5. Measures of Exploitation

Marx’s value theory is a complex doctrine in which three different kinds of speculation coalesce: a philosophy aimed at proving that value is created by a labour substance; an explanation of the social relations of production in capitalism; and a method for measuring exploitation. My opinion is that there is no need for an essentialist philosophy to determine value, no need for a theory of value to explain capitalist social relations, and no need for a labour theory of value to measure the rate of surplus value. All we really need is a theory of production prices, possibly evaluated in labour units, as an instrument to measure exploitation. In the present chapter, I firstly bring to light some conundrums caused by using a wrong standard, then I show how to express the rate of surplus labour with a correct standard.

In section 1, I illustrate two paradoxes ensuing from the labour theory of value. One of them muddles up the explanation of technical change. In short, the labour theory of value is unable to account for the process of technical change in a capitalist economy precisely because it is a purely “technicist” theory of value. The second paradox deranges the equal exchange doctrine. This seems to be postulated by Marx to argue that fundamental capitalist exploitation occurs in the production process and not in the circulation process. Yet, if equal exchange is defined in labour values, there may be cases in which a part of surplus value emerges from the circulation process.

In section 2, I propose giving up the labour theory of value and sticking with a single system approach. Surplus value and the rate of exploitation can be measured in labour units by normalizing prices either with the wage or with labour productivity. These two kinds of normalization are consistent with each other, in the sense that they provide identical measures of the rate of exploitation and the rate of profit. However, they have different properties and can therefore be used to bring to light different aspects of the social relations of exploitation.

Finally, in section 3, I list some decisive hypotheses that are more or less implicitly assumed by Marx and the classical economists. They are decisive in that they impose severe restrictions to the theory of production prices. However, if this is only used to provide a unit of measurement, rather than a philosophy of value, such restrictions can be avoided. If they are redefined with reference to an imperfectly competitive economy, production prices can be used in empirical research to interpret the prices implicit in national account data and input-output tables as “normal” prices.

5.1. Two Paradoxes

The observation that a measure based on embodied labour gives rise to a “technicist” theory of value (Elson 1980; De Vroey 1982) is not undisputed. There are Marxists who think they can rebut it with the following proposition: the technical coefficients of production determine labour values that convey information about the way society allocates socially necessary labour among the various industries, and therefore these values do represent social relations. Such a proposition might make sense, but would not endorse the superiority of labour values. In fact, production prices convey all “social” information conveyed by them, plus that pertaining to the social relations of exploitation.

In reality, the proposition makes sense only if a single lone technique is available. If more than one exists, then the labour value system may not convey correct information on the evolution of the very technical conditions of production. This is a big problem because Marx attributes a great importance to technical progress in the theories of exploitation, capital accumulation and class struggle. Okishio (1961) proves that technical change in a capitalist economy cannot be understood by using labour values. If there is more than one technique, the price system correctly reveals which one is chosen by the capitalists, whilst use of the labour value system could lead to the wrong technique being chosen. This occurs because the profitability criterion adopted by capitalists in the choice of techniques is not based on labour productivity, and not even on the rate of surplus value or the rate of profit as determined in the labour value system. It is based on the rate of profit as determined in the price system.

The case of many techniques brings to light another reason why labour values do not convey correct information about social relations: they do not regulate the actual production conditions when technical change is motivated by profit. And this is paradoxical. Precisely because labour values only provide information on the technical conditions of production, they are unable to account for the process of technical change in a capitalist economy.

Another paradox emerges with the hypothesis of equal exchange. Marx uses the labour theory of value, among other things, to argue that capitalist exploitation takes place under apparent conditions of commutative justice, although he sometimes seems to criticise the validity of this postulation when dealing with the labour transaction. He wishes to point out that value creation is not a consequence of some asymmetry in market relations:

If commodities, or commodities and money, of equal exchange value, and consequently equivalent, are exchanged, it is plain that no one abstracts more value from, than he throws into, circulation. There is no creation of surplus value. And in its normal form, the circulation of commodities demands the exchange of equivalents (Marx 1996, 170).

