## Monday, 1 February 2016

### The Annual Rate of Profit

In the same way that the rate of profit is a derivative of the rate of surplus value, so the annual rate of profit is a derivative of the annual rate of surplus value. The annual rate of surplus value is the ratio of the surplus value produced in a year to the variable capital, advanced for one turnover period. The annual rate of profit is the ratio of the total surplus value produced in a year to the constant and variable capital advanced for a turnover period. This means, however, there are some significant differences between the annual rate of profit, and the rate of profit.

The rate of profit is the annual surplus value measured against the laid-out capital for the year. That includes all of the value of wear and tear of the fixed capital, as well as the capital laid out for materials, and labour-power. It does not include the full value of fixed capital, for the simple reason that this capital is not actually replaced during the year. If we take the total social capital, only a portion of the fixed capital is physically reproduced, on average equal to the value of wear and tear of the total fixed capital. The rate of profit, for the total social capital, is equal to the profit margin. It is the total surplus value produced in the year, measured again the cost of production of the total social product. The value of the fixed capital that is actually replaced, is a cost of production, the total value of the fixed capital used in production is not.

If we consider the situation from the perspective of actual value relations, then a portion of social labour-time has to be set aside to produce the fixed capital that is physically replaced, but does not have to be set aside to cover all of the other fixed capital that does not have to be physically replaced, but which continues to function, as normal, in the production process. The labour-time actually consumed currently to reproduce the fixed capital that is physically worn out and replaced during the year, therefore, forms a part of the cost of production of the year's output, and consequently of the surplus product and surplus value. It is no different than the labour-time that has to be set aside to reproduce the consumed materials, and the consumed means of consumption for producers. The surplus value is then equal to the society's surplus labour-time, over and above the labour-time expended to physically reproduce the means of production, and means of consumption for producers – c + d + v. The rate of profit is the ratio of this surplus labour-time to the labour-time expended reproducing the means of production and consumption – s/ c + d + v.

But, in calculating the annual rate of profit, the surplus value is measured not against the cost of production, but against the advanced capital. Now, it is not the wear and tear of fixed capital that enters the calculation, but the value of the fixed capital itself. That is because, although the fixed capital is not all replaced, it all has to be present for production to take place. For each individual capital, in calculating whether it obtains the average rate of profit, this is fundamental, for the same reasons as discussed in relation to the annual rate of surplus value.

For example, suppose capitalist A has £100,000 of available capital. They allocate it as £50,000 for fixed capital, with a lifespan of ten years, £30,000 for materials, and £20,000 for labour-power. The rate of surplus value is equal to 100%. Their cost of production is then £5,000 for wear and tear of fixed capital, £30,000 for materials, and £20,000 for wages = £55,000. They make £20,000 profit, which means that their rate of profit is 20/55 = 36.36%. Over ten years, the amount they have recovered in the value of their output for wear and tear of fixed capital, allows them to physically replace it, when it is worn out.

Suppose, this output comprises 100,000 units. The price of each unit is £0.75. The cost of production for each unit is £0.55, and the profit per unit is £0.20. The profit margin is equal to 36.36%, i.e. equal to the rate of profit. Put another way, as Marx describes it, the cost of production, k, is equal to c + d + v. In each unit, this is £0.05 (d) + £0.30 (c) + £0.20 (v), with £0.20 of profit. This profit can be labelled p. Then the price of production of each unit is k + p = £0.55 + £0.20 = £0.75. The profit margin is p/k.

But, in terms of the capital that they have advanced, that amounts to £100,000, as opposed to the £55,000 cost of production. The fact that, £45,000 of capital value is tied up in the value of fixed capital, that is not transferred, during this year, to the value of output, is irrelevant, because it is still capital that the capitalist has had to advance for this purpose, and is not then available for other purposes. Measured against the £100,000 of capital advanced, therefore, the rate of profit is 20/100 = 20%.

Suppose that with this £100,000 of capital, the capitalist instead employs it in some different business, which requires less fixed capital, but uses more material.

