is this?

It is because under almost all societies the greater part of the surplus is consumed unproductively by the upper classes rather than being invested productively. So the net accumulation of capital by the upper classes since 1950 amounts to only 16% or so of the surplus extracted from workers over the same period.

The demand for reparations is by its very nature a bourgeois reform. If reparations are to be paid there must be capital whose ownership can be transferred. That in turn presupposes the continuation of private ownership and the continued private exploitation of wage labour. It is a demand that seeks to elevate one group of the historically exploited into a social position well above that of the rest of the exploited population. The effect of pursuing it is to divide the population on race grounds and not class grounds in such a way as to rule out the formation of a specifically socialist politics. Since it is a policy that would only advantage a minority against the opposition of the existing propertied class, its chance of ever being enacted in anything but a symbolic way is zero.

The only effective ‘reparation’ that can be made for past exploitation is to socialise all of the economy and totally eliminate property income. Only that communist approach holds out the prospect of eliminating the poverty and pauperism to which the bottom half of the US population are subjected.

This article was originally published on Paul Cockshott's blog. Visit his YouTube channel here.


Minge-Klevana, Wanda, et al. “Does labor time decrease with industrialization? A survey of time-allocation studies [and comments and reply].” Current Anthropology 21.3 (1980): 279-298.

Top image: Annandale Plantation in Mannsdale, Madison County, Mississippi, in 1910s. From: Wikimedia (adapted).


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