Indepedent Verification of the Turnover Formula.

Please find an independent verification of the turnover formula. It proves that the accuracy of the formula is robust. It remains my sincere hope that we now start using turnover in all our analyses and break with the past practise, now unacceptable, of ignoring turnover because it was believed to be unobtainable.               Brian Green

Turnover (5 simulations) spreadsheet

Turnover Equation (5 simulations-final)pdf

16 Responses to Indepedent Verification of the Turnover Formula.

  1. Boffy says:

    The formula is based upon a fallacy, as I set out in one of my previous comments to your previous post, but which for some reason, did not appear.

    That fallacy is that as you put it,

    “a definite relation exists between gross output (the value of total sales)
    and gross value added (the value of the final sale) the two main series in the SNA.”

    In Volume II, in Volume III, and extensively in TOSV, Marx makes clear that gross output value is NOT equal to total sales. That he says was Adam Smith’s “absurd dogma” that the value of commodities, and thereby of the total commodity product is resolvable into revenues, and thereby equal to National Income – wages, profits, rents, interest and taxes.

    It is not, because, as Marx demonstrates at length that only represents the value added by labour during the current year. The intermediate production represents only the new value added by labour in Department I. Marx specifically states, none of this production includes one penny of value of constant capital. The value of that constant capital – means of production used in the production of means of production – is not included because it is reproduced directly out of current production by Department I. Department I firms either replace that constant capital directly out of their own production, e.g. a farmer who reproduces their seeds directly from their output, or the coal producer who replaces the coal consumed in the steam engines directly out of the coal they produce, or else is reproduced indirectly by other Department I firms.

    If we take the example of the farmer producing grain. We can see this if we examine how their output might be treated, along with that of the miller, and the baker. Suppose, we assume that 1 hour of labour equals £1, and that 1 kilo of grain has a value of £1. The farmer keeps 10 kilos of grain to use as seed, and sells all of their remaining 90 kilos of output to the miller, for £90. They pay £40 of this in wages to their workers, and keep £50 as profit for themselves. For the miller, the grain appears as intermediate goods, that constitute his constant capital. His workers add, £90 of new value, £40 being paid to his workers, and £50, retained by him as profit. The miller sells the resultant flour to the baker for £180. The grain constitutes intermediate production for him, or his constant capital. His workers add a further £90 of new value, £40 paid as wages, and £50 as profit.

    The total value of the end product available for consumption is then £270. If we add up all of the revenues, it is also equal to £270 (£90 in farming, £90 in milling, £90 in baking). So all of this revenue can be used to buy the end product. The baker, cannot consume the whole of the £270 they take in sales, because they must spend, £180, replacing the consumed flour. Moreover, if they want to continue as a capitalist, they cannot consume the £40, of revenue, that must be used to reproduce the wages for their workers.

    Returning to the baker, this £180, does not constitute a revenue for the baker, but must be used as capital. Similarly, the miller cannot consume all of the £180 they obtain from the baker. They must use £90 of it to buy grain from the farmer. This £90 does not constitute revenue for the miller. It is capital. Finally, the farmer can consume all of the £90 they obtain from the miller. All of it constitutes revenue. However, this £90, did not constitute the total value of the farmer’s production. That was £100. £10 of that value was never sold, instead it was directly thrown back into production, by the farmer, as seed, to replace, on a like for like basis, the seed that was consumed in production. Again, this portion of the farmer’s output does not constitute revenue, but is capital, and is directly reproduced out of current production.

    • Wrong again. The SNA has two series the gross series and the net series. The Gross series includes depreciation (wear and tear Marx) while the net series is without capital consumption adjustments. To distinguish the one from the other the BEA uses gross output and gross value added for c+v+s and net output and net value for v+s (national income comprising surplus and compensation). I suggest you do not apply for a job with the BEA because you have made a really basic, kindergarten mistake. In all honesty Boffy you are wasting my time because nothing you have said is relevant.

      • Boffy says:

        You seem again to have completely missed the point. It has nothing to do with wear and tear! When Marx talks here about the consumption of capital (means of production) in the production of means of production, he is not talking about wear and tear, but the consumption of materials (and also wear and tear of fixed capital) in the production of means of production.

        Its precisely because as Marx sets out at length that the consumption of means of production used in the production of means of production are replaced directly from current production out of capital and not from revenue that they do not appear in the Gross Output figure, as he sets out for example, in Capital II, Chapter 20, in his model of simple reproduction, whereby the 4000 of Department I, is not sold, and yet comprises a part of the value of current output.

