What Precisely Was Marx’s Mistake on Depreciation and How it Affects the ‘Transformation Problem’

You have to be very careful accusing Marx of making a mistake in political economy as often he is several steps ahead of you and is redefining terms and ideas to avoid common mistakes. None the less I have not seen a serious defence that Marx’s treatment of depreciation was free of error. Marx made two major mistakes here that are important because they impacted on his great project in political economy.

Marx essentially had two objectives in political economy. The first was to show that profits are the result of exploitation, of unpaid labour. This was not difficult theoretically as Ricardo’s inverse wages-profits relationship implied it – a point well exploited by the so called Ricardian Socialists, Proudhon and Rodburtus who first developed theories of surplus value. This required however completing Ricardos project. Here was the problem, because Ricardo’s schema was based on the labour theory of value, whilst the introduction of fixed capital goods implies that the price of goods did not vary in proportion with the amount of immediate labour embodied in production but with the amount of capital advanced. Marx therefore had to solve this value theory puzzle which had eluded Ricardo.

Because Marx made his mistakes on depreciation he did not see that not only immediate labour, ‘living labour’ in his terminology, but prior labour used to create future value, in creating capital goods, could be a source of value and surplus value – profit. To be clear Marx did not dispute that fixed capital goods do not transmit value to products – he says they do explicitly several times in Capital I. What Marx held falsely was this was exactly offset by depreciation so the net value product of past labour accumulation was zero. This lead Marx to miss a solution to the value theory puzzle posed by Ricardo and Torrens, a solution discovered by Ricardo’s contemporaries after his death, and discovered independently by a number of thinkers on value theory since. Because of this Marx offered an alternative solution – rather he treated the whole economy as one enterprise – and hence this required a process of ‘transformation’ where cases where value is greater that price compensate for when value is less than price, and hence, in the answer to a critic Unlearning Economics reminds us Marx said:

“What has this to do with my theory of value? To the degree that corn is sold above its value, other commodities…are, to the same degree, sold below their value. The sum of values remains the same.”

However this implies two identities, total price=total value and total surplus value=total profits. The problem was the discovery that given Marx’s definition of value as only comprising immediate labour, both cannot hold at once. This was suspected by a number of critics even before Capital III was published. Engels said in effect hold on Capital III will answer all your critcisms, but offered in his famous prize essay competition’ in the preface to volume II a chance for others to answer the question. Rather it inflamed them. The publication of volume III led to the discovery that in Marx’s tables he calculated profit rates in value terms whereas of course they are equalised in price terms. There was no longer a ‘micro’ process to create the macro identity or produce the variation of values around a central price. This was of course discovered by  Ladislaus von Bortkiewicz and his and Winternitz’s solutions showed that both aggregates could not hold simultaneously if one holds Marx’s value theory derived from his theory of depreciation.

Engels held dogmatically that value theory proved that only living labour could create value, and that as a result some of the entries to his ‘Prize essay competition’ were flawed. Marx did not hold that as we shall see – rather he held (through errors in understanding depreciation) that net it could not. If this error were pointed out he might not have held the view and Engels dogmatism on this point (as seen in the preface to Capital III) might not have misled political economy on the true nature of value theory.

The implication is clear the whole ‘transformation problem’ is a residue of Marx’s treatment of fixed capital and depreciation. If the error on depreciation is corrected then the transformation problem may not be a problem at all or it may have been mispecified.

Steve Keen in Unlearning Economics briefly touches on the issue that Marx made a mistake in depreciation but is oblique on what it is. Here I aim to show precisely what that mistake is.

Marx only fleetingly deals with depreciation in Capital I and II, the real treatment is in the section on fixed capital in volume III. Chapter VII part II. I will ignore for convenience Marx’s conception of Moral Depreciation (early scrappage of reductant technologies) and focus only on his accounting scheme. Here he states:

By wear and tear … is meant that part of value which the fixed capital, on being used, gradually transmits to the product, in proportion to its average loss of use-value. (My emphasis)

This section is rather a lengthy explanation of the nature of wear and tear and repairs. Its significance does not reappear until Chapter 10 part II on replacement of fixed capital.

It is their wear and tear, the depreciation gradually experienced by them during their continual functioning for a definite period which re-appears as an element of value of the commodities produced by means of them, which is transferred from the instrument of labour to the product of labour.

Marx sets out that depreciation acts as a cost to be added to the value of products.

the commodity-value … contains an element making good the depreciation in value of the fixed capital, which is not to be replaced immediately in kind but converted into money, which gradually accumulates into a sum total until the time for the renewal of the fixed capital in its bodily form arrives.

