3.1. Exploitation

The socialist argument that capitalism is exploitative can be summarized as follows:Footnote ¹²

1. (1) Producers should receive value equivalent to the value they produce.

2. (2) The surplus value of production is produced by the workers. (This premise is the labour theory of value.)

3. (3) So, workers should receive the surplus value of production.

4. (4) In a capitalist society, most (if not all) of the surplus value of production goes to capitalists, not to workers.

5. (5) Therefore, capitalism is exploitative and unjust.

The notion of surplus value can be defined as the value of the product minus the costs of production. The underlying idea is that productive activities are, well, productive; they create more than they consume, and this ‘more’ is surplus value.Footnote ¹³

One controversial premise in this socialist argument is the labour theory of value (premise (2)). Marginalist defenders of capitalism (see section 4) simply deny this premise, arguing instead that capitalists and entrepreneurs also contribute to the product, and that (in the normal case) workers, capitalists and entrepreneurs receive value equivalent to their respective contributions.

We might wonder whether the more basic part of this socialist critique of capitalism has anything to do with merit or exploitation.Footnote ¹⁴ Candidate injustices include the unequal distribution of the means of production, the pressures by which workers are incentivized to seek and maintain employment, or the misery of the unemployed that is part of these coercive pressures. No matter how we view their order of normative priority, these other injustices also explain why capitalists can extract surplus value, and this explanation adds moral gravity to the alleged exploitation. Yet, that capitalists extract some surplus value does not mean that they extract all of it, and as defenders of capitalism deny premise (2) it is unclear why the share that workers receive is insufficient. So, defenders of capitalism can easily deny premises (2) and (4).

3.2. The meritocratic critique of capitalism

Even if we abandon the labour theory of value and the claim that workers are forced to work for capitalists, the first premise of the socialist argument sketched above supports an alternative critique of capitalism, namely, the argument that capitalism is unfair (and unjust), because it tends to divide the product disproportionately among the contributors to its production. In overview, the argument goes:

1. (i) Contributors to shared production should receive a share of the product commensurate with their contribution.

2. (ii) In a capitalist society the wages of workers are less than commensurate with their contribution to the product.

3. (iii) So, in capitalist societies workers do not get what they merit.

4. (iv) So, capitalist societies are unjust.

Two challenges for this argument are, first, to define ‘commensurate to contribution’ and, second, to establish the empirical generalization that workers tend to receive less than what is commensurate to their contribution (there would also be injustice if they received more than this, but that’s usually not the complaint).Footnote ¹⁵ These are tough challenges, but if they can be met, the argument seems to show that the capital-labour split is unjust – without relying on the labour theory of value, the iron law of wages, or claims about coercion that are easily rejected by defenders of capitalism. Indeed, the restated argument is not about exploitation, but about merit as contribution – and thus based on a normative principle that meritocratic defenders of capitalism accept.

So, to defeat this argument, meritocratic defenders of capitalism must show that workers in a capitalist economy are, in fact, normally paid wages that are commensurate with their contribution to the product (for then premise (ii) is false).

4.1. Assessment of marginal productivity as a measure of merit

Recall that the marginalist argument seeks to establish the premise that, in a capitalist economy, labour receives value equal to its contribution to the product. However, even if we grant the marginalist claim that labour is paid the equivalent of the marginal contribution of the final unit of labour, there are several reasons to question whether this premise is established.

To start with the obvious: the marginal contribution of the final unit of labour is not the contribution of other (inframarginal) units of labour. Indeed, by the assumption of diminishing marginal productivity of the factors of production, other units of labour produce more than the final unit of labour, which also means that the average revenue product of labour is higher than the marginal revenue product that labour is paid. If each unit of labour should receive the equivalent of its contribution to the product, then most units should be paid more than the marginal contribution of the final unit. So, if the marginalist claim that labour is paid the equivalent of the marginal product of the final unit of labour is true, then it is false that labour is paid the equivalent of its contribution to production.Footnote ²⁰

Notice that this argument allows that capital is productive and should be paid according to its contribution to the product. However, the fact that capital contributes to the product is grounds for another critique of the marginalist claim that labour is paid the value of its contribution when it receives the value equivalent of the marginal product of the final unit of labour.

