Presenting the turnover formula at the Historical Materialism Conference.

slide show

Presentation at Historical Materialism pdf

12 Responses to Presenting the turnover formula at the Historical Materialism Conference.

  1. barovsky says:

    Link to the slides is wrong!


  2. I will try and sort it out. However if you click on slide show under the title of the posting on the website it will take you there

  3. Boffy says:

    You say,

    ” The period of circulation was 83 days. This yielded a rate of turnover of 4.4
    over the course of 2017. In other words, over the course of 365 days, 83 days turns over 4.4 times. What does this 83-day period mean? It means that in the course of 83 days, the capitalist employer will have purchased the factors of production (Labour power, materials, components etc) making production possible. Then there will be a period of production followed by a period of sale, the time between selling and being paid for the goods recently produced. Marx described the circuit thus: M.C…P…C+.M+
    It begins with money being paid out and it ends with money returning. The +
    sign represents the capitalist reality of more money coming in than was originally paid out.

    This is wrong on several counts. Firstly, Marx makes clear that the circuit of industrial capital is not M – C…P… C` – M`, which is only the circuit of newly invested money-capital, but is P…C` – M`. M – C…P. He also makes clear that in this circuit, as the basis of calculating the rate of turnover, and rate of profit, M only acts as money as unit of account, so as to be able to make rational calculations nothing more.

    In Capital III, Chapter 4, Engels calculated that the rate of turnover of capital in England around 1850, based upon the turnover of an actual textile company (I guess possibly his own) was 8.5 times. Given that Engels also in that Chapter points out the close connection between rising productivity and increases in the rate of turnover, pointing to a trebling in the rate of turnover due to things such as the Suez Canal, introduction of steamships and so on, I think it highly unlikely that the rate of turnover of capital today is only half what it was in 1850!!!

    On the contrary, assuming a 2% p.a. rise in productivity as a proxy for the annual rise in the rate of turnover of capital, I would say it’s far more likely that the rate of turnover today is well in excess of 30.

    If the rate of turnover is calculated on the basis of Marx’s correct formula for the circuit of industrial capital beginning and ending with P, take something like a McDonalds. It begins its circuit with a quantity of productive capital. Say £0.50 for a burger, £0.25 for salads etc. To make the product requires £0.50 of labour-power. The productive-capital advanced is £1.25. Fixed capital might be say £0.5 million for the building and equipment. But, the restaurant, sells a product every minute. The money can be paid electronically by debit card, and thereby arrives more or less instantaneously into McDonalds bank account. Because, the tills work on the basis of EPOS, the consumption of the raw material is automatically transferred to the company’s purchasing department, and replacement material ordered and shipped – though in reality knowing what that is generally going to be, a regular supply will be made as part of the Just In Time production and stock control system.

    So, the productive-capital here essentially turns over every two minutes or so. In reality, the wages of the workers are paid in arrears, and the materials will also be bought on commercial credit. In actual fact, as Marx sets out in Capital II, this does not matter, because the turnover is based upon the point that the capital value is advanced, not when it is paid for. If there are five service points in the restaurant, this is scaled up five times, in terms of the amount of turnover, not the rate of turnover. If we assume the fixed capital, mostly the building, has a lifespan of 100 years, it adds £5,000 of value in wear and tear, or cost of production p.a.

    Compared to the fixed capital advanced of £0,5 million, the circulating capital advanced on 5 counters is £5.75. Even if we assume that they hold inventory of materials – what Marx calls productive-supply that is likely to be only for say a day, which might amount to around £1,500. Assume the product sells for £4. 5 are sold every minute in a 10 hour day, which is 3000 per day, on the basis of a 5 day week, 50 week year that is 750,000 per year. The £5,000 of wear and tear is then equal to £0.09 per product. The profit per burger is £4 minus (£1.75 + £0.09) = £2,16. The rate of profit is then 2.16/1.84 = 117.39%

    The annual rate of profit, however is £2.16 x 750,000 = £1.62 million/£0.5m + £8.75. = 324%. If they rented the building rather than buying it, the advanced fixed capital would be much smaller,a and the annual rate of profit that much greater. What is clear here is that the higher the rate of turnover of the circulating capital the higher the ratio of fixed capital to circulating contant capital, but the greater the rate of turnover the greater the actual mass of laid out circulating capital. The total laid out circulating capital is 750,000 x £1.75 = £1312500, which is nearly three times the value of fixed capital.

    Assuming that the industrial capital here turns over every two minutes as described, that is 30 times per hour, 300 times per day, 1500 times per week, 750,000 per year. That is rather different than just 4.4 times. Even if this was out by 1000 times, it would give a rate of turnover of 750 times a year. Given that 80% of the economy is now based upon services, this indicates why rates of turnover have risen significantly, and what is more this service industry, actually processes very little in the way of raw materials.