Marx sets out that Capitalists must set up a fund to cover the depreciation so that when the machine is fully worn out a new one can be replaced.

Marx also treats this in terms of a reproduction schema between departments. He finds a problem. Those buying consumer goods must pay an additional element to pay for replacement before the machines have been replaced have been brought and hence before the money to pay for the replacement machines is in the hands of the manufacturer. This section on reproduction is complex and fascinating, and can only properly be tackled through a model of continuous production of machines of different ages with loan and other finance to fund changes in the level of production. This section however was not the source of Marx’s error.

Marx assumes that the level of depreciation is equal to the level of value transferred to the final product and that this sum is equal to the depreciation fund, so that net the two cancel out and so fixed capital, when considered on the basis of the economy has a whole, supplies no net addition to value.

This is a clear and obvious error as the value of the depreciation is always, in a profitable technique, less than the value added in production. The difference is the contribution of the machine to profit – surplus value. If what was done was to replace the value created by the machine a capitalist would in fact have to set aside more that the replacement value of the machine. A machine is only ever introduced if it can create a greater profit that than an alternative technique. If a machine only ever produces what it takes to reproduce that machine it would never be used.

What is missing here is application of techniques at the average rate of profit. If capital is advanced for a machine of certain durability when that capital could have been invested anywhere else, it must be able to price at least the average rate of profit to attract investment. A profit over and above the capital advanced and depreciation fund necessary to maintain the value of capital. No accountant I think could agree that Marx’s treatment of depreciation is sound.

Once you understand this error you can see that NET fixed capital can contribute to value contribution not simply immediate labour. Then all of the criticisms Engels set out against those that held the solution to the classical value puzzle lay in treating fixed capital as releasing accumulated labour at a rate discounted at interest are simply inapplicable. These theorists include – Ricardian theorists, Mill, McCulloch, Longfield and Torrens (after 1830 when he realised that this was a solution to the puzzle which he himself largely posed) and ricardian left thinkers such as Rodburtus, as well as later German ricardian thinkers such as Casper Schmitt.

Marx’s second error though less severe was to assume straight line linear depreciation. More modern theories of economic depreciation, in the tradition of Ladelle, Hotelling and Akermann, based on theories of joint production, recognise that economic depreciation is a fundamentally non-linear process. This is no great criticism as it was an error made by all writers of the period including the originator of the joint production method praised by Marx – Torrens – because they knew no other. This more technical issue requires a fuller treatment than can be given here.

These errors had major consequences. Early critics of Marx said his treatment of the classical theory of value contained errors and in some regards was inferior to Rodburtus. They were right, although Marx;s analysis was also superior to Roburtus in some respects.  This was unfortunate as it gave Austrian value theorists such as Bohn-Bawerk an easy and flawed straw man target to attack objective value theory, and as such in part led to the unfortunate triumph of marginalist economics.

11 thoughts on “What Precisely Was Marx’s Mistake on Depreciation and How it Affects the ‘Transformation Problem’

  1. This is throwing the baby out with the bathwater.

    Marx’s overarching theory was that the capitalist mode of production is one specific historical form of the pumping of surplus labour out of the direct producers.

    Dead labour adding value is ruled out ab initio. Value added = direct labour must always hold in one way or another. Aggregate money value added has an equivalent in aggregate labour time. Therefore, aggregate value added = aggregate labour time. The value of a unit of money is the ratio of aggregate labour time to aggregate money value added.

    The value of sales less the value of non-wage costs equals labour (as measured by money rather than by the clock). This is an accounting identity.

    • How is your statement ‘Dead labour adding value is ruled out ab initio.’ compatible with a correct accounting view of depreciation where dead labour must have value for capital labour subsitution to take place?

      You suggest I think as justification that ‘Aggregate money value added has an equivalent in aggregate labour time. Therefore, aggregate value added = aggregate labour time.’ But there is a time gap between the production through labour time and the realisation of that value through sale of commodities, during which time capital goods have depreciated and capital advanced to funds to pay for labour has to be paid for at the average rate of profit. You confuse ex-ante and ex-poste accounting identities. If treated as an exposte identity then the labour inputs have to be discounted at the prevailing interest rates to match the dimensions of the monetary value of the sale of the commodity at the time of sale. You have made a category error in confusing the cause of value – at the point of input, and the dimesions of that value at point of output. This accounting problem was well known and solved by Ricardo’s immediate successors and ignored by Marx.

