The Annual Rate of Surplus Value

The rate of surplus value, measures the amount of surplus value produced relative to the value of the labour-power, which produced it. Like any rate, however, it is a rate, which applies for a specific period of time. It makes no sense to measure speed by saying I have travelled 100 kilometres, because its necessary to know how long it took to travel that 100 kilometres. My speed is much greater if I travel 100 kilometres in an hour, than if I only travel 100 kilometres in a day.

The same is true with say the rate of interest. If I borrow £100, and have to pay £10 of interest on it, it makes a considerable difference whether this £10 of interest is what I have to pay for borrowing the £100 for a week, or for a year. That is why lenders now have to give an annual equivalent figure for the rate of interest they are charging, rather than just a headline rate, or amount of interest, which is only for a much shorter loan period. It is what the pay day loan companies rely on with unsuspecting, or desperate borrowers. If I borrow £100, and I'm told I only have to pay £1 of interest, which amounts to 1% of the loan, this might seem reasonable, but if that £1 is payable for borrowing the money for just a day, the reality is very different, because if I kept borrowing this £100 over and over again, each day, each time paying it back with the interest, over a year, I would have paid £365 in interest. The actual rate of interest paid for borrowing the £100 for a year – even though it would be just simple interest, as I have repaid the loan and interest in full, when required – would be not 1%, but 365%.

For the lender, it does not even matter whether they lend this money to me, again, after I repay it, or to someone else. A lender, who has a capital of just £100, could lend it to me one day, and when I repay the £100 to them, along with the interest, they immediately lend this same £100 out again, to B, who does the same, and on the third day to C and so on. At the end of the year, although they have only had £100 of capital to lend out, and have only ever loaned out this £100 and no more, they will have received £365 in interest upon it, equal to a 365% rate of interest. That is clearly quite different than had they loaned out this £100 to me for the whole year, at 1%, thereby only receiving £1 in interest upon it, at the end of the year.

This demonstrates an important distinction, described by Marx and Engels, between the capital which is laid out, and the capital which is advanced. Here, £100 of capital is advanced by the lender, but this same £100 comes back to the lender, and is immediately loaned again. At the end of the year, £36,500 has been laid out as the total amount of loans, but only £100 was ever advanced. It was turned over 365 times. Measured against the £100 of capital that the lender possesses, and advances, the £365 of interest represents a rate of interest of 365%, but measured against the £36,500 laid out as loans during the year, that £365 represents only 1%.

This same difference between the rate of surplus value measured against the variable capital advanced, and the variable capital laid out, is equally significant. As with the loan, the period of advance is the time it takes for the capital advanced, as wages to return to the capitalist, so that it can be advanced again. Marx analyses this at length in Capital II, where almost half of the volume is given over to an analysis of the turnover of capital, and its effect on the rate of surplus value, which has a consequent effect on the rate of profit.

In examining, surplus value and the rate of surplus value, Marx points out, In Capital I, that the value of constant capital can be set to zero. That is because the constant capital adds nothing, and takes nothing away from the surplus value. Marx compares it to a vessel used in a laboratory experiment. It has to be there, to allow the chemicals to be mixed and so on, but it should have no impact on the actual experiment. So, we can examine the rate of surplus value, and the effect of the rate of turnover of the variable capital, whilst setting the constant capital to zero.

Suppose, a capitalist farmer has a quantity of food. For simplicity we can allow corn to represent this food, as Marx and others did in setting out such examples. This corn is sufficient to meet the requirements of the workers employed by the capitalist to reproduce their labour-power. It constitutes the variable-capital. But, again its necessary to be more specific about the period of time. Is this amount of corn sufficient to meet the needs of reproducing the labour-power, for a week, a month, a year? In reality, all that the farmer needs is sufficient corn to pay to their labourers, for a single turnover period.

Suppose the corn takes a year to grow. In that case, the farmer will not have a return on their investment until this year has passed, and the new crop is harvested. Only then can they take a portion of this harvest to replace the corn they have handed over to their workers as wages. If the farmer begins the year with a productive-capital of 10,000 kilos of corn (and we have set the constant capital to zero, so none has to be used as seed for production), which is their variable capital, they pay out this corn to their workers each week, until, by the end of the year, it is all used up. So, the wages of the workers amount to 200 kilos of corn per week (assuming a 50 week year).

