Marx After Sraffa: Redux

I

In 1977, Ian Steedman published a book titled Marx After Sraffa. This book was designed to show that after the publication of Sraffa’s (1960) book, Production of Commodities by Means of Commodities, there is no need for an analysis of prices and profits in a capitalist system to go via Marx’s analysis of commodities as ‘values’ measured in terms of labour time (from now on, ‘labour values’) and production and appropriation of surplus as ‘surplus value’. Steedman argued that the reduction of productive technique to a quantitative measure in terms of homogeneous labour in Marx’s analysis is based on a given physical input-output data; and that Sraffa shows that an understanding of the capitalist economic categories such as ‘prices of commodities’, ‘rate of profits’, ‘wage rate’, etcetera can be, not only in terms of their determination but also in terms of their mutual relations, established by a direct analysis of the same physical data without going through the detour of first reducing them to their homogeneous labour values. Hence the Marxist categories of ‘value’ and ‘surplus value’ are redundant. But this was not the end of it. Steedman further argued that actually the reduction of physical data to labour values must entail some kind of conceptual error as the results drawn from those labour-value measures give us erroneous results, for example, the rate of profits and prices of production derived by Marx turn out to be incorrect but more importantly it could be shown that in some cases of joint-production positive profits could exist along with negative surplus value—this is because in a joint production case it is not possible to directly assign labour values to the two (or more) products separately on the basis of any one technique used to produce them. It is only possible by readjusting the two (or all) the processes of production in such a way that the resulting output vector is increased just by one unit of one commodity so that the change in the total labour used in all the processes of production required to increase the output of only one commodity by one unit could be assigned as its labour value. In this case, however, there is always a possibility that the readjustments of processes may require that more labour using processes must be contracted and less labour using processes must be expanded, resulting in total labour used in all the processes to fall, implying negative labour value for the commodity in question. Steedman’s arguments were mostly mathematical in nature, and he did not much probe into the philosophical foundations of Marx’s project to locate the source of the problem or the point where Sraffa makes an advance or a break from Marx. In this article, I try to sketch such an analysis.

II

The subtitle of Marx’s Capital is ‘a critique of political economy’, and the leading representatives of ‘political economy’ for him were Adam Smith and David Ricardo. So let us begin with a brief analysis of what we find in Adam Smith’s Wealth of Nations and Ricardo’s Principles on the question of ‘prices of commodities’ and ‘production of surplus’ and their relation to labour.

III

In opposition to the then Mercantilist orthodoxy that measured wealth of a nation in terms of the stock of precious metals (or international currency) held by the state, Adam Smith (1981 [1776]) argued that the wealth of a nation consists in the per capita annual flow of goods and services. This led to the inevitable problem of how to measure the rise and fall in the wealth of a nation over time as the constituents of it are a heterogeneous collection of things. In the everyday life of Adam Smith’s time, price of a commodity was quoted in terms of certain weight and purity of silver or gold. The problem of calculating the wealth of a nation in terms of the aggregate value of all things produced in a year in terms of silver or gold was that silver and gold were also commodities and their values could fluctuate over time in all sorts of manner as any other commodity’s value, and hence they could not be taken as the standard for measuring the real changes in the wealth of a nation. This is a typical problem of finding an index number.

But instead of looking for a technical solution of this problem in some kind of ‘index number’, Adam Smith sought to find the ultimate cause that gives economic value to a commodity. If the ultimate cause could be found then all the commodities could be reduced to this single homogeneous unit. This led Adam Smith to think of Man’s primordial state when he must have had to act directly against Nature to wrest his basic needs of survival from it. For Adam Smith this primordial act of Man against Nature is both an act of production as well as an act of exchange. Expenditure of labour in the process of production is also a sacrifice in terms of ‘toil and trouble’, which is a payment of price for the product appropriated from Nature. Thus all prices or all economic values must be measured by this ‘originary’ or the ultimate price that measures the ‘real’ value of the commodity as opposed to the ‘nominal’ value measured by the money-commodity as gold or silver:

Labour was the first price, the original purchase-money that was paid for all things. It was not by gold or by silver, but by labour, that all the wealth of the world was originally purchased; and its value, to those who possess it and who want to exchange it for some new production, is precisely equal to the quantity of labour which it can enable them to purchase or command. (Smith, 1981 [1776], p. 48; WN, I.v.2)

In the above quotation Adam Smith mixes up two notions of exchange value that are not identical. The first statement refers to an ex post labouring activity that has been already completed, whereas the second statement refers to an ex ante possibility of a future labouring activity. This has been the central problem in Adam Smith’s treatment of labour in his theory. Now, quantitatively these two notions may give identical results in certain states. Adam Smith argues that in an imagined ancient hunter and gatherer society, which he called ‘the early and rude state of society’, a hunter who specialises in hunting beaver may be interested in exchanging some beaver for some deer hunted by another hunter specialising in hunting deer. At what ratio the two hunters should exchange their commodities, asks Adam Smith. His answer is that ‘naturally’ they would exchange their commodities such that no one gives more of their ‘toil and trouble’ to the other in terms of their commodities, that is, in such a society the exchange ratios between the two commodities will be determined by the relative labour time expended in producing the two commodities:

In the early and rude state of society which precedes both the accumulation of stock and the appropriation of land, the proportion between the quantities of labour necessary for acquiring different objects seems to be the only circumstance which can afford any rule for exchanging them for one another. If among a nation of hunters, for example, it usually costs twice the labour to kill a beaver which it does to kill a deer, one beaver should naturally exchange for or be worth two deer. It is natural that what is usually the produce of two days or two hours labour, should be worth double of what is usually the produce of one day’s or one hour’s labour. (Smith, 1981[1776], p. 65; WN, I.vi.1)

Here Adam Smith’s reference to ‘natural’ is a reference to rational behaviour on the part of the hunters. The point is that if the beaver hunter demands more than two deer in exchange for his beaver then it will be rational for the deer hunters to shift some time of hunting from deer to beaver rather than exchange more than two deer for one beaver—later on such rational behaviour or calculation would be used to explain the gravitation of ‘market prices’ to ‘natural prices’, which Marx, much later, would refer to as law of value. Now, in this state of things one could argue that in the exchange of two deer for one beaver, the beaver hunter (and vice versa for the deer hunter) is indirectly exchanging the amount of labour time it costs the deer hunter to hunt two deer. Thus by offering a beaver, one could persuade the deer hunter to work for an amount of time that would take him to either hunt two deer or one beaver—they are identical amount of toil and trouble to him.

But let us consider another example. Let us suppose it takes 1 year of labour for a farmer A to produce 1 ton of wheat and 1 year of labour for a farmer B to produce 1 ton of processed grapes to produce 10 bottles of wine, but the wine takes additional 2 years to mature. In this scenario, though it may be rational for farmer B to exchange his 10 bottles of processed grape juice after 1 year of labour with 1 ton of wheat, it will not be rational for him to exchange either 1 year or 2 years of fermented wine for 1 ton of wheat. So if farmer B asks for more than 1 ton of wheat in exchange for 10 bottles of wine then the question arises, what could be the basis for it if the sacrifices of labour in the two commodities have remained the same? Here we seem to have introduced another kind of a sacrifice which is different from ‘toil and trouble’—it is simply ‘waiting’ or an amount of time forgone before one appropriates the commodity for final consumption. Thus it appears that not only the ‘labour time’ but also the ‘waiting time’ plays a role in determining the value of commodities. But what if after the first year of labour it took 2 additional years for wheat to grow in the field? In that case, we will again go back to rationally exchanging 1 ton of wheat for 10 bottles of wine. So is it the ‘waiting time’ as such or the discrepancy in ‘waiting time’ for the two commodities that affect the exchange ratio? One could say that the exchange ratios of commodities are determined by both labour time as well as waiting time. As long as we assign equal returns to per unit of both waiting time and labour time in all the industries then it does not matter what percentage of the product is assigned to the one source or the other if their ratios are the same. However, if the ratios of labour time and the waiting time are unequal across industries, then changes in the returns on these two separate times would affect the exchange ratios. The wine and wheat example can be reversed by assuming that in the production of one commodity some material equipment are needed that require 2 years of labour whereas the other commodity needs no equipment. The point to be noted here is that once waiting time is acknowledged as another sacrifice for which a return could be rationally expected then we have introduced another rational source of income other than returns to labouring activity. This was the basis for Jevons (1957 [1871]), Menger (2007 [1871]), Bohm-Bawerk (1959 [1884]) and Wicksell (1934) to develop an independent measure of capital on the basis of time of waiting.

