The formula can be rewritten as: p' = s'n x v/C. Here, s' is the rate of surplus value. Because v is the variable capital advanced, s' x v = s, the surplus value for one turnover period. Multiplying this by n gives the total surplus value for the year. C is equal to c+v, the capital advanced, for one turnover period, rather than laid out during the entire year.
Of course, capitalists and their state, do not keep sets of accounts to facilitate Marxist analysis, and so obtaining the data for such calculations is not easy, if at all possible.
“[The amount of variable capital invested in his business is something the capitalist himself does not know in most cases. We have seen in Chapter VIII of Book II, and shall see further along, that the only essential distinction within his capital which impresses itself upon the capitalist is that of fixed and circulating capital. He takes money to pay wages from his cash-box containing the part of the circulating capital he has on hand in the form of money, so far as it is not deposited in a bank; he takes money from the same cash-box for raw and auxiliary materials, and credits both items to the same cash-account. And even if he should keep a separate account for wages, at the close of the year this would only show the sum paid out for this item, hence vn, but not the variable capital v itself.]” (p 74-5)
In even the best set of national accounts, for the purpose of analysis, provided by the US BEA, it is not only impossible to discern v, because only the total income figures are given, but the figure for c is missing altogether. It could only be discerned by analysing the accounts of individual enterprises, or by approximation from the data from different industry sectors. Even then, only a figure for the laid out capital rather than the advanced amount could be estimated.
Engels gives an example of how the advanced variable capital, for a single enterprise, might be determined and the rate of turnover ascertained. He uses the example from Volume I page 211. However, the process undertaken seems a bit pointless. Having assessed the weekly expenditures from the data provided, Engels says we are not given the figure for circulating capital. So, he assumes it to be £2,500, which is approximately 6 weeks expenditure, on the basis of the data provided. But, the assumption of this figure is an assumption of the number to be calculated, i.e. the advanced circulating capital! If you assume the advanced circulating capital is the equivalent of a six week turnover period, then it is obvious that in a year, there will be approximately 8.5 turnovers, the number that Engels arrives at by a far more circuitous route.
In reality, Engels used his own direct commercial experience from running the family firm in Manchester to know how quickly the capital turned over, and to make his assessment of the size of the variable capital.
The calculation goes like this.
For one week we have:
d 20 + c 358 + v 52 + s 80 = 510.
The 320 of wear and tear on fixed capital does not comprise advanced capital. The relevant capital advanced in that regard is an initial £10,000 paid for the fixed capital. So, the circulating capital for the week amounts to c 358 + v 52 = 410.
In percentage terms this is c 87.3 + v 12.7.
The advanced circulating capital has been assumed as £2,500. Allocating it in these percentages comes to £2,182 for constant capital and £318 for variable capital. The total wage bill for the year is 52 x £52 = £2,704. £2704, divided by 318 = 8.503 turnovers per year.
The rate of surplus value was 80/52 = 153.846%. Using the formula to calculate the rate of profit we get p' = 153.85 x 8.5 = 1307.725. The total fixed and circulating capital amounts to £12,500 - £10,000 fixed, £2,500 circulating. The advanced variable capital is £318. So, we now have 1307.725 x 318/12500 = 415856.55/12500 = 33.268.
Put another way, the weekly surplus value was £80, so the annual surplus is £80 x 52 = £4,160; the advanced capital is £12,500, so p' = 4160/12500 = 33.28%.
Looking at the breakdown of the advanced capital, Engels notes here.
“For that matter we have here an illustration of the actual composition of capital in modern large-scale industry. The total capital is broken up into £12,182 constant and £318 variable capital, a sum of £12,500. In terms of percent this is 97½c + 2½v = 100 C. Only one-fortieth of the total, but in more than an eight-fold annual turnover, serves for the payment of wages.” (p 76)
The editor of the Deutsche Allgemeine Zeitung, Biedermann, had objected to the size of the 1,000% annual rate of surplus value used in Volume II. Engels comments.
“The s'n in the formula p' = s'n (v/C) stands, as has been said, for the thing called in Book II [English edition: Vol. II, p. 295. — Ed.] the annual rate of surplus-value. In the above case it is 153 11/13% multiplied by 8½ or in exact figures, 1,307 9/18%. Thus, if a certain Biedermann [Biedermann — Philistine. A pun, being also the name of the editor of the Deutsche Allgemeine Zeitung. — Ed.] was shocked by the abnormity of an annual rate of surplus-value of 1,000% used as an illustration in Book II, he will now perhaps be pacified by this annual rate of surplus-value of more than 1,300% taken from the living experience of Manchester. In times of greatest prosperity, such as we have not indeed seen for a long time, such a rate is by no means a rarity.” (p 76)
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