They advance £20,000 for fixed capital, £60,000 for materials, and £20,000 for wages. With the same 100% rate of surplus value, £20,000 of surplus value is produced as before. The cost of production is £2,000 for wear and tear of fixed capital, £60,000 for materials, and £20,000 for wages = £82,000. The rate of profit/profit margin is then 20/82 = 24.39%. If 100,000 units are produced, the price of each unit is £1.02, made up of £0.02 (d), £0.60 (c), £0.20 (v), and £0.20 (p). But, the rate of profit of this capital, measured against the advanced capital of £100,000 is identical to the first, i.e. 20%.

The reason that both capitals have an identical rate of profit measured against the advanced capital, is that both produce the same amount of surplus value, and both have the same amount of advanced capital. The reason they have different profit margins is that the second capital lays out a greater proportion of its total capital, in order to produce that profit, than does the first, i.e. its cost of production is higher £0.82 per unit, as opposed to £0.55. To put this another way, a larger portion of the second capital is turned over during the year, than is the case for the first capital.

Suppose, however, that one reason for the first capital having a larger proportion of fixed capital is that it invests in labour saving machines, which raise productivity, and the rate of turnover of the capital. We might then have a situation where the first capital advances the same amounts of capital, but where the profit margin, and the rate of profit measured against the advanced capital are different. Suppose, that the effect of the fixed capital is to enable the 100,000 units of output to be produced and sold, in six months, rather than a year. In other words, it turns over its circulating capital twice rather than just once during a year.

Its laid out capital, assuming the same amount of wear and tear, as before, would then be:-

£5,000 wear and tear

£60,000 materials

£20,000 wages

Total £85,000.

The amount paid for wages remains the same, because the higher productivity created by the fixed capital means that the same amount of labour-power is bought as before during the year, but the amount for materials is doubled, because this more productive labour now processes twice as much in a year as before. There are now 200,000 units produced in a year. The total value of these units including the surplus value is £105,000, giving a price per unit of £0.525. The price of each unit is made up of £0.025 (d), £0.30 (c), £0.10 (v), and £0.10 (p). In other words, the rise in productivity has caused a rise in the organic composition of capital, because the proportion of the total value of output accounted for by materials (circulating constant capital) has risen relative to the value of the variable capital. At the same time, the proportion of the total value accounted for by the value of wear and tear of fixed capital has also fallen. Marx describes this in Capital III, Chapter 6.

“Further, the quantity and value of the employed machinery grows with the development of labour productivity but not in the same proportion as this productivity, i. e., not in the proportion in which this machinery increases its output. In those branches of industry, therefore, which do consume raw materials, i. e., in which the subject of labour is itself a product of previous labour, the growing productivity of labour is expressed precisely in the proportion in which a larger quantity of raw material absorbs a definite quantity of labour, hence in the increasing amount of raw material converted in, say, one hour into products, or processed into commodities. The value of raw material, therefore, forms an ever-growing component of the value of the commodity-product in proportion to the development of the productivity of labour, not only because it passes wholly into this latter value, but also because in every aliquot part of the aggregate product the portion representing depreciation of machinery and the portion formed by the newly added labour — both continually decrease. Owing to this falling tendency, the other portion of the value representing raw material increases proportionally, unless this increase is counterbalanced by a proportionate decrease in the value of the raw material arising from the growing productivity of the labour employed in its own production.”

The capital advanced, in our example, has also changed. £50,000 continues to be the amount advanced as fixed capital, and £30,000 continues to be the amount advanced for materials, because after six months, the capital advanced for materials is recouped in the sale of the output, and thereby turned over, as it is advanced once more. But, for the same reason, only £10,000 of capital is advanced for wages, because after six months, that variable capital is also turned over, and advanced once more. So, the advanced capital is now only £90,000, representing a release of £10,000 of capital, which is now available for accumulation.

The rate of profit measured against the advanced capital is then 20/90 = 22.22%. That represents a rise of just over 10%. But, for the reason described above, the rate of profit on the laid out capital, i.e. the profit margin, moves in the opposite direction. It is now, 20/85 = 23.5%, a fall of around a third. The reason is that originally when the capital turned over once during the year, the laid out capital amounted to £55,000, or 55% of the advanced capital. Now, it is £85,000, which is 94.4% of the advanced capital.