It is not clear whether Adam Smith thought of profits as returns to waiting—he appears to think of it as a rationally expected return on ‘risk taking’. In any case, once a non-labouring income emerges it becomes clear that the ex ante measure of labour will not be equal to the ex post measure of labour. This leads Adam Smith to conclude that his earlier hypothesis that ‘It is natural that what is usually the produce of two days or two hours labour, should be worth double of what is usually the produce of one day’s or one hour’s labour’ is no longer valid once non-wage income categories come into existence. He, however, consistently maintains that the value of a commodity must be measured by the ex ante quantity of labour it can command in exchange. Now, the new theory of value that Adam Smith presents is that though the ‘average’ or ‘natural’ rates of wages, profits and rent are determined in the dynamic socio-historical context of the rate of growth of the economy, at any given moment those rates are known data and thus for any given moment the value of a commodity can be simply calculated by adding up the incomes generated in its production in terms of given wages, profits and rent. Until now we have not introduced material means of production in Adam Smith’s story. When we introduce material means of production then it is clear that the total value of the gross output must be larger than the total net income produced, and therefore every commodity value must also contain the value of raw materials and machines used in its production in addition to the wages, profits and rent generated in its production. Adam Smith claimed that it did not make any difference as the values of all the raw materials, machines, etc., could in their turn are finally resolved into wages, profits and rent. So the value of a commodity can always be ultimately and not immediately resolved into wages, profits and rent:

In the price of corn, for example, one part pays the rent of the landlord, another pays the wages or maintenance of the labourers and labouring cattle employed in producing it, and the third pays the profit of the farmer. These three parts seem either immediately or ultimately to make up the whole price of corn. A fourth part, it may perhaps be thought, is necessary. In the price of corn, for example, one part pays the rent of the landlord, another pays the wages or for replacing the stock of the farmer, or for compensating the wear and tear of his labouring cattle, and other instruments of husbandry. But it must be considered that the price of any instrument of husbandry, such as labouring horse, is itself made up of the same three parts; the rent of the land upon which he is reared, the labour of tending and rearing him, and the profits of the farmer who advances such a rent of this land, and the wages of this labour. Though the price of the corn, therefore, may pay the price as well as the maintenance of the horse, the whole price still resolves itself either immediately or ultimately into the same three parts of rent, labour, and profit. (Smith, 1981 [1776], p. 68; WN, I.vi.11)

This proposition of Adam Smith was severely criticised by Ricardo as well as Marx. Both Ricardo and Marx argued that Smith had made a logical error by calculating prices or values of individual commodities, and thus by implication the total value of the wealth of a nation, by ‘adding up’ independently determined rates of wages, profits and rent. Since these three rates were independent of each other, the total value of the wealth of a nation could rise or fall due to rise or fall in any of the rates leaving others constant. But if the real wealth is given in terms of real goods and services produced in a year, then its total real value should remain fixed irrespective of in what proportions it is divided into its three components. Thus the total must be determined independently of how it is divided into three parts, and if two parts of its division are independently determined then the third part must be whatever remains as the residual. Hence Adam Smith’s ‘adding up’ theory of value must be rejected. ¹

IV

As mentioned above, Ricardo rejected Adam Smith’s so-called ‘adding up’ theory of value on the grounds that the value of total income must be fixed independently of how it is apportioned between various recipients of it. From this point of view, Adam Smith’s explanation of why labour is the ultimate cause of value also becomes problematic. As we have argued above, for Adam Smith it is the sacrifice of the labourer in the act of production that gives value to the commodity in the final analysis. But if labour as ‘sacrifice’ is the cause of value of the commodity then a change in the cause must result in a change in the effect—thus a fall in the real wage, which implies an increase in the sacrifice to acquire a commodity for the labourer, must lead to an increase in the value of the commodity. This contradicts Ricardo’s proposition that the size of the total must be independent of how it is cut for different recipients. Thus Ricardo removes the subjective interpretation of labour and proposes an alternative hypothesis that labour is the ultimate cause of value not because of the subjective aspect of the ‘sacrifice’ by the labourer as a payment of price for the good received but because labour in the act of production is an objective input and since all other inputs of production can be reduced to labour in the final analysis; it is the ultimate cause of value. Thus Adam Smith should not have abandoned his proposition regarding the determination of relative values of commodities in terms of their labour content alone once capitalists and landlords arrive on the scene after that ‘early and rude state of society’:

It cannot then be correct, to say with Adam Smith, ‘that as labour may sometimes purchase a greater, and sometimes a smaller quantity of goods, it is their value which varies, not that of the labour which purchases them’; and therefore, ‘that labour alone never varying in its own value, is alone the ultimate and real standard by which the value of all commodities can at all times and places be estimated and compared;’—but it is correct to say, as Adam Smith had previously said, ‘that the proportion between the quantities of labour necessary for acquiring different objects seem to be the only circumstance which can afford any rule for exchanging them for one another’; or in other words, that it is the comparative quantity of commodities which labour will produce, that determines their present or past relative value, and not the comparative quantities of commodities, which are given to the labourer in exchange for his labour. (Ricardo, 1951 [1821], pp. 16–17)

Then Ricardo asks the question: If two capitalists emerge who advance half a beaver or one deer to the respective hunters and take half a beaver or one deer as profits on their investment, then would that make the rate of exchange between deer and beaver change from one beaver for two deer? And the answer he finds is that there is no reason for the rate of exchange between beaver and deer to change in this new scenario as the old rate of exchange ensures that both the capitalists would be receiving 100% returns on their capital advances and both the workers would also be receiving equal value for 1 day of labour leaving no rational reason for any party to want to change the exchange ratio. Even when we complicate the case by introducing weapons used in killing the two animals that require half a day of labour and introduce it as another part of capital advanced by the capitalists in the two industries, we find that it will not cause the rate of exchange between the deer and the beaver to change, as both the capitalist in this case would be receiving 50% rate of profits. Thus Adam Smith must be wrong if he thought that once the non-wage income emerges the simple rule of exchange that is valid for the ‘early and rude state of society’ will no longer hold.

But then Ricardo had to acknowledge that if it takes 1 day of labour to make the weapon to kill a beaver and another day to hunt for it but only half a day to make the weapon to kill two deer and another day to hunt for it and if both the hunters appropriated all the produce themselves then the exchange rate between beaver and deer must be one beaver for 2.6 deer—note that in this example income only accrues as return to labour and there is no return to ‘waiting’. Now if we push down the income of or wages advanced to the hunters to half a beaver and 1.3 deer, respectively, then at the old prices the capitalist in the beaver industry would receive a rate of profits equal to 33.3% whereas the capitalist in the deer industry would receive a rate of profits equal to 50% (on the assumption that the weapons were also advanced by the capitalists). This situation, however, is not sustainable in the long run as capitalists investing in beaver industry would move their capital to deer industry to receive a higher rate of profits, which is available in the deer industry. Hence, if the two industries have to survive in the long run, then the rate of wages per unit of labour as well as the rate of profits on total capital investments must be equal in both the industries. However, given the technique of production for beaver and deer in our example, this condition can be satisfied if and only if the rate of exchange between beaver and deer must change in favour of the beaver industry. In general terms, if the technique of production of various commodities are such that the proportions of direct to indirect labour (in our case labour spent in producing weapons would be indirect labour whereas labour spent in killing beaver and deer would be direct labour) used in their production are not equal, which is the most general case, then positive profits must be associated with price ratios that are not equal to the ratios of total labour used in their production—thus it violates Ricardo’s first hypothesis. Furthermore, every change in the rate of wages must change the price ratios and therefore most likely change the value of total income, which is the reason why Ricardo had argued that Adam Smith’s ‘adding up’ theory of value must be rejected in the first place. Now, he finds the same problem cropping up in his theory as well:

In the former section we have supposed the implements and weapons necessary to kill deer and salmon, to be of equally durable, and to be the result of the same quantity of labour, and we have seen that the variations in the relative value of deer and salmon depended solely on the varying quantities of labour to obtain them—but in every state of society, the tools, implements, buildings, and machinery employed in different trades may be of various degrees of durability, and may require different portions of labour to produce them. The proportions, too, in which the capital that is to support labour, and capital that is invested in tools, machineries and buildings, may be variously combined. This difference in the degree of durability of fixed capital, and this variety of the proportions in which the two sorts of capital may be combined, introduce another cause, besides the greater or less quantity of labour necessary to produce commodities, for the variations in their relative value—this cause is the rise or fall in the value of labour. (Ricardo, 1951 [1821], p. 30) ²

Ricardo tried to remove this so-called second cause by suggesting that this could simply be because of the arbitrary nature of the measuring standard we use to measure value of commodities. After rejecting Adam Smith’s measuring standard of value in wages of labour on the grounds that if labour required to produce gold falls and as a consequence all prices quoted in gold rises then we conclude that it is gold that has fallen and not all other commodities have risen, thus in the same vein if labour required to produce wage goods (say corn) falls, and therefore prices of all other commodities in terms of corn or ‘labour commanded’ rises then consistency requires that we should in this case as well conclude that it is labour that has fallen and not all other commodities that have risen as Adam Smith had insisted—thus wages have no special status for being the measuring standard of value (see Ricardo, 1951 [1821], p. 18). This led him to revert back to the usual method of measuring value in terms of a commodity-money such as gold or silver. Elsewhere I have argued (see Sinha, 2017, 2018 [2010]) that Ricardo’s point was that with changes in wages the values of all commodities, measured in gold or silver, get affected but this could be because it is the measuring standard that is getting affected—if we could find a commodity that remains unaffected in the face of changes in wages then it could be shown that changes in value caused by changes in wages were only apparent and not real. Sraffa (1951) argues that Ricardo acknowledges that changes in wages would affect the values of all commodities, but he wanted to find a measuring standard such that the rise and fall in the values of all commodities due to changes in wages would cancel out against this measuring standard and leave the value of the total net output constant. No matter what, Ricardo looked for his so-called ‘invariable measure of value’ in vain and compromised by choosing a commodity that has a ratio of direct to indirect labour time close to the average of most of the other commodities such that the effects on values due to changes in wages would be minimised and for further analysis ignored—not an ideal solution of a theoretical problem:

May not gold be considered as a commodity produced with such proportions of the two kinds of capital as approach nearest to the average quantity employed in the production of most commodities? May not these proportions be so nearly equally distant from the two extremes, the one where little fixed capital is used, the other where little labour is employed, as to form a just mean between them?