  2. Boffy says:

    The pdf seems only to present an assertion of a mathematical formula, but no actual evidence from real industries. The spreadsheet itself only appears to provide mathematical calculations based upon the formula with macro level figures for Gross Output and Gross Value Added, rather than specific industry level analysis.

    That really proves nothing, especially, if as I set out above, the assumption about Gross Output Value equalling total sales is fundamentally wrong, as Marx sets out in the text referenced above. The whole basis of marx’s Law of a falling rate of profit is based upon Department I (c) continually rising, as an increasing share of total current output goes to the reproduction of means of production used in the production of means of production, the element of output that is not represented by sales in national accounts, because it is reproduced out of capital not revenue.

    And, if as a result of rising productivity the capital value of Department I (c), i.e. the value of the commodities that comprise its elements is falling, whilst its mass is rising, because for example a £500 PC does the work that previously a £2 million mainframe computer did, that has a significant effect on the annual rate of profit.

    Measurement of the real rate of turnover can only be made by looking at the actual turnover rates of real companies, at by mathematical abstractions of deduced from inadequate national accounts. That is what Engels did, in providing a rough calculation of the rate of turnover in the 1850’s, of being around 8.5 times.

    A look at real companies today shows a wide variation of rates of turnover dependent upon the industry, which as Marx and Engels set out leads to wide variations in the rate of profit/profit margin between those industries, in order to obtain an equalised average annual rate of profit. In all industries I would expect the rate of turnover to be substantially higher than 4.4. Even in industries like shipbuilding, the problem of low rates of turnover is addressed by stage payments etc., though in terms of the rate of turnover of the total social capital that does not really change the situation.

    If you take an Uber driver their variable-capital is turned over each time they get paid by a passenger, for example, which is many times a day, and given that 80% of the economy is accounted for by service industry, that kind of relation and turnover of capital is increasingly dominant.

  3. Boffy says:

    I will try to find time in coming weeks to reply in greater detail to your analysis, but for now I have no more time. I think dealing with the question of the rate of turnover is very important, but I simply think that your analysis and conclusions are wrong by a considerable factor.

  4. Boffy says:


    Several years ago, when you asked Bill Jefferies to review your formula, Bill e-mailed me to ask my opinion. I replied to Bill setting out what is wrong with it. I will set it out again now, because it is still as wrong today as it was back then.

    Your formula’s foundation is Gross output – Gross Value Added, in order to obtain a figure for the value of c, which you equate with the value of intermediate production. You equate Gross Output with the total value of sales. Let me first use the random figures used in my earlier example, which is as independent as the random integers used by your independent assessors, for the values of value added by intermediate producers.

    In my example, we have a grain farmer who supplies grain to a miller, who supplies flour to a baker, who supplies bread to the market. The farmer produces 100 kilos of grain with a value of £100. They use 10 kilos of this output directly, as seed to replace that consumed in production. They sell the remaining £90 of grain to the miller. The miller adds £90 of new value, and sells flour with a value of £180 to the baker, who adds a further £90 of value, and thereby sells £270 of bread as final output. The £270 of bread is bought with revenue (£90 of the farmer, £90 the miller, £90 the baker and their workers)

    Using your formula here total sales (GO) is £90 + £180 + £270 = £540. We then deduct Gross Value Added (GVA) £90 + £90 + £90 = £270. GO £540 – GVA £270 = £270, which is equal to the value of intermediate production. You believe that this is the value of c for the whole economy, but as Marx explains in Capital II, III, and in the first few chapters of Theories of Surplus Value, it isn’t.

    If we take this economy, the actual value of c is £10. That is the value of the seed consumed by the farmer, and which is reproduced directly from his output. The £90 of constant capital consumed by the miller contains none of this value of constant capital consumed by the farmer, as Marx explains in Capital II. The £90 of grain that forms the constant capital of the miller comprises ONLY the value added by the farmer’s labour, i.e. it represents only revenue (v + s). Similarly, the flour bought by the baker, which constitutes his constant capital also actually contains no constant capital. It comprises only the value added by the miller, plus the value added by the farmer, in other words only the combined revenues (v + s) of the farmer and miller.

    If we took the economy as being one enterprise, in the way Marx explains this in Theories of Surplus Value, and assume that the £90 of value added in each case is divided £40 wages £50 surplus value, we would have c £10 + v £120 + s £150. It then becomes obvious that the total value of output is not £270, equal to total sales, but £280, i.e. the value of total sales, plus the value of constant capital reproduced from capital not revenue.