So, it is quite clear that the rate of profit measured against the laid out-capital, is not the same as the rate of profit measured against the advanced capital. Moreover, the higher the rate of turnover of capital, the higher the annual rate of profit, i.e. the profit measured as a proportion of the advanced capital, will be, whilst that same process will cause the rate of profit, i.e. the profit measured as a proportion of the laid-out capital, or profit margin, to fall. Engels gives a number of examples to demonstrate this effect.

“To single out the effect of the turnover of total capital on the rate of profit we must assume all other conditions of the capitals to be compared as equal. Aside from the rate of surplus-value and the working-day it is also notably the per cent composition which we must assume to be the same. Now let us take a capital A composed of 80c + 20v = 100 C, which makes two turnovers yearly at a rate of surplus-value of 100%. The annual product is then:

160c + 40v + 40s. However, to determine the rate of profit we do not calculate the 40s on the turned-over capital-value of 200, but on the advanced capital of 100, and thus obtain p' = 40%.

Now let us compare this with a capital B = 160c + 40v = 200 C, which has the same rate of surplus-value of 100%, but which is turned over only once a year. The annual product of this capital is, therefore, the same as that of A:

160c + 40v + 40s. But this time the 40s are to be calculated on an advance of capital amounting to 200, which yields a rate of profit of only 20%, or one-half that of A.”

(Capital III, Chapter 4)

Marx also makes this distinction clear, in setting out that, as with the annual rate of surplus value, it is the turnover time of only the circulating capital that is determinant. He describes this in Capital III, Chapter 9.

“With 80c + 20v and a rate of surplus-value = 100%, the total value of commodities produced by capital I = 100 would be 80c + 20v + 20s = 120, provided the entire constant capital went into the annual product. Now, this may under certain circumstances be the case in some spheres of production. But hardly in cases where the proportion of c : v = 4 : 1. We must, therefore, remember in comparing the values produced by each 100 of the different capitals, that they will differ in accordance with the different composition of c as to its fixed and circulating parts, and that, in turn, the fixed portions of each of the different capitals depreciate slowly or rapidly as the case may be, thus transferring unequal quantities of their value to the product in equal periods of time. But this is immaterial to the rate of profit. No matter whether the 80c give up a value of 80, or 50, or 5, to the annual product, and the annual product consequently = 80c + 20v + 20s = 120, or 50c + 20v + 20s = 90, or 5v + 20v + 20s = 45; in all these cases the redundance of the product's value over its cost-price = 20, and in calculating the rate of profit these 20 are related to the capital of 100 in all of them. The rate of profit of capital I, therefore, is 20% in every case.”

Suppose that in this example, given by Marx, there was no fixed capital, or that it was completely consumed during the year. In that case, of the 80 c, all of it would be transferred to the value of output, it would all constitute a part of the cost of production. If a greater portion of the constant capital comprised fixed capital, then a value of 30 c, may represent the value of this additional fixed capital, which is not transferred to the value of output. In that case, only 50 c is transferred.

In the first case, the rate of profit is 20/80 +20 = 20%. In the second case it is 20/50 +20 = 28.57%. Finally, if even more fixed capital is used in proportion to the total constant capital, it may transfer only 5 to the value of total output, so that the rate of profit is 20/25 = 80%. Yet all of these different rates of profit, represent the same single annual rate of profit, of 20%, i.e. the surplus value measured against the advanced capital, as opposed to the laid-out capital. Engels gives three examples of this.

“I. A capital of £8,000 produces and sells annually 5,000 pieces of a commodity at 30s. per piece, thus making an annual turnover of £7,500. It makes a profit of 10s. on each piece, or £2,500 per year. Every piece, then, contains 20s. advanced capital and 10s. profit, so that the rate of profit per piece is 10/20 = 50%. The turned-over sum of £7,500 contains £5,000 advanced capital and £2,500 profit. Rate of profit per turnover, p/k, likewise 50%. But calculated on the total capital the rate of profit p/C = 2,500/8,000 = 31¼%

II. The capital rises to £10,000. Owing to increased productivity of labour it is able to produce annually 10,000 pieces of the commodity at a cost-price of 20s. per piece. Suppose the commodity is sold at a profit of 4s., hence at 24s. per piece. In that case the price of the annual product = £12,000, of which £10,000 is advanced capital and £2,000 is profit. The rate of profit p/k = 4/20 per piece, and 2,000/10,000 for the annual turnover, or in both cases = 20%. And since the total capital is equal to the sum of the cost-prices, namely £10,000, it follows that p/C, the actual rate of profit, is in this case also 20%.