    • I am aware of your position on P….P. On page 157 (Chapter VII, Volume 2 Lawrence and Wishart edition) Marx states that it does not matter in the aggregate whether one begins with M or P provided one returns back to the respective point. However, on 187 Chapter IX, he says it does make a difference. In the paragraph beginning “This qualitative identity …” he explains why P….P does not provide the identity of circulating capital while M….M does. I am aware of Engel’s imputation of turnover. I draw your attention to the second part of my analysis on the British economy posted on this website. I compare the turnover of Warbutons, the biggest UK baker, to BP the UK’s biggest oil producer. On the face of it what can have a faster turnover than baking bread. Leaven in the afternoon, bake in the evening, deliver at sunrise. Surely a turnover in the hundreds. However, as it turns out, BP’s working capital circulates faster than Warburtons. Appearances can be deceptive, which is why science is never content with mere appearances. It is all in the data. I am about to post a verification of the accuracy of the formula based on random modelling.

    • Boffy if you presented your data to the Board of Directors of Macdonald’s they would correctly point you to their trading accounts There you would find total revenue for 2017 amounting to $22.719 billion. Current assets amounted to $5.327 billion and liabilities to $2.891 billion. This leaves total working capital of $2.436 billion according to Engels calculations in Volume 3. Measured by revenue the annual rate of turnover $22.719/2.436 yielding 9.33. Because of the nature of Macdonald’s franchising it is difficult to calculate cost of sales and in case unnecessary because the parent company holds little stock. Of course if this working capital turned over 750,000 times a year as you claim Macdonald’s would be bigger than the international derivative’s market never mind the world economy. Marx’s method is to move from the concrete to the abstract and back to the reconstructed concrete. Trading accounts are concrete while your calculations remain trapped in the mists of abstraction and are only useful as an exercise in Taylorism. Your fixation with P….P is leading you into the wilderness. Stop.

      • Boffy says:

        Your calculation of annual sales, and annual amounts of laid out capital demonstrate precisely the problem with your calculation of rates of turnover. The rate of profit figure you arrive at as Marx and Engels demonstrate is a figure only for the rate of profit/profit margin. The problem is precisely that from the data you have presented, we do not know how many turnover of the circulating capital, i.e. materials and labour-power, the laid out working-capital of $2.436 billion represents. That has exactly what needs to be calculated before you can calculate an annual rate of profit!

        You are also wildly wrong in your assumption that if this figure for the number of turnovers of the circulating capital was 750,000 or even 750 million that it would make McDonalds bigger than the international derivatives market. It would make absolutely no difference whatsoever either to their total sales, or their total laid out capital for the year! It does, however, make a significant difference to their annual rate of profit.

        For ease of calculation assume that the figure of $2.436 (rounded to $2.5) billion represents 100 turnovers of the circulating simply means that $0.025 billion of circulating capital is turned over in each turn over period of 0.5 weeks. It means that every 3.5 days it advances $250 million in materials in labour-power, and every 3.5 days, that capital flows back to them in revenues, along with the profit on it, and is available as circulating capital to finance the materials and labour-power to be advanced in the next turnover period.

        I don’t have time at the moment to plough through McDonalds accounts to look for the details of fixed capital, profits and so on. But, purely for the sake of argument let’s assume that their fixed capital is $1 billion, and profit is $1 billion. The advanced capital for one turnover period is then $1.025 billion, and the profit is $1 billion for the year, so that the annual rate of profit is approx. 100%. Assuming the fixed capital, mostly in the form of buildings has a lifespan of 100 years, it loses 1% p.a. or £10 million.

        In that case, their annual cost of production is $10 million + $2.5 billion = $2.6 billion. The $1 billion profit then represents a rate of profit of 38.46%.

      • Boffy says:

        Incidentally, in Engels calculation of the rate of turnover in Chapter 4, he nowhere determines the circulating capital on the basis of current assets minus current liabilities. I have, however, pointed out some time ago the flaw in his calculation, whereby he derives a value for circulating, by working-backwards from the laid-out capital, based upon a calculation of the rate of turnover that itself assumed a figure for circulating capital, so that inevitably the result of the calculation simply confirmed itself.

        In other words, he assumes that the circulating capital is equal to six weeks outlay, which provides him with his rate of turnover of 8.5 times per year, and then uses this 8.5 times rate of turnover to verify from the annual laid out capital the figure for the circulating capital, which of course it does!

        In reality, Engels knew from his own practical experience how long it was approximately for the capital laid out as materials and labour-power to be reproduced, and on the basis of that knowledge fell into the trap of assuming what had to be proved.