To recapitulate, Ricardo severs Adam Smith’s association of labour with the subjective notion of sacrifice and the return received by the labourer as a return for his ‘sacrifice’. This blocks the idea of ‘waiting time’ as another source of income. For Ricardo, labour is the ultimate input in production. Wages are a proportion of income that goes to the labourer on the basis of per unit of labour supplied as input. If all the income goes to labourers as wages then price ratios of commodities are determined by the ratio in which this ultimate input is used in their production. Now, if wages are pushed down, then given the net output some income remains unaccounted for. If we account for this leftover income as profits on capital investment, where capital is now defined as the value of all the means of production and wages, then the leftover net output can be accounted for as rate of profits per unit of capital investment. If the ratios of direct to indirect labour time used in all the industries are equal then a percentage cut in wages would generate equal percentage increase in the rate of profits in all industries, given the value of capital measured by the ratios of the direct and indirect labour inputs used in their production. Thus there is no rational reason for prices to change as all the labourers and capitalists are receiving equal returns per units of labour and capital. However, if the ratios of direct to indirect labour time in all the industries are not equal then a percentage cut in wages would generate unequal rate of profits in different industries, given the old values of capital goods. Thus rational capitalists who are receiving lower rate of profits on their capital investments would withdraw their capital from their old industries and increase their investment in high-profit industries, which will force the prices to readjust in such a way that all industries must again receive the equal rate of profits. Thus prices must now be different from their total labour input ratios. What would be the new price ratios? Ricardo did not have an answer to this question; except that it will not be the ratio of the total labour input, which implies that he loses the exact measure of capital as well as the means to determine the rate of profits. Once he accepted the modification to his first hypothesis, he concentrated his attention on establishing that changes in labour input was by far the most important cause, if not the sole cause, of changes in the price ratios and changes in wage rate was either not a cause of changes in prices or if at all a cause then a very minor one that could be ignored for all practical purposes. This, of course, was not a satisfactory solution to a theoretical problem and Ricardo was well aware of it:

If 1000 bricks vary in relative value to a certain quantity of muslin, produced by the aid of valuable machinery, it may be owing to one or two causes: more or less labour may be required to produce one of them; or wages may have risen or fallen generally. With respect to the first being a cause of variation we entirely agree, but you do not appear to admit that although the same quantities of labour shall be respectively employed on the bricks and the muslin that their relative values may vary solely because the value of labour rises or falls, and yet the fact appears to me undeniable. To this second cause I do not attach near so much importance as Mr. Malthus and others but I cannot wholly shut my eyes to it. (Ricardo’s letter to McCulloch dated 19th March 1822, Ricardo (1952), Works IX, p. 178)

V

Marx had a fair inkling that Adam Smith’s (and also Ricardo’s) idea that in the final analysis all production can be reduced to Man’s direct labouring activity against Nature may be logically flawed; since it may not be possible to reduce the material means of production to zero as one goes back and back in the production chain to draw a long series of labouring activity pure and simple. In Capital vol. II, Marx wrote:

The statement that the entire price of commodities is either ‘immediately’ or ‘ultimately’ resolvable in v + s [wages + surplus] would only cease to be an empty subterfuge if Smith could demonstrate that the commodity products whose price is immediately resolved into c (the price of the means of production consumed) + v + s are finally compensated for by commodity products which entirely replace these ‘consumed means of production’, and which are for their part produced simply by outlay of variable capital [wage advances only], i.e., capital laid out on labour-power. The price of these latter commodities would then immediately be v + s. And in this way the price of the former, too, c + v + s, where c stands for the component of constant capital, would be ultimately resolvable into v + s. Adam Smith himself did not believe he had given such a proof…. (Marx, 1992 [1885], Capital II, p. 450)

Marx’s fundamental attack on political economy was that neither Adam Smith nor Ricardo could explain the source of profits. Both Adam Smith and Ricardo take profits as a given income category in a bourgeois economy. Adam Smith’s argument that profit is a return on ‘risk taking’ can be a reasonable explanation for differential rate of interests on capital due to differential risks involved in different industries, but it cannot be an explanation for the origin of profits since ‘risk’ does not produce anything. Similarly, differences in waiting time can explain price differentials from labour time ratios but cannot explain the origin of profits as ‘waiting’ does not produce anything either. Ricardo also takes a positive rate of profits as given and only analyses how it is affected by changes in the value of wages. So, one of the fundamental project of Marx in Capital was to explain the source of profits.

To answer the question, where do profits come from? Marx first claims that ‘[t]he wealth of societies in which the capitalist mode of production prevails appears as an “immense collection of commodities”; the individual commodity appears as its elementary form. Our investigation therefore begins with the analysis of the commodity’ (Marx, 1977 [1867], p. 125). He argues that an economic good takes a commodity form if it is produced for exchange against some other good. He then posits that a relation of exchange is a relation of equality and asks the question: If one quarter of corn exchanges against 1 quintal of iron then what could be the common substance in the two highly disparate use-values that must be present in equal amount in the two commodities? His answer is that the ‘common substance’ can be nothing else then the fact that both are ‘products of labour’. And, therefore, exchange of commodities represents exchange of equal labour. But, of course, the labour of an ironsmith is qualitatively as different from the labour of a farmer as iron is different from wheat. Marx argues that though it is true that ‘concrete labours’ of an ironsmith and a farmer are qualitatively different; nevertheless underneath them lies expenditure of undifferentiated human energy that can be calculated by a clock.

Leaving aside the problematic nature of Marx’s ‘deduction’ or ‘discovery’ of exchange of equal undifferentiated labour residing underneath the exchange of commodities (see Sinha, 2018 [2010] for a discussion on this point), it is curious that Marx argues this knowing it well from his readings of Ricardo that such a ‘deduction’ would be incorrect for the most general case of capitalist economies. As a matter of fact, Marx had already worked out his solution to the ‘transformation problem’ in his manuscripts of early 1860s and therefore was well aware that the results of his so-called ‘deduction’ was incorrect—he gives a hint of it at the end of Chapter 5 in a footnote, ‘How can we account for the origin of capital on the assumption that prices are regulated by the average price, i.e., ultimately by the value of the commodities? I say “ultimately” because average prices do not directly coincide with the values of the commodities…’ (Marx, 1977 [1867], Capital vol. I, p. 269, f.n. 24, emphasis added). Thus it would be fair to interpret that the so-called ‘deduction’ of equal labour in exchange from the exchange of commodities is a supposition. Marx, at this stage of analysis, could be implicitly assuming equal ratio of direct to indirect labour time for all the industries or at least we can make sense of it by making that assumption.

The strategy Marx employs is to argue that a commodity in a barter exchange relation appears as C₁—C₂, which represents equal undifferentiated labour. By introducing money-commodity as a means of transaction we can expand the relation of exchange to C₁—M—C₂, which does not change the nature of the relation. However, in a capitalist economy, he argues, a capitalist is not interested in selling a commodity 1 to buy another commodity 2 for consumption. His interest is to invest money as capital to withdraw more money at the end of the circuit. Thus a circuit of capital in the sphere of exchange begins with a single capitalist starting with some money capital M, exchanging it for some commodities C, and then exchanging C back for money M. If both the M, before and after the exchanges, remain equal, then the whole process would appear to be a mad exercise. Thus for this circuit to have any meaning for the capitalist, the terminal M must be quantitatively larger than the initial M; in other words, the circuit must be of the form M—C—M’, M’>M. The problem Marx poses to himself is: If equal labour values exchange in the commodity sphere then whence the difference between M’ and M?