Even the final unit of labour employs capital in its productive effort. This capital remains contributory to the product, even if, as Clark argues, the final unit of labour tends to work with capital that is also on the margin of productivity (Clark Reference Clark1908: Ch. 8). The marginalist argument, in short, fails to distinguish between the marginal product of the final unit of labour which is remunerated as the value of its product, and the specific share of the marginal product of the final unit of labour attributable to that unit of labour alone.Footnote ²¹ This lack of distinction leads to a paradoxical outcome; the marginalist theory of wages establishes that (at the margin) labour exploits capital (or the capitalist that provides the capital), since the final unit of labour is paid the whole value of their joint product, so that capital (or the capitalist) contributes to production without receiving anything in return.

The general problem, called the disentanglement problem, is that capital and labour are entangled in the process of production in a manner that makes it impossible to disentangle their respective shares of contribution to the product.Footnote ²² Marginalist defenders of capitalism must find a way to disentangle the factors of production to establish that they are remunerated according to their respective contributions, but this is very hard to do, as Clark recognized:

Clark offers this observation in the context of what he calls a ‘primitive economy’ (Clark Reference Clark1908: 84); an economy where labourers do not work for capitalists, but own the capital they employ. In such an economy the disentanglement problem does not imply any injustice in the distribution of the product, for all expenses and all revenue accrue directly to the individual that owns both capital and labour-power. In a non-primitive society, where there is class distribution of capital-ownership, the disentanglement problem is rough on the meritocratic argument. How can we satisfy the demand that the product be divided according to productive contribution when labour and capital are so entangled that it makes no sense to distinguish between their contributions? The problem is not merely epistemic – that we cannot accurately ascertain the respective contributions of capital and labour – it is ontological; these are no longer separate contributions, but have become a unified productive factor, separable only in theory.

Another problem is that defining merit as marginal revenue product is inadequate, since it ties contribution to the product’s market value, which is not a plausible measure of merit. What should matter for distributive justice is not merely the market value of goods and services produced, but the degree to which one’s efforts are socially productive – which is not measured by market value. Care-work is as socially useful as coding, but the marginal revenue product of the final or average coder is much higher than the marginal revenue product of the final or average care-worker, wherefore coders are paid much more than care-workers per time-unit of labour. This complaint is less about the injustice of the capital-labour split, and more about the distribution among different types of labourers, only some of whom receive any remuneration for their efforts (there is much productive work done in capitalist societies that has no market-value and is not receiving a wage). This challenge says that the standard of merit that matters is distinct from the merit that markets measure, without thereby turning merit into desert – for it maintains that one should receive the value of one’s socially valuable activities, not that the virtuous or harder-working persons should be rewarded for their virtues or efforts.

It might be objected that market prices do tend to offer a social or collective evaluation of merit.Footnote ²³ In the idealized case of a competitive economy under consideration here, the competitive equilibrium prices of goods and services reflect aggregate demand, so prices constitute a collective appraisal of the relative value of goods and services to the members of society. Moreover, the aggregate valuation of members of society seems to be the proper measure of the value of products, and thus of the merit of producers (though externalities need to be factored as well). The price of an apple reveals the value of the apple to the members of society, and the prices of slices of the factors of production reveal their value to producers.