        More importantly, Engels shows the annual rate of surplus value to be 1,307 9/18%. As Marx demonstrates that the annual rate of surplus value continually rises, as a result of rising productivity reducing the value of labour-power, and as a result of the continual rise in the rate of turnover, it would be interesting on the basis of your estimate of an average rate of turnover of only 4.4, to take an actual figure for wages in some company, and thereby to calculate the profit figure that would thereby be produced.

  4. Boffy says:


    I posted several other comments, which do not seem to have appeared.

    I’m afraid you have not read the text you cite from Vol II, p 187 correctly. It is referring to the total advanced capital, i.e. including fixed capital, not the circulating capital.

    Marx makes that clear in the paragraph, and I’m surprised that you failed to notice that he was referring in large part to the case relating to a machine, i.e. fixed capital rather than circulating capital. He says,

    “he 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 constantly replaced in kind while others need not. However the form M … M’ undoubtedly yields this identity of turnover. Take for instance a machine worth £10,000, which lasts ten years of which one-tenth, or £1,000, is annually reconverted into money. These £1,000 have been converted in the course of one year from money-capital into productive capital and commodity-capital, and then reconverted from this into money-capital. They have returned to their original form, the money-form, just like the circulating capital, if we study the latter in this form, and it is immaterial whether this money-capital of £1,000 is once more converted at the end of the year into the bodily form of a machine or not. 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. We assume that value is always advanced in money, even in the continuous process of production, where this money-form of value is only that of money of account. Thus we can compute the average.”

    This question of how to deal with the turnover of the aggregate capital, including the fixed capital is dealt with in Marx and Engels explanation of how to calculate the annual rate of profit based upon the advanced capital – including the total value of fixed capital – for one turnover period of the circulating capital, and that turnover period, as Marx clearly is states is the perio of turnover P..P, not M…M`.

    Marx notes, for example,

    ““Thirdly, the function of money-capital, whether it is a mere circulating medium or a paying medium, effects only the replacement of C by L and MP, i.e., the replacement of the yarn, the commodity which represents the result of the productive capital (after deducting the surplus-value to be used as revenue), by its elements of production, in other words, the retransformation of capital-value from its form as a commodity into the elements that build this commodity. In the last analysis, the function of money-capital promotes only the retransformation of commodity-capital into productive capital.” (Ch. 2, p 74)


    “The circuit of productive capital is the form in which classical Political Economy examines the circular movement of industrial capital.” (Ch. 2,p 88)

    The calculations, by the way, provided in my example of McDonalds were very rushed, and not meant in any way to be accurate – and probably aren’t. But, they were meant to be illustrative of the fact that the rate of turnover today is measured not in turnovers per year, but turnovers per week, and for some industries, turnover per day, of the circulating capital. That is why Just In Time production, has deliveries of materials (circulating constant capital) scheduled every 20 -40 minutes, reflecting the actual turnover time of that circulating capital, and as Marx and Engels describe the variable-capital turns over coincidentally with this circulating constant capital.

    As I set out in my response to Maito on turnover time some time ago, a look at something like a utility company shows the following. Customers pay their bills by direct debit. If these payments are distributed uniformly throughout the year, then deduct 115 days for weekends and bank holidays, and you get 250 days, on each one of which several hundred thousands people pay their bill, so that the company takes in money, that instantly takes the form of money-capital laid out to cover variable-capital, circulating capital, and wear and tear of fixed capital. In effect, its circulating capital is turned over 250 times a year. It need advance no additional capital to cover this circulating capital, because it is all provided by this stream of money. The workers wages thereby are paid, not by an advance of additional capital, but out of the realised value they previously created by 1 day’s labour, and the same is true in relation to the circulating constant capital, whose value has been preserved and realised by that same labour.

    Indeed, because wages are paid a month in arrears, and many materials are bought on 30 days commercial credit, in very many industries there is no need to advance any money-capital for circulating capital at all, because this money-capital is provided by the sale of completed commodities. That is also why the circuit for the turnover is based upon the advance of the physical capital, not the advance of money-capital, or else ridiculous conclusions would follow, whereby the actual money-capital advanced was zero, which then produces an amount of profit, so that the rate of profit on this advanced money-capital would be infinity!

    Or take another example I gave to Maito, which is in relation to VW. Thousands of cars stream from its Wolfsburg plant every day, in batches, on to trains, then distributed across Europe to dealers. At most the turnover time of this circulating capital is a week, but more likely just 2-3 days. The dealers pay VW, but do so mostly on the basis of orders from customers. At the least VW’s circulating capital turns over 50 times a year, and probably more like 100-150 times a year. It is now moving to customers being able to place orders directly with it, online, tailor made to their requirements, on the basis of flexible specialisation, which will make it more like McDonalds with a consequent rise in the rate of turnover.