The transformation of money into capital has to be developed on the basis of the immanent laws of exchange of commodities, in such a way that the starting-point is the exchange of equivalents. The money-owner, who is yet only a capitalist in larval form, must buy his commodities at their value, sell them at their value, and yet at the end of the process withdraw more value from circulation than he threw into it at the beginning. His emergence as a butterfly must, and yet must not, take place in the sphere of circulation. These are the conditions of the problem. Hic Rhodus, hic salta! (Marx, 1991 [1894], Capital vol. III, pp. 268–269)

One of Marx’s central criticisms of political economy was that both Adam Smith and Ricardo did not understand the true nature of wage as an income category. They treated wage as a price paid to the labourer for the labour services performed. Marx argues that wage as a specific form of income for the labouring class is the differentia specifica of capitalism. In capitalism workers, de jury, appear as independent commodity owners exchanging commodities with other independent commodity owners. But the commodity they sell to the capitalists in exchange for wages is not the labour services as such but rather their capacity to work, which Marx called ‘labour power’. And the value of the labour power is determined by the same principle as the value of any other commodity, that is, by the labour time it takes to (re)produce the labourer’s capacity to work. Thus in this specific exchange a specified wage basket of commodities stands on one side and the labour power stands on the other. However, one peculiarity of this particular commodity, the labour power, is that its consumption or use in the production process adds to the value of the raw materials, etc., that it works on. Another peculiarity of this particular commodity is that the workers’ capacity to work is quite elastic—an average worker can or can be made to work any number of hours below a certain natural maximum in a day. In a capitalist economy it so happens that the technique of production has become so productive that the wage basket needed to (re)produce the worker’s capacity to work is produced in much less labour time than the maximum limit to which a worker can work in a day, and therefore the capitalists are able to stretch the working day beyond the labour time needed to produce the wage basket. In other words, workers give more labour time in the process of production than they receive in return as their wages. Thus the value they add in the process of production is higher than the value they take away as wages. This difference represents ‘surplus value’, which is the source of profits.

Thus the total value of a commodity has three components, the first component is the constant capital (c), which is the value of raw materials and means of production used up in the process of production plus the fresh labour added by the labourers, which in turn has two components—variable capital (v), which is the value of the wage goods that workers receive and the other is the ‘surplus value’ (s), which is the extra labour time the worker is made to work over and above the labour time needed to produce the wage basket. In other words, if value of 1 ton of iron is l_i then l_i = c_i + v_i + s_i, where c_i stands for the value of the raw materials, used-up machines, etc., in the production of 1 ton of iron and v_i and s_i, respectively, stand for the value of wage goods received by the workers in producing 1 ton of iron and the difference between the total labour time worked by the workers to produce 1 ton of iron and the value of the wages received by them.

Now, let us analyse the three components of l_i separately. How do we determine c_i? It appears that to determine the value of a commodity one needs to already know the value of other commodities that it uses as its raw materials and other means of production. In Adam Smith’s and Ricardo’s conceptual framework, one could go back and back in the chain of production of means of production till one hit upon a stage where labour all alone against Nature produced the first means of production. But as we have seen above, Marx had rejected this conceptual framework. One way to get out of this circle would be to argue that the values of all the commodities that directly or indirectly go into the production of iron are determined simultaneously. So let us borrow Sraffa’s example of an economic system given by:

90 t. iron + 120 t. coal + 60 qr. wheat + 3/16 labour → 180 t. iron

50 t. iron + 125 t. coal + 150 qr. wheat + 5/16 labour → 450 t. coal

40 t. iron + 40 t. coal + 200 qr. wheat + 8/16 labour → 480 qr. wheat

Let us say that the unknown labour values of iron, coal and wheat are given by l_i, l_c and l_w, respectively. Since the units of labour values are the same as the unit of direct labour, they can be added to each other. Given Marx’s proposition that total value of a commodity is determined by the value of the constant capital plus the direct labour time used in its production, we can convert the above description of a system of production to a set of simultaneous equations such as:

90l i + 120l c + 60l w + 3/16 labour = 180l i 50l i + 125l c + 150l w + 5/16 labour = 450l c 40l i + 40l w + 200l c + 8/16 labour = 480l w

(1)

180l_i + 285l_c + 410l_w + 1 labour = 180l_i + 450l_c + 480l_w

These three equations will solve for the values of l_i, l_c and l_w in terms of labour time along with the value of the net output (165l_c + 70l_w) = 1 labour. Notice that the structure of Equation system (1) ensures that the labour value of the total physical surplus (i.e., the total net output remaining after deducting all the physical inputs from the gross product) must always be equal to the total direct labour time spent in the production process; otherwise the equality relations between the left-hand side and the right-hand side of the equations will not hold. This has curious implications:

If the production system becomes more efficient in terms of requiring less means of production per unit of labour for the same output, for example, say we reduce all the material inputs by half in the three equations leaving the labour inputs and outputs the same, we will notice that the labour value of the total physical net output must remain the same, this time it will be (90l_i + 307.5l_c + 275l_w) = 1 and the labour values of all the means of production would fall from their previous values. If we continue this exercise of reducing the material inputs in the equations while leaving the labour inputs and outputs intact, we will find that when all the material inputs go to zero, the labour values of the gross/net output (180l_i + 450l_c + 480l_w) go to 1 and the values of individual commodities become equal to the direct labour time spent in their production. In this case, there is a finite minimum to the labour values of the gross/net output and the individual commodities, which are given by their direct labour inputs.

Let us suppose that labourers become more efficient in the sense that the system needs only half the labour than before to produce the same output with the help of the same material inputs, in this case the labour value of the same net physical output (165l_c + 70l_w) must fall to ½ units of labour and the labour values of all the three commodities will yet fall again. If we, however, continue this exercise of reducing the labour terms only in the equations or increasing the labour efficiency in the system, then we will observe that as labour terms approach zero, the labour values of the surplus as well as all commodities must also approach zero. Notice that the physical surplus or the net output remains intact but its labour value disappears.

Now, to understand the nature of Marx’s proposition that equal values exchange, let us change the unknowns from labour values to prices such as p_i, p_c and p_w. Since the unit of prices is not in terms of labour time, we will have to convert direct labour units to its counterpart in terms of price, which would be its income or wages.

90p i + 120p c + 60p w + 3/16 165p c + 70p w = 180p i 50p i + 125p c + 150p w + 5/16 165p c + 70p w = 450p c 40p i + 40p c + 200p w + 8/16 165p c + 70p w = 480p w

(2)

180p_i + 285p_c + 410p_w + 1 (165p_c + 70p_w) = 180p_i + 450p_c + 480p_w

The solutions for p’s will confirm Marx’s proposition that l_i/l_c = p_i/p_c, l_i/l_w = p_i/p_w and l_c/l_w = p_c/p_w. It should, however, be noted that this result is contingent on the assumption that labourers receive their share of total net income in the same proportion as their share of the expenditure of labour time in the total expenditure of direct labour time in the economy. If that were not so then Marx’s proposition will no longer hold; for example, suppose coal workers received higher income per unit of expenditure of labour then the ratios of p’s will deviate from the ratios of l’s, and thus Marx’s proposition will no longer be true. Now, as long as we assume that all the three kinds of labour are unskilled or simple labour of equal intensity then, as Adam Smith and Ricardo had argued, a rational calculation on the part of iron and wheat workers will make them move from iron and wheat industry to coal industry bringing down coal prices vis-à-vis iron and wheat and therefore bringing the ratio of p’s in conformity with the ratios of l’s and so the law of value would prevail in the long run. However, let us suppose that the work of a coal miner is more intense then the work of an ironsmith or a farmer. In that case, the coal miner must receive a higher return per unit of labour than the other two workers otherwise coalmining will disappear in the long run. In this case, whatever differential returns that gets established for the coal miner in the society will determine the ratios of p’s; and for Marx’s proposition to hold, one will have to change the values by counting every unit of coal miner’s labour by as higher a proportion as its share in total income. In other words, the measure of labour time itself must become contingent on how the income (or the net output) is distributed among the workers—it is the prices that determine values! Marx admits that in the real world the differentials in returns to labour have very little to do with the actual expenditure of human energy:

More complex labour counts only as intensified, or rather multiplied simple labour, so that a smaller quantity of complex labour is considered equal to a larger quantity of simple labour. Experience shows that this reduction is constantly being made. A commodity may be the outcome of most complicated labour, but through its value it is posited as equal to the product of simple labour. The various proportions in which different kinds of labour are reduced to simple labour as their unit of measurement are established by a social process that goes on behind the backs of the producers; these proportions therefore appear to the producers to have been handed down by tradition. (Marx, 1977 [1867], Capital vol. I, p. 135)

Hence the measure of labour time and consequently the values of commodities are determined by the conventional differentials in returns to various kinds of labour; for example, if in an economy white workers are paid twice the wages than the black workers for the same job, then in the calculation of the labour values of commodities every hour of white labour must be counted as equivalent to 2 hours of black labour. Thus labour values of commodities no longer reflect a technique of production since labour values can be changed by simply changing the wage structure. ³ Furthermore, we should keep in mind that these values are determined on the assumption that all income or net output is accounted for as wages only—no wonder, as we will see below, Marx’s measure of labour value gets into problem once income is no longer completely appropriated by labourers as wages.

