Marx's Theory Of Value

Victor Margariño explains labor theory of value to Vaush

Marx sets his theory of value within the capitalist (or bourgeois) mode of production:

"The wealth of those societies in which the capitalist mode of production prevails, presents itself as 'an immense accumulation of commodities'..." (Marx 2010, first sentence of chapter 1)

Feudal societies, with lords and serfs, and classical societies, such as the Roman empire with its slaves, present other modes of production. Although this exposition starts from the same point as Marx, it deviates from his dialectical method of presentation.

In the capitalist mode of production, workers sell their ability to labor under the direction of others, that is, their labor power, to the owners of firms for money. The workers use this money to buy the goods and services they need to survive. (As emphasized by feminists, the sustaining of the workers includes much care work and household production outside the world of commodity production.) The owners of firms, that is, the capitalists, own the equipment, raw material, and semi-finished goods that the workers use to manufacture these goods and services. They have purchased these means of production on various markets. After the workers have used the means of production to produce a commodity, the capitalists also own the product. The capitalists sell the product of the labor of the workers on the market for money. A commodity is produced for the market, to be used by others. To be bought and sold, it must have a use value, some attributes that make it useful for others. Buying and selling occurs regularly and repetitively under capitalism, not only at the edges of society.

These characteristics of the capitalist mode of production are distinctive. Slaves and serfs are not free to sell their labor power on their own account. Labor power is also not sold by self-employed artisans. Peasants living in a pre-capitalist communal village (for example, the Russian mir) do not produce commodities to be sold to their neighbors. The slaves and serfs producing the goods needed to sustain the owner's estate are not producing commodities.

In capitalist societies, most workers are not producing commodities to satisfy final demand. Rather, they are producing commodities that are bought and sold in a vast network among firms. I like to characterize this network by Leontief input-output matrices in physical terms. National income and product accounts (NIPA) are usually presented in terms of monetary flows. A Leontief matrix shows farmers purchasing tractors of specified kinds, fertilizers, and so on from other industries. The seeds are purchased from agriculture itself. The manufacturers of tractors buy steel, and the steel industry buys iron. For a self-sustaining economy, these quantity flows must be constantly repeated. Even while steel manufacturers are running down stocks of iron in producing the current output, they are also replenishing these stocks with current purchases of iron.

The production of final demand with a given technology implies the distribution of the employed labor force of a nation among industries. For each commodity, how much additional labor would be employed if the net output were increased by one unit of that commodity? In Leontief analysis, the answer to this question yields employment multipliers. An employment multiplier is the labor directly and indirectly employed to produce one additional unit of that commodity in s self-sustaining way. It is also known as the labor value of the commodity. Notice that this labor time will be distributed over many industries. Steel production requires mining of iron, the generation of electricity to operate the mills and mines, the operation of railroads and trucking to ship iron ore to the mills and the steel to where it is needed, and so on. Labor values reflect social relationships between workers not immediately apparent in the buying and selling of commodities.

I now want to point to some more advanced mathematics, easiest to set out when no joint production exists and when the production of each commodity requires inputs, either directly or indirectly, of all other commodities. Sraffa (1960) goes to great lengths, not always successfully, to argue that this approach works with the relaxation of these assumptions. Suppose the Leontief matrix shows the production of n commodities, and that the technique represented by this matrix allows for the production of a surplus product, after the replacement of the means of production used up in satisfying final demand. Then the Leontief matrix has n eigenvalues. Consider the maximum eigenvalue, which is strictly positive and less than unity. The components of the corresponding eigenvector are all strictly positive. With appropriate scaling, this eigenvector is Sraffa's standard commodity.

The standard commodity represents the surplus produced over the course of, say, a year. It is a composite commodity. The means of production used in the production of the standard commodity are in the same ratios as the standard commodity. Proportions of the standard commodity map directly to proportions of the employed labor force. If final demand was the standard commodity, production would expand each of the means of production at the same rate, a rate related to the maximum eigenvalue of the Leontief matrix. If all of final demand were invested, the economy would expand along the von Neumann (1945-1946) growth path.

Given the wage, one can find prices of (re)production associated with Leontief matrices. For a competitive economy, the same rate of profits is obtained in each industry. Inputs are evaluated at prices of production, as are outputs. For any wage not exceeding the maximum wage, prices of production are strictly positive and well-defined, given the technique. In effect, prices of production show an outcome that validates managers of firms in their decisions about which processes to operate in each industry and the levels at which these processes are operated.