    I know that you do not like abstract examples, such as those used by myself and Marx, but perhaps you will make an exception to view this in terms of the example given by Marx in Capital II, as the basis for his models of social reproduction, and which you say are the basis of your own abstract formula. In that example Marx sets out the following scenario.

    Department I

    c £4000 + v £1000 + s £1000 = £6,000

    Department II

    c £2000 + v £500 + s £500 = £3,000.

    Now using your formula we obtain total sales = £2,000 from Department I to Department II, Department II final sales £3,000. So, GO equals £5,000. If we take value added it is in Department I, £2,000, and in Department II £1,000 = £3,000. Deducting GVA £3,000 from GO £5,000 we obtain your figure for intermediate production, which is £2,000.

    Now, it should be fairly obvious that your formula has not told us anything new, or anything that we did not already know from Marx’s explanation 160 years ago! All you have done is to repackage the figure for Department I (v + s), i.e. the value of new value created in Department I, which is sold to Department II in exchange for consumer goods. As Marx pointed out in respect of Adam Smith 160 years ago, this figure most certainly is not a value of c in respect of the total output, because in fact, it comprises not one penny of constant capital. It is comprised entirely of revenue, of the new value added by Department I labour.

    As Marx set out at length, the actual value of total output here is not just the £2,000 of new value created by Department I labour, and sold to Department II plus the new value added by Department II labour. It includes also the £4000 of value of Department I that is not sold, but is instead replaced directly out of Department I capital. As Marx says, if we assume Department I to be one big company, it simply replaces all of this £4,000 of output directly from its own production, in the same way that the farmer directly replaced their seed from production. If we take Marx’s example, for the total economy, the situation is

    c 4000 + v 1500 + s 1500 = 7000.

    As the foundation of your formula GO-GVA is wrong, the further elaboration of your formula is also wrong. I will deal with the problems of your calculations in relation to the rate of turnover separately.

    • Boffy I wonder whether I am addressing somebody who is driven by a method or by a condition, because you are wilful in your distortion of Marx to defend your position. In Marx’s example you cite above, it is you who is doing the repackaging and converting what I wrote to fit your prejudices. At no time did I or Marx describe Gross Output as 5,000. Marx describes in Chapter XX pages 400 and 401 that the value of the annual product was 9000. So did I. What I really said was that if all the exchanges took place simultaneously at the end of the production period, so that the circulation period amounted to 1 (Marx) then gross output according to the SNA would be 11,000 and final sales equal to 9,000. ( This does not deviate one quark from Marx’s method. The 9000 would of course comprise 6000c + 1500v + 1500s. Net output in the words of the SNA would be gross output less the consumption of capital of 6000 yielding 3,000 net output. All correct in every detail.

      I would like my readers to be fully aware of what Marx said about the nature of circulating capital so that they can be aware that your fixation with P….P is not Marx’s method. “This qualitative identity does not come about if we take as our starting point P….P+ the form of the continuous process of production. For definite elements of P must be completely replaced in kind while others need not. However the form M…M undoubtedly yields this identity of turnover.” “In calculating the aggregate turnover of the advanced productive capital we therefore fix all its elements in the money-form, so that the return to that form concludes the turnover.” (Volume 2, Chapter IX, page 187). Could anything be clearer, the qualitative turnover of aggregate circulating capital can only be measured by money and concluded by the return to the money-form.

      With regard to Macdonald’s you have to first understand the question before you can provide an answer. I can just imagine you at a meeting of franchise holders saying all we need is 3.5 days of working capital because within 3.5 days all our working capital will be replenished with a profit. Good luck to you and see you in the bankruptcy courts.

      Finally, I am cutting the discussion now and not allowing you more comment space. You have your own website where you can pursue the matter. The capitalists are not complete fools. They may not understand the nature of value and therefore of their profits, but they do understand the rate of profit. They or their accountants understand that an investment must yield a profit greater than the sum invested. Further they know that their investment takes two forms, fixed and fluid, and that most businesses fail because of the underestimation of the amount of (fluid) working capital needed. If they took your advice, capitalism would have become bankrupt decades ago. Investors and analysists are always concerned with the movement of working capital and inventories, and many sites are devoted just to these estimates.

      What I have provided for the first time is an insight based on the National Accounts into both the movement and the amount of circulating capital which is real, and by that I mean comprehensively concrete. It helps us understand the behaviour of capitalist investment better. I find your analysis not only abstract but wrong because it is based on P….P and I have to conclude that it provides no insight into the dynamics of capitalist production.