This objection raises a number of interesting questions of economic theory, aggregation, interpersonal comparisons, and the relation between value, valuation and merit. Without discussing all of these questions, I see two reasons to doubt that the valuations aggregated in prices reflect merit as (productive) contribution. The first reply focuses on the relation between prices and valuations.Footnote ²⁴ It is true, in a sense, that the price of a product reflects the valuation of the buyers who purchase it. Yet, in the normal case, the price of a product is lower than some buyers would be willing to pay for it, and also high enough that other prospective buyers are priced out of buying it. In other words, the aggregate demand for a product at any given price point hides both consumer surplus and consumer deficit – the utilities of buyers who would have paid more for the product and those who do not buy it, because the price is too high.Footnote ²⁵ The relation between consumer surplus and consumer deficit varies for different goods. When Marshall discusses consumer surplus and collective valuation, he compares salt and pineapples (Marshall Reference Marshall1890: Bk. 3, Ch. 6, sec. 3): salt is an essential commodity that trades even at very high prices, whereas pineapples are a luxury, suggesting that there is a much higher consumer surplus for salt than for pineapples. The prices of salt and pineapples thus do not reflect their relative social valuations, and so do not reflect their social values. Or consider again the case of care-work. Care-work is essential for most families, and many families would be willing to allocate a larger share of their wealth to care-work than they do, yet a host of factors (including the nature of the work, social norms, stereotypes and gender roles) mean that care-work is cheap in the sense that the price of daycare, schooling, and care for the infirm and elderly is lower than many families would be willing to pay. So, the price point of a commodity or service does not reflect the social or collective valuation of that commodity or service.

The second reply starts by drawing attention to a difference between goods and services and labour power as factor of production. The market value of factors of production does not reflect the collective valuation of these factors by society as a whole, but the collective valuation of these factors by capitalists (or entrepreneurs as defined by Clark). It might be ‘democratically attractive’ to outsource the standard of merit and process of appraisal to the aggregate demand of society as a whole, since it tracks with egalitarian, universalist and anti-paternalistic commitments. Yet the attraction wanes as the subset of members whose demand is aggregated narrows. Capitalists (including here entrepreneurs) are a privileged subset of society defined by their opportunities to employ factors of production in the pursuit of profits, and in reality this subset is a minority of society.Footnote ²⁶ So, the demand-side of the pricing of labour power reflects the valuation of only this privileged subset, which means that the prices do not reflect a collective or ‘democratic’ valuation of the value of labour power. Of course, the capitalist demand for labour power is a function of aggregate demand for commodities, but reflection is not identity.

In sum, there are several independently sufficient reasons for rejecting the marginalist notion of contribution as the standard of merit employed in the normative principle of merit. In the following section I look at two alternatives.

5.1. The Nash bargaining solution

John F. Nash (Reference Nash1950) shows that a two-person bargaining game – such as negotiations between an employer and a labour union where the parties are bargaining for the split of a surplus value of cooperation – has a unique solution, if these assumptions are satisfied:

If these assumptions are satisfied, the expected outcome from a bargain where the bargainers have equal bargaining power is the one that maximizes the product of the utilities of the bargaining parties. With linear utility for the value of the product, the utilities can be understood as the share of the product that the parties receive minus their (opportunity) costs of entering into the bargain, that is, what they could expect to receive without the bargain (their so-called BATNAs: best alternative to a negotiated agreement). So, for two-player games, the outcome maximizes (x − a)*(y − b), where x and y are the values received by each player, x + y is the total value of cooperation (v), and a and b are the opportunity costs of cooperation for the bargainers.

Bargaining strengths are not always equal. For unequal power games, we can let k and h express the relative bargaining advantage of the players (h + k = 1 and 0 < h, k < 1), in which case the expression to maximize is ${(x - a)^k}{(y - b)^h}$$$ . The share that goes to each player can then be calculated from:

$${{(y - b)} \over {(x - a)}} = {k \over h}$$

If we assume equal bargaining advantage (h = k = ½), then the sharing of product becomes a pure function of the total utility of cooperation and BATNAs of the cooperators. And if the bargaining parties have equal BATNAs, the result is an equal distribution of the product.Footnote ³¹

If we assume that bargaining takes place among equals with different BATNAs, then the division of the product can be determined directly from the BATNAs via the Nash bargaining solution. For example, a capitalist (K) and a worker (W) are considering cooperation. On their own, the capitalist can make $1,000 and the worker $500; together they can make $2,500. So, the question is how they should share the product (with shares S _k + S _w = $2,500). Plugging in these values, the Nash solution provides $1,500 to the capitalist and 1,000 to the worker.Footnote ³² Figure 2 illustrates the case and thus also the Nash solution.Footnote ³³

Figure 2.

Illustration of Nash Solution.