  5. Boffy says:

    I found your calculations in relation to Warburton’s and BP. Unfortunately, the methodology for calculating the rate of turnover is wrong. I will repeat here, the comment I have made in relation to that post.

    The method calculating the rate of turnover here is wrong. The rate of turnover is that for the circulating capital alone, not the aggregate advanced capital. Using inventories as a proxy also leads to error.

    The simple fact is that the turnover time for a baker is the production time plus the circulation time. The production time for a baker is the working period, plus the time for the bread etc. to bake in the ovens. This is often done several times a day, both by the large bakeries, as well as by local bakers, and by the bakers based in Sainsbury’s, Tesco etc.

    They base their production batch on the amount they believe they can sell. Large bakeries generally sell their bread to supermarkets etc. on the basis of commercial credit, but as set out elsewhere, this is really irrelevant for calculating the rate of turnover of the capital. Discounting commercial credit, the baker is paid by the shops they supply each day, or more frequently. The baker in Sainsbury’s etc. gets paid as their cakes and so on are bought by customers.

    In other words, taking Marx’s circuit of industrial capital, we have P an amount is advanced for labour-power to bake the bread let’s say for a day, but large bakeries produce several batches a day, using shift working. An amount of circulating constant capital is advanced as flour, yeast, and so on, together with auxiliary materials for heat and light. The bread is baked and now forms commodity-capital C`. It goes to the shops, and is sold. The money realised in the sale, is transferred, nowadays largely electronically and instantaneously into its account, M`. If the capital operates on the basis of simple reproduction so that m is consumed unproductively. M is then once more converted into the elements of productive capital C (MP + LP) and Production continues. The circuit is complete, within 24 hours.

    The labour-power is usually already employed, and the materials will be regularly delivered, for large bakeries on the principle of Just in Time, so that the aspect of circulation time comprised of converting M into C…P is instantaneous. At the least, therefore, this circulating capital turns over around 300 times a year, and it is the turnover of the circulating capital, not the aggregate capital including the fixed capital that is the basis of the rate of turnover used by marx and Engels for the calculation of the annual rate of surplus value and annual rate of profit.

    • Boffy, Einstein once called the speed of light “the universe’s speed limit” because nothing travels faster. There is another universal limit in economics, it is called inventory to sales ratios. Particularly inventory/cost of sales ratios. These annual ratios tend to be below 10 or 8 when calculated against cost of sales. Generally, capital cannot circulate faster than the inventory cycle because goods that have been produced but not sold have not been converted back into money capital. The figures you have assembled have no basis in reality. A piece of glass is the ultimate dialectical material. It can either be turned into a piece of glass or into a window. In the case of glass it reflects only the room where the studious sit, but as a window it looks out into the real world. I suggest you treat glass as a window, look at the data and stop theorising all the time.

  6. Boffy says:

    As someone who has run several businesses, and worked in a variety of others I find this statement incredibly naive for the reasons I have given in a previous comment. The actual commodities held in inventory need not be the same commodities, whilst the level of inventories may never vary, whilst the rate of turnover of the circulating capital can vary considerably.

    Incidentally, I worked at an old style glaziers back in the 1970’s. One of my jobs each month, was to climb a ladder and count the inventory of each type and thickness of glass we held in stock. The level of stock was kept pretty static each month. But, my main job was to calculate bonuses for the cutters, and for the glaziers out on site. I can tell you that the turn over of this glass varied considerably each month, dependent upon whether we were about to do the glazing of several thousands windows on a new housing estate or not. If we were, the variable-capital, represented by the bonuses paid to the cutters (and more specifically to the glaziers, who had a very generous bonus scheme when interpreted correctly, as of course, I did, when I began to do the calculations) went up considerably, as did the circulating capital represented by the glass that was cut, and then glazed each day. A lot of glass and labour-power went out at one end, resulting in a lot of revenue coming in, as that capital was turned over, and the builder paid for the work done, and a lot of glass came in at the other end, to replace that consumed. But, the level of inventory remained more or less constant.

    Before that I worked at a clothing manufacturer, and the same was true. The amount of cotton drill in various colours, of nylon, and polyester held in inventory remained pretty much the same, but the amount of each that was turned over varied considerably, dependent upon the size of contracts that were being fulfilled. As I was also responsible for purchasing the material, I can tell you that in the real world that was done according to the amount of material that was about to be turned over. The amount held in stock simply acts as a reservoir to ensure that production is continuous.

    • Boffy says:

      Incidentally, Einstein was a theoretical physicist, not an experimental or practical scientist. I think he did very well indeed from his theorising!

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