  2. Every one might be right. There are two main transactions. One recording the costs (what you pay) after manufacture. The other the revenue (Value received by the entity after the sale.) The difference is profit.

    I read on the internet that Engels and his family were capitalist factory owners in Manchester. Their factories (mills) and employees made yarn for textiles. The interesting thing was Marx asked Engels to let him look at the books or for a copy of the books. He did this to learn how the real thing worked. How many economists go that far? Engels spent some time managing the factories. So, Engels should have understood the books and could have explained any thing to Marx.

    Any how, I’m not an expert on Marx.

    Depreciation in accounting is based on the “accrual” and “going concern” aspects of accounting. These concepts are why depreciation is done. They are covered in the beginning of accounting text books.

    If we had used cash basis of accounting instead of accrual, we would recognise the purchase of Kapital machines the day they were purchased. In accrual method there is no initial expense just a change of cash asset for Kapital asset. The expensing of the asset to be done after the purchase in the accrual method because it was not done at the purchase. Depreciation is the method used. Depreciation does not pay for repurchase of Kapital.*****

    p. 35-37,44-46, 55, 188
    Principles of Cost Accounting, by Edward Vanderbeck
    Google Books has preview. Enter Search in book, “factory account books”
    Enter search box on left “depreciation” to get:
    p.24-27 figure 1-11 ***** (Depreciation cost eventually reaches costs of goods sold, after it passes through “work in progress”, “Finished goods inventory”, and then to “Cost of goods sold”) ************************

    With the going concern concept one tries to recover all the costs even up to replacing the equipment so the business can continue.

    So, that delayed “cost”, like said in your article, must go to the product or companies’ cost. (Cost is paid). “Cost is what you pay, value is what you get.” -Warren Buffet Accounting, is a historical**** recording process.

    So, it records the costs are “accrued” (past tense).

    After a while the goods that were sitting some where are sold. Their cost were recorded in the finished goods inventory account.

    Once the goods are sold that value (the price received) is revenue and that is an other journal entry at an other time. (value is what you get.) That would be an other transaction.

    “Profit is what you get (value) minus what you pay (cost).” The depreciation cost were put into the finished goods inventory. When the good is sold the total cost of goods sold is expensed and the revenue is income. Two separate journal entries.

    The what you pay (the goods going out).
    March 2, 1845
    Cr. Finished goods inventory (includes depreciation) $10
    Dr. Cost of goods sold Expense $10
    Note:(Cost of Goods out of Factory)

    The what you get (Value)
    May 1, 1845
    Cr. Sales Revenue $250
    Dr. Cash $250
    Note: (Value of goods into Factory)

    Note profit= $240

    At the end of period accounting, revenue account balances are credited to profit and loss and expenses account balances are debited to profit and loss. This clearing of the revenue and expense accounts to the profit and loss account give Revenue-Expenses=Profit.

    The accountants freely admit that they do not have a perfect depreciation system.

    • You are strictly correct in that in accrual accounting it is a transfer of assets rather than building a fund to repurchase equipment, but at scrappage the firm must have sufficient assets on hand to maintain capital stock and maintain value of the firm, so depreciation if often and correctly visualised in this manner.

      Your treatment in accounting terms is useful and shows where the error is. As a German family the Engels were likley to have used the German system of historical cost accounting. Modern methods of current value depreciation accounting were not developed until the latter decades of teh 19th C and then only after some debate over which side of the balance sheet to record it. Historical cost accounting gives no accurate valuation of the current value of the capital stock. Clearly for capital stock to be used and replaced value must be greater than cost, however Marx assumed that for capital goods they were the same. This is on reflection a very odd and very basic error as it is exactly the mistake Marx accuses vulger economists of in misunderstanding the difference between the value of labour and the value of labour power.

      • “You are strictly correct in that in accrual accounting it is a transfer of assets rather than building a fund to repurchase equipment,…”

        “Your treatment in accounting terms is useful and shows where the error is.”

        Thank you. I was beginning to wonder if what I had to say would help or not, as I am out of my depth in Marx.

        Here is my opinion:

        I’m trying to take Professor Bezemer’s lead by eschewing unaccountable economics. I figure real economists understand accounting. Understanding a little accounting makes it clear that much public economics is completely unrealistic.

        Bezemer, Dirk, 2009. “No one saw this coming. Understanding financial crisis through accounting models,” Research Report 09002
        http://ideas.repec.org/e/pbe95.html
        http://ideas.repec.org/p/dgr/rugsom/09002.html
        This might be how I found out about professor Keen.