The area (Max _K -Max _W -D) is the set of mutually advantageous bargains; the line (Max _K -Max _W) is the set of mutually advantageous and efficient bargains. Max _k is the best possible bargain for the capitalist, and what they could get if their bargaining advantage is complete (k approaches 1, h approaches zero); Max _w is the best possible bargain for the worker, and what they could get if their bargaining advantage is complete (h approaches 1, k approaches zero). When, as in our example, the bargainers have equal bargaining advantage, the slope of the line that connects D and N is 1.

The Nash bargaining solution is more complicated for n player games,Footnote ³⁴ and difficult to apply to a complex economic system. Yet we could imagine that capital and labour are two blocs, and then the Nash bargaining solution could compute the capital-labour split as it would for any other two-player game. This would leave us with the question of the proper distribution of the shares that go to capital and labour respectively within the blocs that receive them, but the Nash bargaining solution seems to offer a sensible reply to how the surplus of production in a capitalist economy should be divided between capital and labour.

There are, however, three problems with using the Nash bargaining solution as a measure of productive contribution, which is the definition of merit shared by critics and defenders of capitalism.Footnote ³⁵ (One of these problems is shared by the Shapley value, and is discussed below.)

First, the Nash bargaining solution involves no measure of productive contribution, and so cannot be said to distribute the product as a function of contribution to the product. The Nash bargaining solution varies with bargaining power and opportunity costs of cooperation for the producers (the a and b values). One might regard opportunity costs as a measure of the efforts that the cooperators bring to the cooperative relationship, for opportunity costs measure the sacrifice made by cooperators. Thus construed, the Nash bargaining solution offers an answer to the problem of constructing a measure of effort that could be used in a desertist theory of distributive fairness, for (assuming equal bargaining power), the distribution it recommends is then a function of the differential efforts.Footnote ³⁶ However, though a desertist standard of merit as effort might be attractive, it is not the standard of merit as contribution to the product that is the standard of merit shared by meritocratic critics and defenders of capitalism.

The second problem is that the Nash bargaining solution assumes that we have a way to value the BATNAs of the bargaining parties (the values a and b in the formula above). When it comes to the capital-labour split, we seem to have two options. We can abandon the project, for how on earth could we calculate the value to capital or labour of not being part of a capitalist economy? The alternative is to say that the value of non-cooperation is the same for both capital and labour, namely, zero, for there is no alternative to cooperation – by assumption, in a capitalist society, nothing is produced without both capital and labour.Footnote ³⁷ That proposal immediately yields the result that capital and labour should share the full product of cooperation equally. An interesting result, but unacceptable to most defenders of capitalism.

5.2. The Shapley value

The Shapley value, developed by Lloyd S. Shapley (Reference Shapley and Roth1989) calculates the expected payoff for a player entering into a multiplayer cooperative game as a function of the values of the coalitions that can be created with and without that player.Footnote ³⁸ It can be shown that the Shapley value is the only measure of expected utility from such a cooperative relationship that satisfies the following axioms:Footnote ³⁹

The Shapley value assumes that utilities of players can be translated into a medium of exchange so that it can be transferred between the players (e.g. money), that the cooperative relationship can be characterized without reference to non-cooperators, that coalitions can be characterized by their total value, and that supply costs (the costs of creating, monitoring and enforcing coalitions) can be ignored (Roth Reference Roth1989: 2).

Remarkably, the expected value for each player turns out to also be the value of his or her expected marginal contribution to a cooperative relationship when calculated and weighted across all possible configurations of that relationship (Young Reference Young and Roth1989: 268–269). This marginal contribution is calculated as the average marginal contribution that players provide across all permutations of the coalition – where the marginal contribution for a given permutation is the value they add to the cooperation at their point of entry.

To illustrate, take an example with one capitalist (K) and two workers (W ₁ and W ₂).Footnote ⁴² The capitalist can produce nothing without the workers, but the workers can produce nothing without capital. Working together, K and W ₁ can produce $20 worth of goods, K and W ₂ can produce $10 worth of goods, and all three working together can produce $40 worth of goods. Seeing that the total value of cooperation exceeds what they could produce on their own or in pairs, they decide to cooperate and share the product.