Marx intends to show that exploitation is perpetrated in the production sphere and not in the market. To this end, he seems to accept the theory that accounts for the employment relationship as if this were based on a contract of commodity exchange. Then, assuming that a worker’s commodity–the use value of labour power–is traded in a competitive market, he discovers that her compensation coincides with the reproduction cost of her living labour, in other words, that the labour exchange appears to be an equal exchange. In a competitive reproduction equilibrium, transactions are supposed to be regulated by the “law of value”, and “according to the law of value, exchange is between equivalents, an equal quantity of labour for an equal quantity of labour” (Marx 1989a, 213). Embodied labour determines the true value of a commodity, and transactions at true values fulfil commutative justice. When the wage coincides with the value of labour power, commutative justice ensures distributive justice too, because reproduction costs (let us say, investments in human capital) are what a worker deserves to be paid for.

Equal exchange in the “labour market”, though, is a strange phenomenon. It is a real occurrence, in the sense that “production based on exchange value, on the surface of which that free and equal exchange of equivalents takes place, is basically the exchange of objectified labour as exchange value for living labour as use value” (1986a, 438). Yet, “from the point of view of capital, the exchange must be merely apparent, i.e. an economic category other than exchange, or else capital as capital and labour as labour in antithesis to it would be impossible. They would exchange for each other only as equal values” (247). They only appear to be equivalent in the circulation process.

The production sphere is the place where the fundamental capitalist misdeed is carried out. Capitalists implement production plans by using their authority. They compel workers to work efficiently and produce commodities whose value added is higher than the wage. Labour transmits to commodities a value consisting in the quantity of living labour bought by the employer. The capitalist’s authority is a power of command in the production process, not a form of market power, and is what the employer actually buys with the employment contract. The acquisition of this authority implies the subsumption of labour capacities and thence the ownership of the commodities produced by them. Therefore, according to a bourgeois right, the surplus value arising from the production process legitimately belongs to the capitalist. And nobody who believes labour time is a commodity can say that the wage is unjust because it is determined in an unequal exchange.

There are two problems with this speculation. Firstly, “an equal quantity of labour” is exchanged with “an equal quantity of labour” only in a system of “commodity production in general”, i.e. in a non-capitalist economy. Thus, when labour values are transformed into the production prices prevailing in a capitalist economy, a paradox may arise. In fact, since the rate of exploitation determined in the labour value system does not coincide with that determined in the price system, there could be cases in which at least a part of exploitation appears to take place in the market. To bring this oddity to light, suppose ev<ep, that is, v((I–A)q–gL)/vgL<p̆((I–A)–gL)/ p̆gL, and normalise prices, p̆, in such a way as to yield the invariance postulate (b.2), vgL= p̆gL. Then the wage bill in the price system coincides with the quantity of labour embodied in the workers’ consumption. According to Marx (1998, 232), “from the standpoint of the total variable capital of society, the surplus value it has produced is equal to the profit it has produced”. Disappointingly, this is not true. In fact, since the rate of exploitation is not affected by normalization, it happens that ev<ep whatever the standard. Therefore it is v((I–A)q–gL)< p̆((I–A)–gL), which means that although the aggregate variable capital in the labour value system is identical to that prevailing in the price systems, the surplus value earned in the latter is greater than that produced in the former. Since production prices diverge from labour values to ensure market equilibrium, it is as if the surface appearance of market exchanges had yielded a surplus value over and above that produced in the labour value system. Remember that the real rate of exploitation is ep, not ev, and that an equal exchange postulation, defined as the exchange of “an equal quantity of labour for an equal quantity of labour”, serves to argue that exploitation does not take place in the circulation process. Yet, when labour values are transformed into production prices in such a way as to ensure the invariance of variable capital, it may happen that the market generates a part of surplus value. Precisely because value is determined in the production process as embodied labour, it can be proved that there are cases in which exploitation emerges from the circulation process.

Secondly, if what capitalists buy in the “labour market” is the workers’ subordination, labour time is simply a temporal limit to the obedience obligation, and cannot be considered a commodity consisting of a flow of some substance that transmits value to products. Therefore, the notion of equal exchange as an exchange of equivalent labour values portrays a situation that, rather than merely apparent, is merely fictitious.

On the other hand, Marx knows very well that wages are determined not by the crossing of demand and supply curves, but by a bargaining process. The “labour market” is not a market proper, but a battleground for class struggle. Thus, if the force that determines the rate of surplus value is not the energy of labour power, but bargaining power, what need is there of an equal exchange assumption to explain exploitation, let alone to unmask a capitalist ideology?1

In any case, the gist of Marx’s reasoning can be upheld in a much simpler way. If one wishes to make it clear that capitalist firms may enact fundamental exploitation without resorting to any form of market power, it is sufficient to assume perfect competition in the price system. This counterfactual assumption is all that is required to argue that surplus value emerges from the production process and not from the circulation process.

