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.