Market prices can be expected to deviate from prices of production. The possibility of such deviations is known as the realization problem. These deviations can be expected to result in disinvestment in some industries and expanded investment in other industries. Furthermore, the level of effective demand may lead to the overutilization or underutilization of capacity. Likewise, the level of employment consistent with effective demand need not match the size of the labor force looking for work. Capacity utilization and unemployment are separate questions; relative prices cannot be expected to vary so as to solve both problems simultaneously. Furthermore, decisions that are validated by prices of production at one moment of time cannot be expected to be validated at another time. The size and composition of final demand and technology are continually changing, not completely exogenously.

A simple labor theory of value asserts that prices of production are (proportional to) labor values. Marx explicitly rejects that theory:

"If prices actually differ from values, we must, first of all, reduce the former to the latter, in other words, treat the difference as accidental in order that the phenomena may be observed in their purity, and our observations not interfered with by disturbing circumstances that have nothing to do with the process in question. We know, moreover, that this reduction is no mere scientific process. The continual oscillations in prices, their rising and falling, compensate each other, and reduce themselves to an average price, which is their hidden regulator. It forms the guiding star of the merchant or the manufacturer in every undertaking that requires time. He knows that when a long period of time is taken, commodities are sold neither over nor under, but at their average price. If therefore he thought about the matter at all, he would formulate the problem of the formation of capital as follows: How can we account for the origin of capital on the supposition 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 commodities, as Adam Smith, Ricardo, and others believe." (Marx 2010, last footnote in chapter 5)

And again:

"The calculations given in the text are intended merely as illustrations. We have in fact assumed that price = values. We shall, however, see, in Book III, that even in the case of average prices the assumption cannot be made in this very simple manner." (Marx 2010, last footnote in chapter 9, section 1)

Marx adopts a simple labor theory of value in the first volume of Capital for illustration and for methodological reasons in explaining the origin of returns to capital. But he knows the theory is false.

The relationship between labor values and prices is particularly transparent in the production of the standard commodity, assuming single production. Accordingly, assume that the net output of the economy is the standard commodity and that the standard commodity is the numeraire in which wages are denominated. Then the value of the means of production, C, is the same, whether calculated in labor values or prices of production. Likewise, net output, V + S, is the same, whether calculated in labor values or prices of production. These aggregate quantities are independent of how net output is divided among payments to workers, V, and returns to capital, S. The rate of profits in the system of prices of production is the same as the rate of profits in the system of labor values:

r = S/(C + V) = (S/V)/((C/V) + 1) = e/(1 + occ)

where e is the rate of exploitation, also known as the rate of surplus value, and occ is the organic composition of capital. I believe these invariants solve the notorious so-called transformation problem. They match Marx's assertions in volume 3 of Capital.

Marx, of course, does not write about Leontief matrices and their eigenvalues and eigenvectors. The analysis of both Leontief and Marx, however, views production as a circular process in which commodities are produced, with labor, by means of commodities. Furthermore, Marx does write about a commodity of average organic composition. And Sraffa’s standard commodity is exactly that commodity.

Sraffa's theory of prices of production is an open model, with a degree of freedom for the functional distribution of income. If the wage or the rate of profits is taken as given, the model is closed. Other closures are possible. Formally, one could assume households are intertemporal utility maximizers (Marglin 1984). In this sense, Marx's theory of value is consistent with marginalist economics. This closure could provide multiple equilibria. Given final demand and technology, the quantities of capital goods used as inputs are solved by the model. They are not data, and the marginalist revolution was, at best, mistaken on a fundamental level. Political economy is not an analysis of the allocation of scarce resources among alternative uses. Rather, it includes an analysis of the conditions needed for the material reproduction of capitalist societies.

References

• Bukharin, Nikolai. 1972. Economic Theory of the Leisure Class. New York: Monthly Review Press.
• Leontief, Wassily W. 1936. Quantitative Input and Output Relations in the Economic Systems of the United States. Review of Economic Statistics 18 (3): 195-125.
• Marglin, Stephen A. 1984. Growth, Distribution, and Prices. Cambridge: Harvard University Press.
• Marx, Karl. 2010. Capital: A Critique of Political Economy, Volume 1. Marx-Engels Collected Works V. 35. Lawrence & Wishart.
• Sraffa, Piero. 1960. Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory. Cambridge: Cambridge University Press.
• von Neumann, John. 1945-1946. A model of general economic equilibrium. Review of Economic Studies 13 (1): 1-9.