5.2. A Single System Approach

A way out of the labour value impasse is to give up equation (1), and stick with equation (3) as the sole correct representation of values. The double system approach to value determination gives way to a single system approach: “There is only one economy, one system, not two. There is no ‘underlying’, hidden economy, which operates in values” (Duménil and Foley 2008). In other words, the only solution to the transformation problem is its dissolution.

Many Marxists, however, are unhappy with a value theory that seems to free the definitions of value and surplus value from their labour origin. Indeed, this is a serious problem for those who wish to remain faithful to a notion of abstract labour as a natural substance, as they can no longer maintain that value and surplus value are created by the energy supplied by abstract labour in the valorisation process.

Nonetheless, it is still possible to measure surplus value in labour units. It can be done in two different ways. One consists of normalizing prices with the wage and redefining them as labour commanded, as I did in chapter 4. Then surplus value becomes a quantity of labour commanded by profits, and the rate of surplus value, a ratio between two quantities of labour.

The other way consists of using aggregate living labour as a standard. Sraffa (1960, 10–1) suggests this way by assuming p̆(I–A)q=1 and L=1, which is tantamount to making the value of net output equal to living labour.2 He does not mention the transformation problem. Messori (1978, 115–6), who does, proposes to normalise prices with the invariance postulate (b.1), i.e. precisely with assumption p̆(I–A)q=L, and justifies this proposal by arguing that living labour is the sole macroeconomic variable that does not change when distribution changes.

You obtain the same result by normalizing prices with labour productivity, and this is the gist of the so-called “new interpretation”. It is attributed to Duménil (1980; 1983–4) and Foley (1982); but see also Wolff, Roberts and Callari (1982) and Lipietz (1982). Following these contributions, other authors3 have proposed reinterpretations that adopt labour productivity as a numeraire.

So, let y represent the average productivity of labour and normalise prices in this way:

$y=\frac{\hat{p}\left(I-A\right)q}{L}=1$ (10)

The net output is equal to the labour force employed, and one could argue that the approach boils down to a dissolution of the transformation problem that satisfies the exigency to measure prices in labour units. This looks like a re-reading, if not a re-writing, of Marx. It is not a new solution to the transformation problem. Still, it is an analytically sound solution to a philosophical problem.

With this standard, the wage share in net output becomes a share of living labour. Then the rate of exploitation can be written as

$e_p=\frac{\hat{p}\left(I-A\right)q-w_{p}L}{w_{p}L}=\frac{L-w_{p}L}{w_{p}L}=\frac{1-w_p}{w_p}$ (11)

Now we can confidently say the rate of surplus value is a ratio between unpaid labour, L–wpL, and paid labour, wpL. If 1 is a working day, wp is the part spent to produce the wage, so ep is a ratio between the number of hours the average worker works for the capitalist and the number she works for herself. I say average because the rate of exploitation ep holds in the aggregate, not in individual companies or industries. In fact, at a microeconomic level of analysis, value added, profits and wages are determined in terms of production prices. Microeconomic rates of exploitations, calculated in “labour time-equivalents of prices”,4 are not uniform.

To tell the truth, the new interpretation interprets itself as a “monetary” theory of labour value. In fact equation (10) can be rewritten y=p̆(I-A)q/L=1/ p̆m, where the scalar p̆m is the “value of money”. So, y is called “the monetary expression of value”, or “the monetary expression of labour time”, and represents the quantity of money corresponding to a unit of labour. The value of money, p̆m, also defined as the “labour expression of money”, is the quantity of labour time measured by a unit of money. In the new interpretation, “labour value” is immediately represented by “money”, which seems consistent with the view that the form of existence of value postulated by Marx is money, rather than labour (Key 2015).