Up till now we have been assuming that all the net income generated in the economy is appropriated by the labourers themselves as returns to their labour inputs in production, and hence the material means of production have not yet become ‘capital’ in Marx’s sense. But once we push down the returns to the labourers from 100% of total income to less than 100%, then a surplus income emerges. Till now we have homogenised heterogeneous labour by taking the income differentials as the multiplication factors for measuring homogeneous labour. In the current context, the same principle translates into measuring direct labour inputs by equating one to one their proportion of wage bill to the total wage bill in the economy with their proportion of direct labour input to total direct labour input in the economy. Now, the surplus that has emerged needs to be accounted for as ‘profits on capital’. As we have seen in the context of Ricardo, if the indirect to direct labour ratios (or in Marx’s case c/(v + s)) are equal across industries then a percentage decline in wages across industries would generate equal percentage returns on capital across industries given the measure of capital on the basis of the old prices, and therefore there will be no rational reason for prices to change; but if the ratio of direct to indirect labour (or c/(v + s)) are not equal across industries, which is the general case, then industry-wise returns to capital will be unequal given the measure of capital on the basis of the old prices. In Marx’s terms, when surplus value emerges then, on the basis of the old prices, the industrial rate of profits must be given by: r_j = s_j/(c_j + v_j) = (s_j/v_j)/(c_j/v_j + 1), where j represents the industry. Since s_j/v_j is assumed to be equal for all industries, unequal c_j/v_j would result in unequal r_j. This, Marx maintained, following Smith and Ricardo, cannot be a stable position in the long run as rational calculation by capitalists would generate movement of capital from low-profits industries to high-profits industries forcing prices to readjust by relatively raising the exchange ratios of low-profits industries compared to high-profits industries. Ricardo had understood that once this happens then capital can no longer be measured by the old prices and so he had to give up the project of determining prices and the rate of profits and concentrate on analysing only changes in those variables.

Marx also poses the problem in desperate terms but then goes on to provide a solution for the determination of new set of prices and the equal rate of profits in the system:

We have shown, therefore, that in different branches of industries unequal profit rates prevail, corresponding to the different organic composition of capital [c_j/v_j], and, within the indicated limits, corresponding also to their different turnover times, so that at a given rate of surplus-value it is only for capitals of the same organic composition—assuming equal turnover times—that the law holds good, as a general tendency, that profit stand in direct proportion to the amount of capital, and that capitals of equal size yield equal profits in the same period of time. The above argument is true on the same basis as our whole investigation so far: that commodities are sold at their values. There is no doubt, however, that in actual fact, ignoring inessential, accidental circumstances that cancel each other out, no such variation in the average rate of profit exists between different branches of industry, and it could not exist without abolishing the entire system of capitalist production. The theory of value thus appears incompatible with the actual movement, incompatible with the actual phenomena of production, and it might seem that we must abandon all hope of understanding these phenomena. (Marx, 1991 [1994] Capital vol. III, p. 252, emphasis added)

Marx’s solution to this problem was simple but unfortunately incorrect. He correctly reckons that if all industries must receive equal rate of profits then it must be the average rate of profits of the system. He, however, proposes to derive the average rate of profits from the given labour value magnitudes by dividing the aggregate surplus value in the system by the aggregate of constant plus variable capitals in the system. In other words, if Σs_j = S and Σ(c_j + v_j) = (C + V), where j = 1, … n, then Marx’s average rate of profits (r) is given by S/(C + V). After calculating the average rate of profits (r), he applies this rate of profits to mark up the values of each sector’s constant plus variable capital by the average rate of profits to derive the so-called ‘price of production’ of each commodity. In other words, the price of production for each commodity is given by (c_j + v_j) (1 + r) = (c_j + v_j) {(C + V + S)/(C + V)}. It is evident from the above equation that Σ(c_j + v_j) (1 + r) = C + V + S and Σ(c_j + v_j)r = S. In other words, total prices of production are equal to total labour values and total profits are equal to total surplus values. Marx’s contention is that in a competitive capitalist economy commodities do not exchange in proportion to their labour values but rather in proportion to their prices of production. But this in itself does not invalidate the basis of his analysis of capitalism in terms of labour values and its three main components, since the average rate of profits and the prices of production are derived from value magnitudes and cannot be derived otherwise; and given the result that the sum of the prices of production is proportional to the sum of values, and the sum of profits is proportional to the sum of surplus values, it stands as a proof that the source of profit is surplus value. The competitive mechanism of the capitalist system only succeeds in obscuring this fundamental truth by a reallocation of the total produced surplus values among the capitalists, but the nature of the fundamental relation between the capitalists and the workers, analysed on the basis of labour values of commodities, remains intact at the level of the system as a whole:

The price of production includes the average profit. And what we call price of production is in fact the same thing that Adam Smith calls ‘natural price’, Ricardo ‘price of production’ or ‘cost of production’, and the Physiocrats ‘prix nécessaire’, though none of these people explained the difference between price of production and value. We call it the price of production because in the long term it is the condition of supply, the condition for the reproduction of commodities, in each particular sphere of production. We can also understand why those very economists who oppose the determination of commodity value by labour-time, by the quantity of labour contained in the commodity, always speak of the prices of production as the centres around which market prices fluctuate. They can allow themselves this because the price of production is already a completely externalized and prima facie irrational form of commodity value, a form that appears in competition and is therefore present in the consciousness of the vulgar capitalist and consequently also in that of the vulgar economist. (Marx, 1991 [1894], Capital vol. III, p. 300)

This clearly does not solve the problem, however. Since the ratios of prices of production are not equal to the ratios of labour values any more, the measure of capital on the basis of their labour values becomes illegitimate, and hence Marx’s determination of the average rate of profits of the system is not the correct average. In other words, Ricardo’s problem remains unsolved. We still do not have the determination of either prices or the average rate of profits. Marx apparently was well aware of it as he goes on to admit:

The development given above also involves a modification in the determination of a commodity’s cost price. It was originally assumed that the cost price of a commodity equalled the value of the commodities consumed in its production. But for the buyer of a commodity, it is the price of production that constitutes its cost price and can thus enter into forming the price of another commodity. As the price of production of a commodity can diverge from its value, so the cost price of a commodity, in which the price of production of other commodities are involved, can also stand above or below the portion of its total value that is formed by the value of the means of production going into it. It is necessary to bear in mind this modified significance of the cost price, and therefore to bear in mind too that if the cost price of a commodity is equated with the value of the means of production used up in producing it, it is always possible to go wrong. (Marx, 1991, pp. 264, emphasis added)

It is curious that even though Marx rejected the Classical idea of deriving labour as the ultimate factor of production by reducing production to Man’s direct labour against Nature and consistently criticised Adam Smith and Ricardo in his Theories of Surplus Value for reducing all capital to only wage advances and forgetting the material means of production in their enquiry of the rate of profits, he nevertheless throughout maintains that commodities are ‘products of labour’. As a matter of fact, Marx from a very early stage had rejected the idea of starting the analysis of production from the imagined primordial relation between Man and Nature. In his Economic and Philosophic Manuscripts of 1844, Marx wrote: ‘Do not let us go back to a fictitious primordial condition as the political economist does, when he tries to explain. Such a primordial condition explains nothing’ (Marx, 1964 [1844], p. 107) and 1 year later in The German Ideology, Marx and Engels wrote: ‘The premises from which we begin are not arbitrary ones, not dogmas, but real premises from which abstraction can only be made in the imagination. … These premises can thus be verified in a purely empirical way’ (Marx & Engels, 1991 [1845], p. 42).

However, by the time we get to the ‘Introduction’ to the Grundrisse, which was written in 1857, Marx appears to question the idea of beginning of analysis from empirical givens. Here Marx seems to suggest that beginning with a concrete empirical reality may be a false beginning. He argues that a quick reflection on such concrete reality as ‘population’ makes it clear that it is a chaotic whole unless it is understood in terms of more abstract categories such as classes, which in turn rest on further abstract categories such as capital and wage labour and so on. Thus starting from the most abstract categories and building up to the understanding of concrete reality is ‘obviously the scientifically correct method’. Marx further argues that the theoretical construct of building up from most simple or abstract categories to the concrete empirical whole does not represent some sort of real historical unfolding as Hegel thought. On the contrary, it is the state of development of the current stage of society in which the theoretician finds himself embedded is what determines his ability for abstraction—the more complex and advanced a society is, the more clearly it can see the abstractions. Hence Adam Smith and Ricardo, who were situated in the late 18th and the early 19th century Scotland and England, respectively, could see labour as such as an abstract category because the society in which they were embedded had become highly manufacturing oriented with extensive division of labour and free movements of workers from one branch of production to another. Whereas the Mercantilists’ and Physiocrats’ visions were constraint by the predominance of one kind of specific labour such as commercial or agricultural, which did not allow them to see the abstract aspect of labour in general.

Though the ‘Introduction’ was drafted to be the Introduction of A Contribution to the Critique of Political Economy published in 1859, Marx decided not to include it in the publication since he thought it ‘anticipated the results which still had to be substantiated’ and replaced it with a relatively brief ‘Preface’. In the ‘Preface’, on the question of the beginning, he simply states that ‘the reader who really wishes to follow me will have to decide to advance from the particular to the general’ (Marx, 1970 [1859], p. 19). Instead of any elaboration on the question of ‘scientific method’ and of ‘beginning’ of analysis, we find in this brief ‘Preface’ a general statement of historical materialism, which he presents as ‘the guiding principles of his studies’:

In the social production of their existence, men inevitably enter into definite relations, which are independent of their will, namely relations of production appropriate to a given stage in the development of their material forces of production. The totality of these relations of production constitutes the economic structure of society, the real foundation, on which arises a legal and political structure and to which correspond definite forms of social consciousness. The mode of production of material life conditions the general process of social, political and intellectual life. It is not the consciousness of men that determines their existence, but their social existence that determines their consciousness. (Marx, 1970 [1859], pp. 20–21)

Here we find that the object of analysis is no longer characterised as ‘concrete whole’ such as ‘population’, ‘nation state’, etc., but rather a mode of production, a stage in human history; the foundations of which are determined by how men relate to each other through their labour. Thus the subject matter of economic analysis is defined by human labour—it is the ensemble of human relation in the act of production of their material conditions of existence. We find a continuation of this theme in Capital, published in 1867. In fact, Capital was supposed to be in ‘continuation’ of A Critique and the first chapter of the first edition of Capital was supposed to be a summary of it. In the ‘Preface’ to the first edition of Capital, Marx proclaims that ‘What I have to examine in this work is the capitalist mode of production, and the relations of production and forms of intercourse [Verkehrsverhaltnisse] that correspond to it’ (Marx, 1977 [1867], p. 90).