      • Boffy says:

        When as you have in your last few replies you resort to insults rather than argument, as well as apparently wilfully distorting what I have said, and then resorting to censorship its clear that not only have you lost the argument, but that you know you have lost the argument, and can’t defend your position. Your present your argument based upon data outside of any theoretical framework, which clearly results from your failure to understand Marx’s theory.

        So, continuing to discuss on that basis is indeed pointless, and as you say, I am free to illustrate the inadequacies of your understanding of Marx’s theory and the fallacy of your argument on my own blog, which I will do, in detail, when I have disposed of other pressing work.

  5. Boffy says:

    I would ask one point of clarification. You have played a lot of emphasis on inventories, which ou mistakenly confuse with the advanced circulating capital. But, setting that aside I would ask how have you measured to inventories of BT, or Virgin Media, or Netflix, or Hilton Hotels, or Electronic Arts or Sage?

    In other words, 80% of the economy is accounted for by service industries, which by and large carry no inventories, because their production is immaterial rather material. So, what relevance does inventories have for this 80% of the economy. As far as I can see, even less than it does for calculating the rate of turnover of the rest of the economy.

  6. Anti-Capital says:

    Here’s a question: IIRC you maintain that fixed capital greatly exceeds circulating capital in the advanced capitalist economy. However, the US Dept. of Commerce’s Quarterly Financial Report shows net property plant and equipment in the US manufacturing sector for the 4th quarter 2016 at approximately 1.62 trillion dollars. The Commerce Dept’s Annual Survey Manufactures for 2016 measures costs of all materials, products, packaging, parts, raw materials, fuels, etc. used in production at 2.66 trillion dollars. Changes in inventories are pretty much insignificant in this matter. So presuming that manufacturers are recapturing the cost of materials, parts etc in final sales, how do you reconcile that with your assertion? Thanks

    • Good Question. You reduce fixed assets to plant and equipment. I use the total figure of $3.589 trillion which includes the figure you provide for plant and equipment but which also includes structures and I.P. However, I do understand why you limit yourself to $1.62 trillion. The real problem lies with the figure of $2.66 trillion for inventories and work in progress. It exceeds the gross output figure for that year of $2.185 trillion found in the BEA Tables under GDP-by-Industry, Gross Output series. Gross Output as you are aware is the sum of all sales in Manufacturing comprising both intermediate and final. I find it difficult to reconcile how the figure of $2.66 trillion is compatible with gross output unless turnover is less than 1 per annum which is unlikely. It also exceeds by many multiples the actual inventory spot figure (BEA Table 5.85B Q4 2016) of $745.3 billion. Could you provide the link to the report you quote from by the Chamber of Commerce. Once I have studied it further I will get back to you.

  7. Anti-Capital says:

    link to the QFR (historical data):

    link to ASM for 2016:

    The 2.66 trillion is for costs of all supplies, products, parts, fuels, used in production.

  8. I have followed your link. As I suspected, what you are looking at is duplicated annual sales for manufacturing. This is why it is bigger than the gross output figure. You are in fact comparing flows to stocks. Both inventory and fixed assets are stocks. A statistical snapshot at the end of the year of the existing value of inventories and assets. That is why they can be compared to each other. They cannot be compared to a flow. Only if that flow is reduced to a single turnover, which in the case of manufacturing is about four and a half times per annum can we end up with the stock of goods in any single period. And then if we remove the unpaid element we arrive at the stock of circulating capital which can be compared to the stock of fixed capital as I have done. Clearly the stock of circulating capital will tend to exceed the stock of its biggest component, inventories.

    I hope this answers your objection. Thanks for the link, I will use the tables in the future.

  9. Anti-Capital says:

    Wasn’t and objection, just a question.

    So are you stating, in essence, that the total cost of materials etc has to be diminished as to its “gross cost” by the turnover rate, i.e divide the $2.66 trillion by the 4.4 to arrive at the real figure? That was the answer I came up with after submitting the question, which would put the circulating capital at about $600 billion, equal to about 36% of the value of net PPE.

  10. Almost there. You need to subtract the unpaid element from $2.66 trillion first.. Remember capital only represents cost price, ie the labour which is paid. Once you subtract net surplus from gross output reducing the figure of $2.66 trillion you arrive at the cost of gross output (what the capitalists pay for) which when divided by turnover yields working capital. It is important to use the net surplus not the gross surplus which includes depreciation. Net surplus is best arrived at by deducting compensation from the national income data found in Table 6.1 (National Income section). National income does not include depreciation whereas GDP does.

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