It must also be said that a single system approach can be developed without any reference to equation (3), and a labour productivity standard can be applied to any conceivable price system (Mohun 1994, 407; Duménil and Foley 2008). Equation (3) is the one that determines prices at the highest level of abstraction compatible with that of Marx’s analysis of value. At a different level of abstraction, the labour productivity standard could be applied to a fix-price oligopolistic economy with differential profit rates, as better argued below. Finally, note that some new interpreters5 define the wage without specifying the workers’ consumption bundle and take the money wage as a variable, possibly determined by class struggle. Marx himself does so in his less abstract investigations into wage dynamics.

Several Marxists have contested the new interpretation from a methodological or a philological point of view. To mention just a few: Roemer (1990) observes that abandoning the dual system approach opens value determination to arbitrariness; Shaikh and Tonak (1994), that it turns the whole relationship between surplus value and profit on its head; Mongiovi (2002), that it redefines value in a trivial way; Fine, Lapavitsas and Saad-Filho (2004), that it wrongly assumes value to be immediately represented by money; and Petri (2015), that it adds nothing to the comprehension of what determines profits.

In any case, although methodological and philological concerns are understandable, it must be acknowledged that the new interpretation is analytically sound. Moreover, it has fostered Marxists’ commitment to empirical research (Mohun 2004; Foley 2019). Among other things, it has also helped convince many Marxists that the labour theory of value can be abandoned without prejudicing the theory of exploitation.6

Finally, it might be interesting to compare the two ways of measuring surplus value in labour units: “labour commanded” and “the monetary expression of labour time”. Recall equation (5). Then notice that, since the rate of exploitation is a pure number, it must be ec=ep, or L*/L=(1–wp)L/wpL. The ratio between the labour commanded by surplus value and that commanded by the wage is equal to the ratio between unpaid and paid labour. Hence, one is free to use either measure, depending on which aspects of exploitation one wishes to bring to light.

With the new interpretation, aggregate surplus value can immediately be expressed as surplus labour. It is also interesting to note that, by reducing value added to living labour, the wage rate coincides with the wage share in net output. Amongst other things, normalization with labour productivity seems to reinstate the linear relation between surplus value and the wage, S=(1–wp)L, which is another way of saying that the profit share, π=S/L, and the wage share, ω=wpL/L, add up to one (Gattei and Gozzi 2010). However, some caution is required: it is not possible to re-propose Marx’s microeconomic argument–that a reduction of paid labour from 6 to 5 hours in a 12-hour working day raises the surplus value of a firm from 6 to 7. With the new interpretation, the linear relation between surplus value and the wage only holds in the aggregate, and only by virtue of a normalization convention.

An advantage of the labour commanded measure, on the other hand, is its ability to convey the idea that exploitation is based on the power that capitalists exert in the labour process. Smith’s notion of “command”, i.e. “power to purchase”, can be easily converted into Marx’s notion, i.e. “power”. This is because, in the “labour market”, the capitalist purchases power over his workers. Valorisation can be accounted for as a process by which the exploitation of living labour in current production engenders an increase in the quantity of labour that capitalists can command in future production.7

Another interesting aspect of this measure is that it can be taken as expressing a worker’s point of view on capitalism and its overthrow. The factor of exploitation, 1+ec=(L+L*)/L, is a ratio between the labour commanded by value added and the labour embodied in it. It could also represent a comparison between the value of net output in a capitalist economy and its value in a socialist economy.8 The labour theory of value turns out to be of some utility after all. It can be seen as a counterfactual (Screpanti 2003) implicitly used by workers in collective decision-making; when they struggle to reduce exploitation, they are fighting against capitalism. A lessening of exploitation implies a cutback in capitalist power. Exploitation would be zeroed, L*=0, if commodities were exchanged at labour values, as would occur in a hypothetical socialist economy.

Finally note that, whilst reduction of the exploitation rate to a ratio between two quantities of living labour holds true only in the aggregate, its reduction to a ratio between two quantities of commanded labour holds true at the microeconomic level too.

5.3. Back to the Real World

Having proved that production prices are better than labour values as instruments to measure exploitation, I must now say that not even the classical theory of prices should be taken at face value. Marx adopts the Smithian and Ricardian model of market competition (or “perfect liberty”) with all its implicit assumptions, such as no oligopoly or monopoly power, no entry and exit barriers, no product differentiation. Especially important is the assumption of flexible market prices. These are supposed to vary as increasing functions of excess demands, with produced quantities varying as increasing functions of market prices. The market adjustment process is expected to cause a gravitation around a reproduction equilibrium, yielding market clearing and profit rate uniformity. This model may perhaps be appropriate to agriculture and financial markets, but certainly not to a modern industrial economy.

