Developments in Value Theory

Previously I have discussed how Marx’s well known aggregate equalities have been shown to hold under single-system interpretations of his theory of value. In the July 2018 edition of the Cambridge Journal of Economics, there is a noteworthy paper by Ian Wright that reconciles the classical labor theory of value with Marx’s prices of production within a dual-system framework. As with single-system interpretations, Marx’s equalities also hold under Wright’s approach. However, they do so in a different way. Here, I want to offer some thoughts on the difference.


The classical labor theory of value in the form developed by Ricardo ran up against the difficulty that, under a capitalist tendency toward equalization of profit rates, prices of production (or what the classical political economists called ‘natural prices’) generally differ from labor values, as these were traditionally conceived.

Marx offered a resolution to the difficulty by arguing that, under capitalism, prices of production differ from values in a systematic way that nonetheless preserves key aggregate relationships; namely, total price equals total value, total profit equals total surplus value, and the average price rate of profit equals the average value rate of profit. He reasoned that production processes involving higher (lower) compositions of capital would produce commodities that had prices of production above (below) their values.

Early dual-system interpreters of Marx rejected his suggested transformation of values into prices. They argued that, while aware of the issue, he had failed to handle correctly the complication that a commodity’s price differs from its value not only because of deviation in its own composition of capital from the average but because such deviations also apply to the inputs.

More Recent Interpretations

Later, single-system interpreters of Marx argued that the dual-system critique was based on a misunderstanding. They argued that the amount of labor required to produce a commodity is not independent of the mode of production that is in place. Under capitalism, in this view, a commodity’s value will depend not on the value of the inputs but on the prices (or prices of production) of the inputs.

Adopting this perspective, single-system interpreters were able to reproduce Marx’s aggregate equalities as well as his result that individual prices of production deviate systematically from values. In these interpretations, both values and prices can be expressed equivalently in either monetary or labor-time terms, with conversion between the two based on the monetary expression of labor time.

Ian Wright’s contribution establishes, within a dual-system setting, that if classical labor values are defined in a way that is consistent with the dual-system definition of prices of production, labor values turn out to be proportional to prices of production. This is in contrast to prior results within the dual-system framework in which labor values seem incompatible with production prices under capitalism. But it is also in contrast to single-system interpretations (and Marx, as Wright notes) in that production prices do not deviate systematically from values. Before considering this difference, it is worth briefly considering how the result is obtained.

In the labor theory of value, a commodity’s value includes the direct labor and all indirect labor necessary for its production. The production of a particular commodity requires various inputs and so indirectly requires that labor be performed to produce these inputs as commodities. The production of these inputs, in turn, will require that labor be performed to produce the various commodities going into their production, and so on, ad infinitum. Although the interconnections are infinite, the more removed from the production of the particular commodity the indirect labor requirements become, the smaller their impact will be. Basically, the input requirements, described in a matrix A, will be applied successively to form part of a geometric series ΣAi that converges on I/(I – A), where I is an identity matrix.

Wright argues that to be consistent with the dual-system approach to prices, the value of a commodity should include not just the direct and indirect labor needed to produce technical inputs but also the indirect labor necessary to produce the commodities that will be consumed by the individual capitalists connected to the commodity. Without this last requirement being met, production of the commodity will not be viable under capitalist conditions. Wright shows that once the requirements of capitalist consumption are included in the dual-system definition of value, classical labor values are proportional to prices of production.

This approach could perhaps be regarded as converting Ricardo’s “93 percent labor theory of value” into a 100 percent labor theory of value.


Despite clear differences between Wright’s dual-system approach and single-system interpretations of Marx, and differences in their implications, there appears to be a similarity in possible justification. In an earlier post, I discussed a rationale for single-system interpretations along the lines that while classical labor values, traditionally understood, might represent the cost of a commodity to society as a whole, they do not represent cost from the perspective of the individual capitalist or capitalists making investment decisions. What matters to the individual capitalist is the amount of money capital (representing an amount of socially necessary labor) that must be advanced, and this will depend on the prices, not values, of the inputs into production.

Applying this line of reasoning, it could be said that Wright’s dual-system definition of value captures the cost of the commodity not to the individual capitalist but to the capitalist class as a whole. The consumption requirements of the individual capitalist will need to be met in real terms by production elsewhere in the economy and so will require employment of labor-power by capitalists as a class.

Alternatively – although some might resist this line of reasoning – Wright’s interpretation of value could be tied to the perspective of the individual capitalist on the basis of the notion of opportunity cost. What Marx viewed as a gap between the profit and surplus value applying to a particular commodity might instead be regarded as an opportunity cost to the individual capitalist that needs to be factored in to the value of the commodity.

If the foregoing is a reasonable depiction of matters, we appear to have the following situation. On the one hand, single-system interpretations successfully reproduce Marx’s aggregate equalities and systematic relationship between capital composition and value-price differentials (although a temporal interpretation is required if Marx’s profit rate law is to be replicated). On the other hand, Wright’s dual-system approach successfully reconciles the classical labor theory of value to capitalist conditions.