It appears that Marx’s notion of ‘human labour’ as the ‘substance’ of value is based on the idea of a mode of production as an ensemble of human relations mediated through human labour—the play is all about human labour—this is Marx’s fundamental metaphysics. In capitalism, according to Marx, humans relate to each other through their labour at two levels. First of all there is extensive division of human labour in society, which is regulated through the market mechanism of commodity exchange—it is the impersonal market that regulates the social division of labour. Thus underneath the relations of commodities lies the proportion of total labour allocated to the production of various commodities. The other relation of production of a capitalist economy is that the labourers do not appropriate their products but sell their capacity to work as a commodity to the capitalist for a wage (or a bundle of commodities). This again is regulated by the market and is represented by the proportion of total labour allocated to producing the total wage-basket. Now if the total labour allocated to producing the total wage-basket is less than 1, then the rest of the total labour must be allocated to producing commodities that are appropriated by the non-working class, in this case the capitalists. This must also be represented by the proportion to total labour allocated to producing the commodities appropriated by the capitalists—this proportion of the total labour is surplus value, which is appropriated by the capitalists as profits. The source of the surplus value, however, can only be explained when we ‘leave this noisy sphere [market for commodity exchange], where everything takes place on the surface and in full view of everyone, and follow them into the hidden abode of production, on whose threshold there hangs the notice “No admittance except on business”’ (Marx, 1977, pp. 279–280).

Marx’s idea of understanding social relations in terms of relations of ‘human labour’ in the course of the reproduction of a society’s economic foundations was not only highly ingenious but persuasive as well, since most of the human beings throughout history have been associated with production and their incomes or their claim on material means of livelihood have been directly associated with their labouring activities. However, since the development of technique of production that made ‘surplus production’ possible (i.e., a greater net output than the minimum requirements for the direct producers) also made it possible for some human beings to live without having to work. This led to the politics of dominance of man over man, by which the surplus output could be appropriated by a group of humans without having to work for it. This naturally lends itself to the proposition that the appropriation of the surplus product by the non-workers is a taking of something by force that did not belong to them. Notice that the above proposition implicitly assumes that the claim to the product naturally belongs to the direct producer. Thus, if the entire surplus naturally belongs to the labourers as a return to their labour then, of course, any taking of the surplus product by the non-workers is one and the same thing as the robbery of the labour of the workers. It is the conflation between a justification of someone’s right to appropriate or own a product of economic value with the production of economic value itself that lies at the core of Marx’s metaphysics of human labour.

The conflict between Marx’s metaphysics of human labour and physics of production explains the discrepancy between Marx’s reasoning and his mathematics. From a purely scientific point of view, the human contribution to production is nothing but a contribution of mechanical energy, which in essence is no different from animal’s energy or even energy contributed by machines in the process of production. As horses or bullocks could be replaced by tractors in agriculture, humans can also be replaced by mechanical machines and robots once they become cheaper to employ than humans. This does not mean that such technical changes must lead to fall in the physical surplus production—if that was the case then such labour replacing techniques will not be introduced in the first place. This brings us to enquire into the nature of the surplus. According to the first law of thermodynamics, the total energy in the universe is constant thus no surplus can be produced in the universe as a whole. If, however, we restrict a domain within the universe and create an ‘inside’ and ‘outside’ then a surplus can be produced in the ‘inside’ domain by taking energy from the ‘outside’. One can think of economic production as a technique that converts energy from one form to another, and thus surplus production must necessarily entail converting some ‘outside’ energy of nature, which has no economic value, to a form of energy that has economic value—this was fundamentally the approach the Physiocrats took in defining surplus output; however, they recognised the role of nature only in the agricultural sector. Thus surplus production in the field of economics is simply an aspect of the technique of production that converts some free energy of nature into a form that has economic value to society—that is why wine maturing in the cellar or crops growing in the fields adds to the surplus. This scientific approach displaces or rather blocks the question regarding the origin or the cause of economic value of commodities as it takes for granted that there exists a set of produced commodities that have economic value in a given society. The presence of human labour as part of productive technique does not introduce any problem since we can easily calculate the energy contributed by the labourer in the labouring process on the input side and the energy contained in the total wage basket withdrawn by the labourer from the output side—there is no particular need of considering wages as ‘cost of production’ when production is looked at from a purely scientific point of view rather than from the point of view of the capitalist, which creates the Classical and Marxian confusion in terms of whether to consider wages or the labouring activity as the input and how to account for the discrepancy between them. In the scientific context, it is possible that the energy that the workers put in the production process is greater or equal or even smaller than the energy they withdraw from the economic system in the form of wages. Capitalism is quite compatible with labourers withdrawing more energy in the form of wages than what they put in the production process so long as they do not withdraw all the surplus energy produced and that human labour remains an essential part of the technique. Marx’s idea that only human labour contributes to economic value in the process of production unwittingly harks back to the classical notion of labour being the ultimate cause of value.

VI

Sraffa (1960) stays clear from all the humanist moorings of Classical Economics and Marx. ⁴ As we have alluded to above in section III, the rationalisation of positive returns to capital in the subjective aspect of sacrifice of waiting is the obverse side of the idea of returns to labour as sacrifice of one’s comfort. The revolution of 1870s that swept economics had rejected the Classical idea that labour is the ultimate cause of value. Instead, they argued that the ultimate cause of value is scarcity, which is fundamentally a subjective condition of the intensity of our desire for something in relation to its availability. If something is not freely available in the amount that will satiate us then we are willing to pay a price for it, which can be a sacrifice of our comfort or sacrifice of anything we possess that gives us positive utility—there is nothing special about loss of comfort or leisure (i.e., labour) as a sacrifice for acquiring something of value. In this context, forgoing consumption is not different from forgoing leisure and therefore, if forgoing leisure (i.e., labour) must receive a return for it (i.e., wages), then forgoing consumption, which is how capital investment can be interpreted, must also receive a return as profits. Now the question is: How do we measure the sacrifice of consumption? Let us suppose a farmer A sacrifices 1 quintal of consumption of wheat just harvested and uses it as seed for production of wheat in the next harvest cycle and another farmer B sacrifices 1 quintal of wheat to use as seed for production of wheat and then another harvest cycle to turn it into bread. Should the two farmers receive the same return on their equal sacrifice of consumption of 1 quintal of wheat? The answer is no; because farmer B has sacrificed 1 quintal of wheat for two time periods whereas farmer A has done it only for one. Therefore, farmer B must receive higher profit. What we have noticed here is that the notion of sacrifice of consumption has a time dimension as the notion of labour. This gave rise to the idea that capital could also be measured on time dimension as ‘time of waiting’ by going back and back in the production cycle of any commodity till we hit upon the primordial state. This was the approach taken up by Jevons, Menger, Böhm-Bawerk and Wicksell and had become highly influential in the profession as the alternative to the classical (and Marx’s) explanation of profits in terms of some kind of deduction from what legitimately belonged to the workers. In the late 1920s, Sraffa had set himself a task of demolishing the theories that rooted economic calculations or the cause of prices and profits in human subjectivity or human psychology and rational behaviour. But the successful destruction of it would also amount to destruction of the old labour theory of value as they are the two sides of the same coin.

Sraffa soon realised that in a commodity producing society where means of production are produced by separate industries and bought and sold by each other in the manner as any final or consumption goods are, then it is impossible to trace back production of any commodity to its primordial state—production of commodities always requires commodities. No matter how far back we go in the chain of production some commodity residue will always remain—the road to the primordial stage is theoretically blocked forever. Though it is true that by going back and back in the production chain one can always reduce the commodity residue to negligible proportion and thus ignore it in the calculation of a long chain of labouring activity, it so happens that at what stage the commodity residue becomes negligible depends upon the rate of wages—if wages are relatively high, then the commodity residue will become negligible more quickly than when wages are comparatively low, and the commodity residue will never become negligible if wages are zero. This reveals a fundamental mistake in understanding the relationship between wages and profits when we root our theory of production in the idea of primordial relation of Man to Nature—if we could reduce the production chain to the primordial stage then we could reduce all capital investment to a long series of only wage advances and in this case if wages go to zero then the rate of profits must become infinity; however, if there must remain a commodity residue, no matter how far back we go in the production chain, then when wages go to zero the rate of profits must reach a finite maximum. This theoretical insight had a momentous implication for Sraffa’s theory—later Sraffa (1960) credited Marx for this insight:

The notion of a Maximum rate of profits corresponding to a zero wage has been suggested by Marx, directly through an incidental allusion to the possibility of a fall in the rate of profits ‘even if the workers could live on air’; but more generally owing to his emphatic rejection of the claim of Adam Smith and others after him that the price of every commodity ‘either immediately or ultimately’ resolves itself entirely (that is, to say, without leaving any commodity residue) into wage, profit and rent—a claim which necessarily presupposed the existence of ‘ultimate’ commodities produced by pure labour without means of production except land, and which therefore was incompatible with a fixed limit to the rise in the rate of profits. (Sraffa 1960, Appendix D, p. 94).

