The capitalist law of exchange
On this basis of equivalent exchange, Marx analysed with considerable historical and contemporary detail how capital (any sum of money invested in order to make more money) creates surplus-value in the production process, and then how surplus-value creates capital as an accumulation process.
In essence this was what now would be called a macroeconomic approach. All individual capitals are treated qualitatively as identical, differing only in quantity. Any individual capital in these terms is representative of all capitals, and Marx talked in terms of “capital in general”. As long as his focus was on the economic categories representing class, this was sufficient for his purpose of exposing and analysing the deepest determinations.However, it was only a first step. The freedom of markets entails competition, for each individual capital pursues the highest profit on its investment, and this entails mobility of capital in addition to the previously presumed mobility of labour. If capitals are perfectly mobile, then competition must ensure an equalized rate of profit on average over repeated production periods. Thus, in an economy where capitalists as employers allocate social labour, the principle of the equalization of the rate of profit determines natural prices, while the principle of the equalization of the advantages of production tends to equalize wages, or more generally rates of exploitation (ratios of unpaid to paid labour, because workers are still free to move from sectors where they are more exploited to sectors where they are less exploited). There is no reason to presume that the equalization of the profit rate is actually achieved - rather it is a tendency, whose long run achievement is continually disrupted by empirical contingency. Marx called the prices at which the rate of profit is equalized prices of production: they are Smith’s natural prices when capitalist employers determine the distribution of labour among branches of commodity production.
Such a determination is the capitalist law of exchange.Prices of production in general are different from the natural prices-proportional-to- labour time required of equations (1), (2) and (6). For once capital-in-general is individuated into competing capitals, those competing capitals will have production processes that typically differ in technology. There will be a whole spectrum of ratios of non-labour to labour inputs, from highly mechanized almost completely automated technologies to those that are very labour-intensive. Highly automated capitals employ very little labour; very labour-intensive industries employ a lot. With perfect labour mobility enforcing a uniform rate of surplus-value, highly automated capitals produce very little new value and very labour-intensive industries a lot. Therefore the prices at which each capital would earn the same rate of profit cannot be prices-proportional-to-values. Hence capitalist exchange (except under very special analytical assumptions) must be non-equivalent exchange. This entails that value is realized at prices of production in different sectors from where it was produced. The competition among capitalist firms that enforces the tendency for rates of profit on invested capital to be equalized effectively redistributes surplus-value among the sectors of commodity production.
In principle, this does not affect equation (6), for in the aggregate value added is invariant to where it is produced: the total number of hours of labour remains the same. Hence writing p for the vector of prices of production:
Equations (6) and (8) have the same interpretation: prices distribute social labour across net output. They differ in that distribution according to whether commodity exchange or capitalist exchange is considered, but for prices to be bearers of social labour time, what matters is only that there is a distribution.
The social division of labour allocates portions of social labour to production processes, and it does this through a decentralized price mechanism. Prices, qualitatively, are always the bearers of social labour, and, quantitatively, total net output, evaluated at whatever prices are, must always equal total hours worked at the prevailing value of money. Because of this, equation (8) also serves to define the value of money in a world of capitalist exchange and allows for a more general notion of money than the commodity gold.The redistribution of surplus-value through competition also does not affect the sale of labour-power for a wage, because there is no capitalist production process of labourpower, no rate of profit earned on its production and no technology of production to consider. Hence the left-hand side of equation (2) is not affected by the difference between commodity exchange and capitalist exchange:
where, as in equation (8), the value of money is understood more generally than the value of the commodity gold. However, the wage cannot be proportional to the labour value of the wage bundle of commodities (which means that the latter does not determine the value of labour-power under capitalist exchange), and it is also unnecessarily restrictive to presume the whole wage is always spent, so that budget constraint part of equation (2) can be dropped. Equations (8) and (9) together imply that the value of labour-power is the wage share of money value added, so that, however prices are conceived, profits remain the measure of unpaid labour, the rate of surplus-value is the profit-wage ratio, and capitalist exchange is founded on exploitation.
We have emphasized that, equations (8) and (9) apart, the capitalist law of exchange entails that value appears in places other than where it is produced, and that this is not contingent or accidental but systemic.
This feature of Marx’s account is particularly important, and its implications are under-recognized. For unequal or non-equivalent exchange implies that surplus-value is redistributed. In principle, the magnitude of these redistributions can be calculated by multiplying each capital’s wage bill by the uniform rate of exploitation, and comparing the resulting surplus-value produced in each firm or sector with the actual profits accruing there. However, in practice this is complicated by another factor.For non-equivalent exchange is a more general phenomenon than just the requirements made of prices by different technological structures. Consider again the equivalent exchanges of commodity exchange and of capital in general. Once a commodity has been produced, it has to be sold, and this requires human activity. Similarly, it takes human activity to assemble labour and non-labour inputs ready to commence production. However, selling an already produced commodity changes the form in which value exists (from a commodity form to a money form), but it does not change its amount. Similarly, using a sum of money to purchase labour and non-labour inputs again changes the form in which value exists (from a money form to a productive form), but it does not change its amount. Marx called the labour that is actually value-creating “productive labour”, and the labour that alters only the form in which value exists but not its amount (typically commercial and financial labour) “unproductive labour”. He also called “unproductive” the pure labour of supervision. However, all of these activities must be paid for, and the only source for their payment is the production of new value. Hence a more careful specification of what labour is to count as value-creating requires a further elaboration of unequal or non-equivalent exchange.