Their respective Shapley values are calculated as the average of their marginal contribution across all permutations of the cooperative relationship. That is, they might enter in the order K, W ₁, W ₂ or in the order W ₁, K, W ₂, or in the order W ₁, W ₂, K, and so on through the six possible permutations. In the first case, the marginal contribution of K is 0, in the second it is $20, and in the third it is $40. Table 2 shows permutations, marginal contributions and Shapley values (measured in $).

Table 2.

Contribution Permutations and Shapley Values

The Shapley value tells us the worth of the contributions of capitalist and workers, and thus also what share of the product each should receive, if we accept the principle of distribution according to contribution.

Why does the capitalist receive almost half of the revenue? Because the capitalist is marginally productive as the second in any two-person coalitions they could be part of, whereas the workers make no marginal contribution without the capitalist. So, the capitalist is marginally productive in four of the coalitions, whereas the workers are marginally productive in three each. The example thus illustrates a capitalist bargaining advantage that is a general feature of capitalist economies – the ratio of capitalists to workers is less than one, so there are more productive coalitions available to the capitalist.

The above example also illustrates how the Shapley value as a measure of contribution avoids the problems of Clark’s marginalist proposal discussed in section 4, and, therefore, how a wage system that reflects Shapley values might be said to satisfy the principle of merit.

If wages track Shapley values, it is no longer the case that labour is paid the value of the marginal revenue product of the final unit of labour; rather, labour is paid the value of its marginal revenue product independently of where it actually is in the schedule of hiring or what the final unit of labour is paid (in fact, it no longer matters which unit of labour is the final unit, for even the least productive unit of labour is factored in with other units in terms of its marginal productivity averaged across the cooperative possibilities). In addition, the Shapley value avoids the disentanglement problem, since it calculates the specific marginal contributions of capital and labour as functions of what they add to the productivity of each other.

So, by contrast with Clark’s marginalist proposal, the Shapley value offers a measure of productive contribution that can serve as a satisfactory standard of merit. And, by contrast with the Nash bargaining solution, the Shapley value is a function of productive contribution rather than the (opportunity) costs of cooperation. So, the Shapley value offers the attractive and substantive notion of productive contribution needed to substantiate the principle of merit.

One problem, though, is that the Shapley value varies with different partitions of the units. This problem is especially troubling if we want to use the Shapley value as a way to measure the relative productivities of capital and labour. If, for example, we measure the productivity of capital rather than the capitalist in the example above, and say that we divide capital into two parts (K ₁ and K ₂), both of which are necessary for workers to do their work (say, resources and technology), then the Shapley values would be (see Appendix for calculations):

$${K_1}{:}12.5\,\,\,\,{K_2}{:}12.5\,\,\,{W_1}{:}9.2\,\,\,\,{W_2}{:}5.8$$

While the total product is constant and capital and labour make the same contributions as before, simply counting the capital differently changes the Shapley value and adds almost $7 to the capitalist share of the product – and subtracts an equal amount from the share that goes to workers. Without the partition, the capital-labour split is 18.3:21.7, which delivers 46% of the product to the capitalist; after the partition the capital-labour split is 25:15, which delivers 62.5% of the product to the capitalist. Surely, the contribution of the capitalist did not increase (nor did that of the workers decrease) merely by partition, but the Shapley value issues that result.

A more general problem – and this is also the third problem for the Nash bargaining solution flagged above – is that we have no reason to believe that the capital-labour split in a (suitably idealized) capitalist economy would tend to track either the Shapley value or the Nash bargaining solution. In other words, the Shapley value and the Nash bargaining solution can serve as prescriptions for the capital-labour split that we should want an economy to satisfy, but they are not predictions of the capital-labour split that we can expect to result from a capitalist economy working without external interference. The Nash solution presumes that capital and labour have equal bargaining power, an equality we cannot assume that capitalism supplies of itself. The Shapley value measures marginal contribution as a function of possible cooperative relations, whereas wages in a capitalist economy are a function of actual cooperative relations; (average) possibility is not actuality.