If so, the two approaches constitute two separate theories. Both theories appear to be valid in their own right. It then becomes a question of which theory is more useful for understanding economic reality. I am not qualified to offer an opinion on that, but the answer to the question likely depends on the uses to which the theories are to be put.


3 thoughts on “Developments in Value Theory

  1. Basics of Value Theory
    Comment on Peter Cooper on ‘Developments in Value Theory’

    Value and Profit Theory are false since Ricardo and Marx.#1, #2

    In order to see where Value Theory fails, one has to start with the most elementary version of what Keynes called the “monetary theory of production”.

    As the analytical starting point, the elementary production-consumption economy is defined with this set of macroeconomic axioms: (A0) The economy consists of the household and the business sector which, in turn, consists initially of one giant fully integrated firm. (A1) Yw=WL wage income Yw is equal to wage rate W times working hours. L, (A2) O=RL output O is equal to productivity R times working hours L, (A3) C=PX consumption expenditure C is equal to price P times quantity bought/sold X.

    Under the conditions of market clearing X=O and budget balancing C=Yw in each period, the price is given by P=W/R (1). The price P is determined by the wage rate W, which takes the role of the nominal numéraire, and the productivity R. This translates into W/P=R (2), i.e. the real wage is equal to the productivity. Eq. (1) is the macroeconomic Law of Supply and Demand.

    Monetary profit/loss of the business sector is defined as Q≡C−Yw (3) and monetary saving/dissaving of the household sector is defined as S≡Yw−C (4). It always holds Q+S=0, or Q=−S (5), in other words, the business sector’s nominal surplus = profit equals the household sector’s nominal deficit = dissaving. Vice versa, the business sector’s deficit = loss equals the household sector’s surplus = saving. Under the initial condition of budget balancing C=Yw, total monetary profit is zero. Eq. (5) is the most elementary version of the macroeconomic Profit Law.

    What is needed for a start is two things (i) a central bank which creates money on its balance sheet in the form of deposits, and (ii), a legal system which declares the central bank’s deposits as legal tender.

    Deposit money is needed by the business sector to pay the workers who receive the wage income Yw per period. The need is only temporary because the business sector gets the money back if the workers fully spend their income, i.e. if C=Yw. Overdrafts are needed by the household sector for consumption expenditures if the households want to spend before they get their income.

    For the case of a balanced budget C=Yw, the idealized transaction pattern of deposits/overdrafts of the household sector at the central bank over the course of one period is shown on Wikimedia.#3

    The household sector’s deposits/overdrafts are zero at the beginning and end of the period. Money is continually created and destroyed during the period under consideration. There is NO such thing as a fixed quantity of money. The central bank plays an accommodative role and supports the autonomous market transactions between the household and the business sector. From this follows the average stock of transaction money as M=kYw (6), with k determined by the transaction pattern.

    If employment L is doubled, the average stock of transaction money M doubles. In a well-designed fiat money economy, growth is not hampered by a lack of the transaction medium. NO capitalist with a sack of gold coins is needed to advance the wage bill.

    See part 2

  2. Part 2

    In sum, (i) money is a generalized IOU, (ii) money is created and destroyed by the transactions between the household and the business sector, (iii) the value of money is given by (2) W/P=R, i.e. is equal to the productivity, (iv) the workers get the whole product, (v) profit is zero.

    Because there is only labor input in the elementary production-consumption economy, eq. (2) represents the essence of the Labour Theory of Value.

    Eq. (2) can be generalized for two different products and then the Law of Value says P1/P2=R2/R1, i.e. the price relation is inverse to the productivity relation, that is, the whole price structure is objectively determined by the productivities. Note that macroeconomic profit is zero because of budget balancing, i.e. C=Yw. Macroeconomic profit does only appear if C>Yw and this has NOTHING AT ALL to do with capitalists or value creation.

    A well-defined monetary market economy is different from the wooly idea of capitalism. Profit has NOTHING to do with surplus value or exploitation but with deficit-spending/dissaving of the household sector. Profit cannot be attributed to a factor. This is the fundamental methodological defect of classical and neoclassical Distribution Theories.

    Egmont Kakarot-Handtke

    #1When Ricardo Saw Profit, He Called It Rent: On the Vice of Parochial Realism

    #2 Profit for Marxists

    #3 Wikimedia, Idealized transaction pattern

  3. On a programmatic note, the proposal of Paul Cockshott, Allin Cottrell, and Heinz Dietrich that “law should recognise that labour is the sole source of value and that in consequence workers, and their Unions, will have a claim in law against their employers if they are paid less than the full value of their labour” (Transition to 21st Century Socialism in the European Union) would be a perfect example of a directional measure, a truly transitional measure.

    Unlike every iteration of Trotsky’s “Transitional Program” or the early Communist International’s “transitional slogans,” this example can’t be realized even under the most left-social-democratic iteration of a capitalist economy, as small businesses not in full compliance would also be affected by the resulting “class action” or group lawsuits.

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