        In order to better understand economics I have figured that learning accounting is of much more value and a higher value and priority than much of the economics stuff. Even to the point of trying to avoid the economics. Any “economist” that doesn’t understand double entry bookkeeping or ignores dynamics in the real world is already mistaken.

        I think spending time on accounting is the better course than economics. Accounting is stock flow consistent. Professor Keen’s superior models are set up systematically using double entry bookkeeping. The dynamic math I already understand. But, the accounting is more important because it comes first and is the logic. The idea is, if standard economics path goes nowhere or strait down, is to do some thing more constructive or make a better path like professor Keen and professor Bezemer.

        My problem is getting drawn into the economics instead of learning more accounting. Is it sheer volume of economic discourse because of the controversies because most are mistaken (equilibrium, counterfactual (stupid) assumptions, excessive aggregates {rocks} )?

      • “You are strictly correct in that in accrual accounting it is a transfer of assets rather than building a fund to repurchase equipment,…”

        “Your treatment in accounting terms is useful and shows where the error is.”

        Thank you. I was beginning to wonder if what I had to say would help or not, as I am out of my depth in Marx.

        Here is my opinion:

        I’m trying to take Professor Bezemer’s lead by eschewing unaccountable economics. I figure real economists understand accounting. Understanding a little accounting makes it clear that much public economics is completely unrealistic.

        Bezemer, Dirk, 2009. “No one saw this coming. Understanding financial crisis through accounting models,” Research Report 09002
        http://ideas.repec.org/e/pbe95.html
        http://ideas.repec.org/p/dgr/rugsom/09002.html
        This might be how I found out about professor Keen.

        In order to better understand economics I have figured that learning accounting is of much more value and a higher value and priority than much of the economics stuff. Even to the point of trying to avoid the economics. Any “economist” that doesn’t understand double entry bookkeeping or ignores dynamics in the real world is already mistaken.

        I think spending time on accounting is the better than on economics. Accounting is stock flow consistent. Professor Keen’s superior models are set up systematically using double entry bookkeeping. The dynamic math I already understand. But, the accounting is more important because it comes first and is the logic. The idea is, if standard economics path goes nowhere or strait down, is to do some thing more constructive or make a better path like professor Keen and professor Bezemer. Keen’s work can be improved on.

        My problem is getting drawn into the economics instead of learning more accounting. Is it sheer volume of economic discourse? Is the discourse so large because of the controversies because most are mistaken (equilibrium, counterfactual (stupid) assumptions, excessive aggregates {rocks} )?

  3. An other thing about economics. Almost most all economic variables are not stocks. So, the position, state, or stock levels are almost never discussed. It is as if being rich, poor, or bankrupt makes no difference.

    Most variables discussed are flows or change in flows (acceleration). Some of those flows even look like levels but are not! Take for instance “quantity”, Q, in supply and demand curves. Q, is not a “quantity” or level it is a flow of supplied goods or demanded goods! But they call it a quantity. In math terms it would not be written Q, but dq/dt or Change in q per year (or change in time). That is how a flow is written mathematically.

    GDP is a flow of goods. If you summed GDP over a time period it would be akin to change in wealth over the period or some thing like that. Some depreciation is in the GDP flow calculation. If you added the initial wealth to that you might get the level of wealth at the final time. Oh, but they will give you the change in GDP, but not the sum. dw/dt or delta w/ delta t might be a better notation. If some thing destroyed or obsoleted a lot of accumulated wealth that doesn’t seem to count negatively.

    Examples of a level variables would be, number of employed, number of unemployment, and debt. Oh, they say many economists say debt doesn’t matter. Who would believe that debt doesn’t matter?

    Econ seems to be infatuated with flows and often ignores the levels.

  4. “A machine is only ever introduced if it can create a greater profit that than an alternative technique.”

    A profit which can only be maintained to the extent the free market assumption is violated by enforcing a monopoly over said class of machines (e.g. via patents), as without such a monopoly the machine simply lowers the socially necessary labour required to produce a commodity, and hence lowers the exchange value of said commodity – and as Marx showed in Volume I, the source of surplus value does not lie in exchange; the profit comes from denying the machine to society at large, not from introducing the machine per se:

    “If a machine only ever produces what it takes to reproduce that machine it would never be used.”

    Sure – but even if a machine produced out of thin air, it would not create any exchange value if it were available to be used by everyone equally; here you implicitly conflate use value with exchange value.

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