Unequal exchange means that Marx’s analysis has deep and in some dimensions very non-intuitive implications. Even very large productive capitalist firms are small relative to the whole system of capitalist production, the division of labour it creates, and the enormous resulting pool of surplus-value in the whole world capitalist economy.
Thus each capitalist firm makes a negligible contribution to the pool of surplus-value through the exploitation of its own workers. The profitability of any firm rests on its ability to secure a share of the pool of surplus-value through its competitive strategy. In extreme cases, such as land rents and intellectual property royalties and rents, the appropriators of surplus-value may make no contribution at all to the pool of surplus-value through production and the direct exploitation of workers. In many cases strategies that increase a productive firm’s share of the pool of surplus-value, such as cost reduction through technical change or shifting to lower-wage labour-power, also do contribute to enlarging the global pool of surplus-value. However, the contribution any particular firm makes to this pool is bound to be small compared to the effects of its competitive strategy on its share of the pool.The resulting apparent disconnection between the realization of surplus-value in particular firms or sectors and the expenditure of productive labour in actual production leads to widespread illusions and misconceptions in understanding the capitalist economic system. The most common misconception, which Marx’s detailed analyses in volume III of Capital (1894 [1981]) were aimed at dispelling, is that value and surplus-value are not actually produced by the expenditure of labour at all. Victims of this misconception (which include everyone educated to look at the world through the lenses of neoclassical price theory) will be led to one or another of the fallacious theories of value anatomized in Marx’s Theories of Surplus- Value, such as the idea that value is the “economic (consumer) surplus” realized from the transfer of assets from agents who subjectively value them less to agents who subjectively value them more through exchange. From these points of view the distinction between productive and unproductive labour, which was fundamental to the classical political economists and Marx, becomes incomprehensible.
Similarly, the perennial flourishing of enthusiasms for imaginary economies based on completely automated production of goods, services such as information processing, intellectual property creation, or financial manipulations that seem to involve negligible labour expenditure rests on the same misunderstanding. The dreamers of these alternative economic universes confuse the mode of appropriation of surplus-value with the conditions of production of surplus-value. From the point of view of a software seller with a powerful monopoly of a proprietary system subject to network externalities, who can sell the same software over and over again with negligible costs of production, the pool of surplus-value does indeed seem to be limited only by the software seller’s own imagination and competitive ruthlessness. In these cases (which are more and more prominent in the contemporary globalized economy) there can be very high degrees of increasing returns to scale and diminishing average costs to the appropriation of surplusvalue. However, the core lesson of the theory of value of the classical political economists is that the actual source of value and surplus-value lies in the expenditure of productive labour.
“Dual system” interpretations of the theory of value and the “transformation problem” The interpretation of Marx’s theory of value we have offered in the last section is sometimes called a “single-system” theory, because it emphasizes the relationship between the theoretical categories of value and price and real-world money prices. Another influential body of work on the theory of value takes a different, “dual-system”, approach, based on a system of “values” proportional to embodied labour coefficients that coexists with the phenomenal system of money prices. These embodied labour-coefficient values are determined according to the principles we have called the commodity law of exchange, in which mobility of labour leads to natural long-period prices of commodities proportional to the labour time required to produce them. Dual-system theorists identify Marxian categories such as the value of labour-power and the rate of exploitation in terms of this underlying, but not directly observable, system of values. In the dual-system framework, the question arises as to the relation between the system of values and the system of observable prices of production. The study of this relation constitutes the “problem of the transformation of values into prices of production” or, more compactly, “the transformation problem”.
The discussion of the transformation problem revolves around the mathematical investigation of the relation between equation (3), which is taken as defining values proportional to embodied labour coefficients, and the representation of profit-rate equalizing prices derived from Sraffa’s work:
where p is a vector of relative prices and the other symbols have the meanings we have assigned already. The main difficulty encountered in the transformation problem is in reproducing the invariance claimed by Marx in chapter 10 of Volume III of Capital (1894 [1981]) for the total value of production, variable capital, surplus-value, and hence the rate of surplus-value and profit rate between the value and price of production schemes. This difficulty has led theorists in this tradition either to assert a meaning to value and its significance which, because of its detachment from the prices of equation (10), is vulnerable to the charge of arbitrariness (for example, Sweezy 1942); or it has led them to abandon a labour theory of value altogether, to concentrate on the analysis and implications of equation (10) (for example, Steedman 1977).
From the point of view of the single-system approach, it is more natural to pose these issues in terms of an “inverse transformation problem”, which takes observed prices, output, and productive labour inputs as given and seeks to recover the abstract labour time embodied in commodities produced in each line of production. One way to solve this problem is to assume that rates of exploitation of productive labour are equalized across different sectors by the mobility of labour, which determines the abstract labour time imputed to each sector of production, and identifies the redistribution of surplusvalue between sectors in a pattern that is consistent with the economy-wide rate of surplus-value defined earlier in our discussion.