Sraffa’s theoretical story begins with a subsistence system, which is similar to Adam Smith’s ‘early and rude state of society’ or Marx’s ‘simple commodity production’. The characteristic of this system is that it produces exactly equal to what it uses as inputs—there is no net output production in the sense that all the income received by the labourers appears as necessary consumption similar to feed for the horses. So suppose such a system is given by:

90 t. iron + 120 t. coal + 60 qr. wheat → 180 t. iron

50 t. iron + 125 t. coal + 150 qr. wheat → 285 t. coal

40 t. iron + 40 t. coal + 200 qr. wheat → 410 qr. wheat

180 t. iron + 285 t. coal + 410 qr. wheat → 180 t. iron + 285 t. coal + 410 qr. wheat

In price terms this system can be represented by:

90p i + 120p c + 60p w = 180p i 50p i + 125p c + 150p w = 285p c 40p i + 40p c + 200p w = 410p w

(3)

180p_i + 285p_c + 410p_w = 180p_i + 285p_c + 410p_w

The condition of ‘subsistence’ that the aggregate of all inputs must be equal to outputs reduces this system of equations to only two independent equations and thus given any commodity as the measuring standard, say p_w = 1, we can uniquely determine the values of p_i and p_c. Thus the exchange ratios that will ensure the historical viability of this system are uniquely and completely determined by the objective input-output data alone—no information about human subjectivity in terms of demand or rational human behaviour etcetera is needed from outside.

Now, let us suppose this system becomes more productive and it produces more output than what it uses as inputs, such as:

90p i + 120p c + 60p w → 180p i 50p i + 125p c + 150p w → 450p c 40p i + 40p c + 200p w → 480p w

(4)

180p_i + 285p_c + 410p_w → 180p_i + 450p_c + 480p_w

Now the constraint of the aggregate equation of the subsistence system no longer holds, and therefore technically we do not have an equation system any more. We have three independent inequalities with only two unknowns—the excess values of outputs must somehow be accounted for on the left-hand side to turn it into a system of equations again. In this case, we do not know what exact ratio in which the three commodities must exchange, there can be several exchange ratios that can allow for this system to get back its original means of production to reproduce itself. It was at this stage that Classical economists and Marx thought that they needed extra information from outside the equations and introduced the idea of market mechanics (the gravitation of ‘market’ prices to ‘natural’ prices) and rational behaviour on the part of the agents that lead to adjustment of supplies with demands in such a way that the system comes to rest when each unit of capital receives equal returns. Thus on the basis of this extra information, one can introduce one more unknown in the system as the rate of profits such that:

90p i + 120p c + 60p w 1 + r = 180p i 50p i + 125p c + 150p w 1 + r = 450p c 40p i + 40p c + 200p w 1 + r = 480p w

(5)

(180p_i + 285p_c + 410p_w)(1 + r) = 180p_i + 450p_c + 480p_w

Now we can solve for the relative prices and the rate of profits simultaneously.

It is my contention that Sraffa rejects this approach. The assumption of rational behaviour by the agents turns the system into a mechanism, where supplies adjust to demands to bring about equal returns to factors and this requires knowledge of how changes in inputs relate to changes in outputs for every industry on the side of supply and consumers’ subjectivities on the side of demand. Sraffa was of the opinion that the analyst does not have excess to such information. He argues that instead of making any assumption about human behaviour and the technique of production, one may stick to the data available after the ‘harvest’ without asking the question: Why people did what they did or how things would change if the system is not in ‘equilibrium’ of demand and supply? He succeeded in showing that there is enough information in this system of equations to not only determine the unique set of prices and the rate of profits, but the fundamental propositions of Classical Economics and Marx can be made to stand as an alternative to the economics that roots itself in human subjectivity.

Let us rewrite Equation system (5) without assuming that rates of profits across industries are equal:

90p i + 120p c + 60p w 1 + r i = 180p i 50p i + 125p c + 150p w 1 + r c = 450p c 40p i + 40p c + 200p w 1 + r w = 480p w

(6)

(180p_i + 285p_c + 410p_w)(1 + R) = 180p_i + 450p_c + 480p_w

where r_j’s represent the industrial rate of profits and R stands for the weighted average rate of profits of the system as a whole. Clearly, the average rate of profits of this system is given by (165 t. coal + 70 qr. wheat)/(180 t. iron + 285 t. coal + 410 qr. wheat). This ratio is mathematically undefined because it is a ratio of disproportionate heterogeneous goods. It appears that the average rate of profits cannot be found without the knowledge of prices, which is supposed to homogenise these two collections of heterogeneous goods. Below we will show that this is not the case. For any given system of ‘basic goods’, ⁵ its average rate of profits can be determined independently of the knowledge of prices.

Since R is the unknown average rate of profits of Equation system (6), let us first assume that all industries receive the average rate of profits—this assumption must be possible given the mathematical property of the arithmetic average. In this case, our equation system turns into:

90p i ’ + 120p c ’ + 60p w ’ 1 + R = 180p i ’ 50p i ’ + 125p c ’ + 150p w ’ 1 + R = 450p c ’ 40p i ’ + 40p c ’ + 200p w ’ 1 + R = 480p w ’

(7)

(180p_i’ + 285p_c’ + 410p_w’)(1 + R)= 180p_i’ + 450p_c’ + 480p_w’

Notice that if r_j’s are not equal to R, then the respective prices would change when we apply R as their rate of profits to the respective industries. We, however, know that multiplying any equation by a constant does not change the information set of the equation system in any way. So, let us multiply the equation for iron industry by 4/3 and the equation for coal industry by 4/5. This turns our Equation system (7) to:

120p i ’ + 160p c ’ + 80p w ’ 1 + R = 240p i ’ 40p i ’ + 100p c ’ + 120p w ’ 1 + R = 360p c ’ 40p i ’ + 40p c ’ + 200p w ’ 1 + R = 480p w ’

(8)

(200p_i’ + 300p_c’ + 400p_w’)(1 + R)= 240p_i’ + 360p_c’ + 480p_w’

Sraffa called this system of equations the standard system and proved that there always exists one and only one set of multipliers that will convert any given system of production of basic goods to its standard counterpart. Notice that in Equation system (8), R becomes well defined as the ratio (40 iron + 60 coal + 80 wheat)/(200 iron + 300 coal + 400 wheat) must always be equal to 1/5 or 20%, no matter what prices happen to be, as this ratio is a collection of heterogeneous goods collected in the same proportion. Hence R is determined without the knowledge of what prices happen to be.

Let us go back to our Equation system (6) with the presumption that the industrial rates of profits are not equal. Now, if the industrial rates of profits are not equal, then some will be greater than the average and some will be smaller than the average. Let us call r_i = (R + e_i), r_c = (R + e_c) and r_w = (R + e_w). Thus we can write our Equation system (6) as:

90p i + 120p c + 60p w 1 + R + e i = 180p i 50p i + 125p c + 150p w 1 + R + e c = 450p c 40p i + 40p c + 200p w 1 + R + e w = 480p w

(9)

(180p_i + 285p_c + 410p_w)(1 + R) = 180p_i + 450p_c + 480p_w

By definition {(90p_i + 120p_c + 60p_w)e_i + (50p_i + 125p_c + 150p_w)e_c + (40p_i + 40p_c + 200p_w)e_w} = 0. Without loss of generality, let us assume that e_i > 0 and e_c and e_w < 0. Now, again rescale the equation system back to its standard counterpart by multiplying iron-equation by 4/3 and coal equation by 4/5. We obtain:

(120p i + 160p c + 80p w ) 1 + R + e i = 240p i 40p i + 100p c + 120p w 1 + R + e c = 360p c 40p i + 40p c + 200p w 1 + R + e w = 480p w

(10)

(200p_i + 300p_c + 400p_w)(1 + R*)= 240p_i + 360p_c + 480p_w

We should expect the average rate of profits of Equation system (10), that is, R*, to be greater than R simply because we have increased the total weight of iron industry in the system which has a higher rate of profits than the average. However, from inspection we can see that R* = R = 20%. From this, it follows that all the e’s must be equal to zero. ⁶ In other words, all the industrial rates of profits must be equal and equal to R*, that is, r_i = r_c = r_w = R = R*. Now we can plug the value of r_i = r_c = r_w = R = R*= 20% in Equation system (6) and solve for prices—the nature of the surplus equations system now reduces to the same as the equations for the subsistence system. Thus we do not need the market mechanics and rational human behaviour to solve for prices in this case either—the required information could be found out by rearranging the objectively available data. In other words, the condition of a uniform rate of profits is a structural property of our system of equations and not a behavioural property of the economic system.