At the end of the year, however, the workers have produced the new crop, which we can assume amounts to 15,000 kilos of corn. A surplus of 5,000 kilos of corn has been produced, which represents a surplus product/value of 50% over the variable capital that was advanced to produce it. The capitalist sets aside 10,000 kilos out of this 15,000 kilos, as this is required to reproduce the variable capital, used in its production. If we assume simple reproduction, so that the capitalist does not accumulate any of their surplus, they consume the surplus 5,000 kilos themselves, along with their family, and perhaps sharing some of it with the local clergy as tithes, and so on. They start the new year, in exactly the same position as they started the previous year, with 10,000 kilos of corn, which constitutes their variable capital.

As Marx sets out in Capital III, and in Theories of Surplus Value, this is, in fact, the basic requirement for social reproduction not just that the variable-capital, but that the constant capital as well must be physically reproduced, “in kind”. It is why he says the rate of profit must be calculated on the basis of the current reproduction cost of this consumed capital, and not on the basis of the historic prices paid for it. If productivity rises, so that the labour-time currently required to reproduce that capital, and so its value, falls, the rate of profit rises, and vice versa.

But, Marx demonstrates in Capital II, that it is not just these changes in productivity, and so changes in the value of the consumed capital, which affect the rate of surplus value, and rate of profit. If we suppose that, instead of it taking a year to produce corn, it now only takes six months, i.e. social productivity has risen, this has a dramatic effect. The capitalist farmer now only requires sufficient corn to feed their workers for six months rather than a year. In other words, they only need a variable capital of 5,000 kilos of corn. The workers continue to be paid their wages of 200 kilos of corn per week, so that at the end of 25 weeks, all of the 5,000 kilos of variable capital has been used up. But, now the harvest is produced, which amounts to 7,500 kilos of corn.

Measured over this 6 month turnover period, this 7,500 kilos represents a surplus of 2,500 kilos over the advanced capital. It represents a rate of surplus value, still, of 50%. But, this is now a rate of 50%, for just six months, not a year. Having harvested the 7,500 kilos, the advanced capital of 5,000 kilos has already been reproduced, in the workers output. The capitalist farmer, now sets this 5,000 kilos aside, once more, to replace the 5,000 kilos they advanced at the start of the year.

In the next six months, the workers are once more paid 200 kilos of corn in wages, but now these wages are being paid out of the workers own production, and not out of the capital advanced by the capitalist. At the end of the year, the workers will have produced a further 7,500 kilos of corn, and again for that period of turnover, the rate of surplus value will be 50%.

However, if we examine the situation for the year, then as Marx demonstrates, the situation is totally different. Now, the capitalist farmer starts with an advanced capital of 5,000 kilos of corn, rather than 10,000 kilos. This 5,000 kilos of corn is now sufficient to employ all of their workers for the year, with a weekly wage of 200 kilos, because after six months, these 5,000 kilos have been reproduced, and returned to the capitalist, to be paid out once more as wages. The wages of the workers remain 10,000 kilos for the year, but only 5,000 kilos of capital are now required to achieve this; half what was previously required.

At the end of the year, the total output remains 15,000 kilos as before. If this 15,000 kilos is measured against the amount of capital laid-out during the year, of 10,000 kilos, then the rate of surplus value is still 50%. But, this would be false, because the capital actually advanced by the capitalist is not 10,000 kilos of corn, but only 5,000 kilos. Previously, they had to have 10,000 kilos of corn in hand, to cover the wages of their workers for the whole year, and they could not have continued production for the year without it. Now, they only require 5,000 kilos of corn, to continue production, because it only has to last half a year, until it is replaced out of the workers' own production.

The total surplus produced during the year, is then still 5,000 kilos, as before, but measured against the advanced capital of 5,000 kilos, this now represents a rate of surplus value of 100%, which is double the rate of surplus previously. As Marx demonstrates, this Annual Rate of Surplus Value, is equal to the rate of surplus value, measured against the variable-capital advanced for a single turnover of that variable-capital, multiplied by the number of times that variable-capital is turned over during the year.

“If we analyse this rate more closely, we find that it is equal to the rate of surplus-value produced by the advanced variable capital during one period of turnover, multiplied by the number of turnovers of the variable capital (which coincides with the number of turnovers of the entire circulating capital).” (p 299)

As Marx sets out, at length, in Capital II, the rate of turnover of capital is measured against the circulating capital, and this effectively means the variable capital, because it is the variable capital which processes the circulating constant capital, and thereby determines its rate of consumption and renewal, and not the fixed capital.  The reason for this, is because of the distinction that Marx makes in Capital II, between fixed and circulating capital, a distinction which was wrongly presented by Adam Smith and others.  It is that the circulating capital is completely consumed in the production process of a turnover period - be that period a week, month, or year - and must be physically reproduced at the end of it.  But, the fixed capital, is not completely consumed, and can continue to function in further turnover periods, unaffected by its wear and tear, in this respect.