III. Let the capital rise to £15,000 owing to a constant growth of the productiveness of labour, and let it annually produce 30,000 pieces of the commodity at a cost-price of 13s. per piece, each piece being sold at a profit of 2s., or at 15s. The annual turnover therefore = 30,000×15s. = £22,500, of which £19,500 is advanced capital and £3,000 profit. The rate of profit p/k then = 2/13 = 3,000/19,500 = 15 5/13%. But p/C = 3,000/15,000 = 20%.

We see, therefore, that only in case II, where the turned-over capital-value is equal to the total capital, the rate of profit per piece, or per total amount of turnover, is the same as the rate of profit calculated on the total capital. In case I, in which the amount of the turnover is smaller than the total capital, the rate of profit calculated on the cost-price of the commodity is higher; and in case III, in which the total capital is smaller than the amount of the turnover, it is lower than the actual rate calculated on the total capital. This is a general rule.”

(Capital III, Chapter 13)

This also makes clear the distinction of the rate of profit, p/k, or profit margin, which is the basis for the calculation used in The Law of The Tendency for The Rate of profit to Fall, and the real rate of profit, or annual rate of profit, p/C. In Case I, the advanced capital is £8,000, but the laid out capital, during the year is only £5,000, because a portion of the capital advanced represents the value of fixed capital not transferred to the value of production during the year. The rate of profit, p/k, is calculated on the laid-out capital of £5,000, giving a rate of 50%. But, the real rate of profit, the annual rate of profit is 2/500/8000 = 31.25%.

In Case II, the laid out capital is equal to £10,000, the same as the advanced capital. This may be because, although the proportion of fixed capital has risen, and a larger amount of value is, therefore, not transferred, the circulating capital itself turns over more times. The extension of that is given in Case III. There the total capital advanced is equal to £15,000, and yet the laid-out capital is £19,500. The reason for that, is that the circulating capital turns over more frequently.

Suppose, that the amount of fixed capital of this £15,000, was £12,000. It may transfer only £1,200 of its value to production through wear and tear. Of the remaining £3,000 of capital, £2,500 is advanced for materials, and £500 for wages. If we deduct the £1,200 of wear and tear for the year, the laid out capital amounts to £18,300, which means that the circulating capital turns over 6.1 times. That gives a rate of profit, p/k, or profit margin of 15.38%, whereas the real or annual rate of profit is 3000/15000 = 20%.

Once again, this demonstrates how the rise in productivity, which brings about a rise in the rate of turnover of capital causes the rate of profit, p/k, to fall whilst the real rate of profit p/C rises. This difference is also important for understanding the basis for calculating prices of production.

The price of production is equal to k + p, but the amount of p, is determined by the average rate of profit calculated on the advanced capital, not the laid out capital. If this were not the case, then capitals with different rates of turnover of capital, would obtain different real rates of profit on the capital they advance. Marx describes this in Capital III, Chapter 9.

“Since the general rate of profit is formed by taking the average of the various rates of profit for each 100 of capital invested in a definite period, e.g., a year, it follows that in it the difference brought about by different periods of turnover of different capitals is also effaced. But these differences have a decisive bearing on the different rates of profit in the various spheres of production whose average forms the general rate of profit...

“Take, for example, a capital of 500, of which 100 is fixed capital, and let 10% of this wear out during one turnover of the circulating capital of 400. Let the average profit for the period of turnover be 10%. In that case the cost-price of the product created during this turnover will be 10c for wear plus 400 (c + v) circulating capital = 410, and its price of production will be 410 cost-price plus (10% profit on 500) 50 = 460.”

This is clearly different than a price of production calculated as k + kp', which would be, 410 + (410 x 10%) = 41, giving a price of production of 451. I have set out the effects of this rising rate of turnover of capital in increasing the annual rate of profit, whilst reducing the rate of profit, and the consequent effect on prices of production, elsewhere.