Indeed, the theory of perfect competition was not even justified in Smith’s times (remember his invectives against the cabals or monopolies who fix prices to squeeze the buyers). In The Wealth of Nations, Smith portrays an ideal state of “perfect liberty”, which works almost as a normative principle of social organization (McNulty 1967, 397), rather than as an explanation of the real market process. Ricardo, instead, believes that the theory describes the normal functioning of markets. But did it really account for the market process in the first half of nineteenth century? After all, Marx himself observes the tendency of company size and market power to grow in the advanced capitalist countries.9 Thus, by complying with that theory of competition, he accepts a cliché of the science of his times, but at the price of an improper level of abstraction.

Farjoun and Machover (1985) suggest that competitive production prices are precisely ideal prices. In the real world, profit rates have no tendency to converge to uniformity, and market prices, no tendency to converge to competitive prices of production.10 This fact can be explained by the theory of “normal pricing”, as developed by post-Keynesian economists. Markets are regulated by oligopolistic competition. Normal prices are fixed by applying a gross mark-up to direct costs (labour costs plus circulating capital), which are calculated by firms with a view to normal capacity utilization in the long run. The mark-up magnitudes differ across firms and industries, and reflect the diverse “degrees of monopoly”, so that profit rates are not uniform.11

The classical economists implicitly assume another decisive hypothesis: that the market adjustment process is stable. If it were not so, production prices would be irrelevant, as market prices would not gravitate around them. Marx has more than an intuition about market instability, especially when dealing with crises (Screpanti 1984), yet when it comes to value determination, he reasons as if the gravitation process were stable. The trouble is that stability has not been proved to hold in general, neither in neoclassical equilibrium models nor in classical gravitation models. This problem does not arise with normal prices, which are sticky and tend to vary with costs rather than with excess demands, and which are production prices coinciding with market prices.

Let us now distinguish between competitive production prices and oligopolistic production prices, the latter yielding uneven rates of profit. Normal prices are production prices, since they are regulated by production conditions. From an analytical viewpoint, they are determined by rewriting equation (3) as p=(l+pA)U, where U is a diagonal matrix of different mark-ups.12 Notice that restricting input costs to circulating capital as a basis for price determination is not a simplifying hypothesis in this case, but the illustration of a usual practice of firms. Moreover, there is no need to assume constant returns to scale throughout, as is done in the equations that determine competitive production prices.13 It is sufficient to observe that, in practice, direct costs are constant in a neighbourhood of normal capacity utilization.

The fundamental proposition argued in this book is still valid: oligopolistic production prices yield a correct theory of value, as they express both the technical and social conditions of production, now including the market power by which a firm may exploit consumers and the workers of other firms.

Simply put, the need to adapt Marx’s theory of prices to a modern industrial economy justifies “a systematic and principled rejection of the concept of a uniform profit rate” (Farjoun 1984, 12). All Marxists should learn such a lesson. The assumption of differential profit rates within a fix-price model is, first of all, more general than the assumption of uniformity. In fact, the theory of perfect competition can be considered as a special case: the limit case in which all the degrees of monopoly are nil.

This is often assumed in order to simplify theoretical problems and prop up some strong ideological tenets; and therefore, it can be legitimately assumed with critical intentions. Marx himself assumes competition with a somewhat critical intention: the “law of value”, established through the market process, brings about an “equal exchange” situation that should rule out all the explanations of exploitation based on some form of asymmetry in market power.

Yet, Marx also follows Ricardo in believing the assumption of perfect competition to be rather realistic. Wrongly so, for it does not describe the real market structure and market process in a modern capitalist economy.

Normal prices do not have this flaw and correctly account for the actual working of value formation in an economy based on oligopolistic competition. Therefore, they are not only more general, but also more realistic than competitive production prices. And precisely for this reason, they work quite well in empirical research, where measurement is effected ex post. The conventional prices of national accounts and input-output tables can be interpreted as normal prices.14 The rate of surplus value is calculated as a ratio between the summation of all other incomes and the wage bill. Then, if one wishes to enlighten empirical findings by measuring exploitation in labour units, it is sufficient to redefine surplus value and the wage bill by normalizing them with the wage rate or the productivity of labour.

---