The rate of surplus value, therefore, is the surplus value measured against the laid-out variable capital for any given period.  If  the rate of surplus value is 100% for a day, it is 100% for a year, because the laid out variable capital for a year is 365 times the variable capital laid out for a day.  The rate of surplus value is only the same as the annual rate of surplus value, if the circulating capital turns over exactly once during the year, i.e. if the advanced circulating capital, is the same as the laid out circulating capital.

As Engels sets out in Capital III, Chapter 4, because the rate of profit is a derivative of the rate of surplus value, as Marx had set out in Chapter 2, this same distinction between the rate of surplus value, and annual rate of surplus value, applies also to the rate of profit, and the annual rate of profit. The rate of profit, like the rate of surplus value, is measured against the laid out capital.  Where the rate of surplus value is measured against the laid out variable-capital only, the rate of profit is measured against the total laid out capital, both the variable capital, and the laid out constant capital, including, therefore, that which goes to replace the wear and tear of the fixed capital.

But, the annual rate of profit, like the annual rate of surplus value, is measured against the capital advanced for a single turnover period.  However, as Marx sets out in Chapter 9, the capital advanced for a single turnover period includes the total value of the fixed capital, rather than just the wear and tear of that fixed capital, because all of that fixed capital must be present, for production to take place.  Where the annual rate of surplus value is the surplus value produced in a year, measured against the variable capital advanced for a single turnover period, therefore the annual rate of profit is the surplus value produced in a year measured against the value of the total fixed capital, plus the value of the circulating constant capital, plus the variable capital, advanced for a single turnover.  As with the annual rate of surplus value, the more turnovers per year, the higher the annual rate of profit, relative to the rate of profit.  Unlike the rate of profit, it does not include the wear and tear of fixed capital, because the total value of fixed capital is used.

As with the annual rate of surplus value, it only coincides with the rate of profit if the total capital, including the fixed capital, turns over exactly once during a year.

Suppose, the capitalist farmer has their original 10,000 kilos of corn, which constitutes their variable capital. Because, this advanced capital now only has to last for six months, rather than a year, the capitalist farmer could employ twice as many workers. Each worker would receive the same amount of wages as before, but with twice as many workers employed, the total amount paid out in wages, each week rises to 400 kilos, so that after 25 weeks, the whole 10,000 kilos has been used up. But, now this larger number of workers produce a harvest twice what it was previously. After six months, they now produce 15,000 kilos of corn. In a year, they will produce 30,000 kilos of corn. In six months, the surplus produced is 5,000 kilos, and in a year it is 10,000 kilos.

So, the original 10,000 kilos of corn required as advanced capital, now produces a surplus double what it was previously, because with the higher rate of turnover of the variable capital, it is capable of employing twice as many workers, who produce twice as much surplus value, over the same period.

As the rate of turnover rises, because of increases in social productivity, so this annual rate of surplus value rises, even if the rate of surplus value, itself remains constant, or even falls. For example, here the rise in the rate of turnover of capital (for the reasons set out above, Marx always measures the rate of turnover on the basis of the turnover of the variable-capital, and not of the fixed constant capital) led to a release of 5,000 kilos of variable-capital, which could be used to double the workforce. Such a rise in employment would tend to cause wages to rise, as the demand for labour-power rises relative to the supply.

Suppose wages rise by 10%, so that now 11,000 kilos of corn must be advanced to cover the six month period. The output after six months remains 15,000 kilos, but the surplus has now fallen to 4,000 kilos. The rate of surplus value has then fallen to 36.36%, from 50%, when it turned over just once during the year. But, the total produced during the year is 30,000 kilos, and the surplus is 8,000 kilos. Measured against the advanced capital of 11,000 kilos, therefore, the annual rate of surplus value is now 72.73%, as opposed to 50%, when the capital turned over just once a year.

It is obvious, therefore, that this difference between the rate of surplus value, and the annual rate of surplus value, diverges by greater amounts the more the rate of turnover of the variable capital rises. Moreover, because the rate of profit itself is a derivative of this rate of surplus value, it is also clear, as Marx mentions in Capital II, and as Engels analyses in Capital III, Chapter 4, that a similar difference exists between the rate of profit, and the annual rate of profit. As social productivity continually rises, and the rate of turnover of the variable-capital rises, so the annual rate of surplus value, and the annual rate of profit rises, even as the rate of surplus value, and rate of profit, may themselves remain constant or even fall.

See Also: Capital II, Chapter 16 - The Turnover of Variable Capital