Now let us introduce labour in the system explicitly and draw out a complete structural relation of any given system of production. We go back to Sraffa’s original example of a three-commodity economy:

90 t. iron + 120 t. coal + 60 qr. wheat + 3/16 labour → 180 t. iron

50 t. iron + 125 t. coal + 150 qr. wheat + 5/16 labour → 450 t. coal

40 t. iron + 40 t. coal + 200 qr. wheat + 8/16 labour → 480 qr. wheat

This can be represented in price terms as:

90p i + 120p c + 60p w 1 + r + 3/16 w = 180p i 50p i + 125p c + 150p w 1 + r + 5/16 w = 450p c 40p i + 40p c + 200p w 1 + r + 8/16 w = 480p w

(11)

(180p_i + 285p_c + 410p_w)(1 + r) + w = 180p_i + 450p_c + 480p_w

Converting it to its standard counterpart, we get:

120p i + 160p c + 80p w 1 + r + 4/16 w = 240p i 40p i + 100p c + 120p w 1 + r + 4/16 w = 360p c 40p i + 40p c + 200p w 1 + r + 8/16 w = 480p w

(12)

(200p_i + 300p_c + 400p_w)(1 + r) + w = 240p_i + 360p_c + 480p_w

Now, let us normalise our standard net output to one, that is, put (40p_i + 60p_c + 80p_w) = 1, and call it the standard commodity, which is our money-commodity. Now if wages are given in terms of this money-commodity, that is, as a proportion of the standard net output, then we can derive the average rate of profits of this system for all the values of wages starting from zero to its maximum value (40p_i + 60p_c + 80p_w), because the ratio of total profits to total capital remains in the standard proportion and therefore can be determined without the knowledge of prices. This gives us a relationship between wages and profits, which is given by: r = R*(1 – w), where w is given in terms of the standard net output and R*, which we have already derived from Equation system (10), is the maximum rate of profits of the system—it is the ratio of net output to total capital or the productivity of the system. This relationship between the productivity of the system and the rate of profits and wages is derived on the basis of the objective data without any knowledge of prices. Thus it is the fundamental structural property of our system of equations. Since the standard system is only a rescaled system of the actual system of observation they are algebraically equivalent systems and, therefore, the mathematical properties of the two systems must be identical. In other words, the relationship r = R(1 – w) must also hold for the observed system, if the wages and prices in the observed system is measured by the standard commodity as the chosen money-commodity. What we directly observe in the standard system in terms of physical data must show up to be true in the empirical system in terms of its calculations in prices:

Such a relation is of interest only if it can be shown that its application is not limited to the imaginary Standard system but is capable of being extended to the actual economic system of observation. … But the actual system consists of the same basic equations as the Standard system, only in different proportions; so that, once the wage is given, the rate of profits is determined for both systems regardless of the proportions of the equations in either of them. Particular proportions, such as the Standard ones, may give transparency to a system and render visible what was hidden, but they cannot alter its mathematical properties. … The same rate of profits, which in the Standard system is obtained as a ratio between quantities of commodities, will in the actual system result from the ratio of aggregate values. (Sraffa, 1960, pp. 22–23)

As we move wages from zero to its maximum value, we find that as wages and the rate of profits change, the set of prices change too. But these prices change only to ensure that for every given w, prices adjust in such a way that the structural property of the equation system, r = R(1 – w), is satisfied throughout—that is, prices play the role of accounting for the distribution of income, which is determined independently of prices. Here the word ‘change’ should not be understood in terms of movements of variables in historical time. The structural relationship described by r = R(1 – w) only maps the values of wage rate given in terms of the standard commodity for all possible rates of profits from 0 to its maximum value R, for a given R; or alternately, it maps the values of r for the whole range of wages from 0 to 1, measured in terms of the standard product for a given R. In the historical time scenario, however, a change in wages or the rate of profits could lead to changes in production decisions and hence changes in the input-output data that could change the value of R itself. One could interpret the long-term ‘natural prices’ of Classical Economics as predictions of changes in the rate of profits due to changes in wages over historical time on the basis of their assumption of constant returns to scale for all the industrial productive techniques that leaves R unchanged over the historical time. Sraffa, however, does not make any such heroic assumptions.

Notice that when all the income goes to wages, then the value of the net standard output is equal to the value of the net output of the observed system, since in this case the prices would be proportional to labour values and both the systems use the same technique and one unit of labour to produce their respective net output. For any other rate of wages the values of observed net output will not be equal to the value of the standard net output. However, the ratios of net output to total capital will remain constant with respect to changes in prices throughout the variations of wages from zero to its maximum value, as R* or R is determined independently of prices.

The above analysis of Sraffa shows how both the classical notion of labour value and the Marxian notion of surplus value are fundamentally flawed. As we have mentioned above, if production could be reduced to a long series of labour alone, as the classical economists maintained, then a rate of wages equal to zero must imply an infinite rate of profits. But here we clearly see that there is a finite maximum rate of profits, R, associated with a zero rate of wages. Furthermore, the solution of the system of equations (11), that is, the determination of prices and the rate of profits of the system, remains exactly the same if instead of reducing wages to zero we reduce all the labour inputs to zero. This, however, is an impossible scenario in Marx’s framework as, for Marx, only labour can add value to the means of production and surplus value and profits are only a positive proportion of the added labour, a zero labour input in productive technology must imply zero surplus value and zero profits. But this is evidently not true as is confirmed by the solution of Equation (11). We have pointed out above that Sraffa credited Marx for the idea of the finite ‘maximum rate of profits’, but it does not mean that Marx had well understood the consequence of this theoretical discovery for his own theory—given his formula for the average rate of profits as r = S/(C + V), Marx could see that r would remain a finite positive number even when V goes to zero; however, if we put the same formula in terms of the rate of surplus value or exploitation then we can see that r = (S/V)/(C/V + 1) becomes mathematically meaningless when V becomes zero—in other words, similar to the Classical case, in Marx’s case too, the rate of surplus value becomes infinite when wages go to zero and leave the rate of profits mathematically undefined. As pointed out above, human labour is simply one input that provides mechanical energy to the production technique; the same mechanical energy can be provided by a machine or a robot. There is no scientific reason to think that replacement of human labour by robotic labour must cause the technique to cease to produce surplus output or the system of production must become so infinitely productive that all commodities become free and the system of production must move out of the realm of ‘economic field’ or of ‘necessity’.

So in the light of the above analysis, what aspects of Classical and Marxian Economics we can rehabilitate? It is quite clear that Sraffa establishes that ‘profit is a non-price phenomenon’. This is what Sraffa believed was the central aspect of Classical Economics and Marx. Adam Smith had clearly stated that wages and the rate of profits are determined in the dynamic context of history and for any point of time they are given ‘norms’ and prices are determined by ‘adding up’ the given distributional variables. In other words, it is the distribution of income that determines prices. In Sraffa’s interpretation (see Sraffa, 1951), Ricardo had started off with the proposition that ‘it is the profits of the farmer that regulate the profits of all other trades’; implying that in agriculture both inputs and outputs can be treated as a single commodity ‘corn’. In this case, the rate of profits could be determined in physical terms as a ratio of corn output to corn input independently of prices, and thus prices of all other commodities must adjust such that all industries receive the same rate of profits. It was the criticism by Malthus, who argued that ‘in no case of production, is the produce exactly of the same nature as the capital advanced. Consequently we can never properly refer to a material rate of produce…’, that led Ricardo to abandon his ‘corn-profit model’ for the determination of the rate of profits and move to a general labour theory of value. Marx’s theory of surplus value and his derivation of the rate of profits prior to the derivation of prices of production were also designed to show that profit is a non-price phenomenon. Sraffa’s method of deriving the system’s average rate of profits independently of prices and then applying them to production equations to derive the prices follows Marx’s procedure almost step by step except that instead of deriving the production equations in terms of labour values from the empirical input-output data, Sraffa derives the equations of his standard system from the same input-output data. As Sraffa explains:

There are besides, many possible applications [of the Standard commodity], which I have not mentioned in the book {Sraffa 1960}, in problems discussed by Marx. Take, e.g. the determination of a general rate of profits, from the rate of surplus value: Marx takes an average of the rates of profits obtained in the production of the different commodities on the basis of ‘values’, and gets, as he acknowledges, an approximately correct result. An exact result could however be obtained by taking, instead of a simple average, a weighted average: & it can be shown that the appropriate weights can be derived directly from the proportions in which the comm.{odities} enter the ‘St{andard} com{modity}’. (Sraffa’s draft response [written on 12.2.1961] to Eaton’s ⁷ review of his book, Sraffa Papers [(N.D), 3/12/111: 132], underlining in original)

By establishing the proposition that the question of appropriation of the surplus value is independent of the question of economic valuation of it, Sraffa succeeds in removing the conflation between the problem of production of the surplus product and its appropriation, which, as we have argued above, sits at the core of the discrepancy between Marx’s physics of production and his metaphysics of human labour.