2 The theory explained

Marxian political economy uses the concept of " socially necessary abstract labor-time" to modify the Ricardian LTV. To some, this modification is profound enough to support the claim that Marx's theory is not, after all, a labor theory of price of the Ricardian sort, but a new type of value theory.

Marx goes to some lengths in the first chapter of Capital to spell out the significance of three aspects of value - its substance, magnitude, and most unusual of all, its form. His theory would therefore seem resistant, at least, to reduction to just one such aspect, the magnitude. The substance of value is labor. The magnitude of value is the number of labor hours. The form of value is, roughly, that institutional framework within which a society's production decisions can be directed through the free exchange of commodities. This aspect of value as a social process, unexamined by Marx's predecessors in classical political economy, cannot be reduced to magnitudes.

The phrase "socially necessary", far from being an arbitary adjunct to the theory (as charged by Robert Nozick), expresses that societal perspective, radically distinct from neoclassical economics. Whereas the latter starts with the individual's perspective and exchange, Marx starts with the perspective of society as a whole. "Social production" involves a complicated and interconnected division of labor of a wide variety of people who depend on each other for their survival and prosperity. Individual labors are contributions to the whole. "Abstract" labor refers to a characteristic of commodity-producing labor that is shared by all different kinds of heterogenous (concrete) types of labor. That is, the concept abstracts from the particular characteristics of all of the labor and is akin to average labor. Socially necessary abstract labor is measured in hours of application of labor-power but can only be realized in exchange: only labor which produces a commodity that is a use-value to someone else (which they can afford and are willing to buy) counts as socially necessary.

2.1 Some definitions

Marx's LTV holds that the labor needed to produce a commodity includes both labor directly expended on production of the commodity and labor expended on the production of means of production used up in its production. For example, if twenty workers are used for a year to produce means of production used by twenty workers in the next year to produce a consumer good , the good embodies the labor of forty workers. (This example assumes that technology is unchanged between the two years.)

The amount of labor done by an average worker under the prevailing conditions in a society (for instance the technology and transportation in use) will produce the same amount of value regardless of the manner of that labor. Greater value can be produced by trained workers or by workers using leading-edge technologies: the increase in value is created by the training process or the work required to create the technologies.

However, a lazy or inept worker (who spends more time producing an item) does not produce more value than an industrious one. Rather, the first worker's time produces less because the value depends on what is socially necessary. That is, the value of a product is determined more by societal standards than by individual conditions.

2.2 Exploitation

Marx used his LTV to derive his theory of exploitation under capitalism. He assumed that all commmodities sell at prices equal to values (with both measured in the same units). In his era, this "equal exchange" represented a standard of fair exchange: an hour of labor could be used to purchase the product of an hour of labor.

In effect, he asked, "under equal exchange, how is it that a capitalist can sell commodity X at price P and make a profit?" If a boss hires labor at value and then sells the commodity at value, where does profit come from?

Unlike Ricardo or the Ricardian socialists, Marx distinguished between labor-power and labor. "Labor-power" is the ability of workers to work, given their muscles and brains. "Labor" is the actual activity of producing use values (goods and services) and value. In his examples, Marx assumed that the value of labor-power (v) was constant, determined by prevailing socioeconomic conditions. (In his time, this was seen as "subsistence.") The profit or surplus-value can arise if workers do more labor (L) than is necessary to pay the cost of hiring their labor-power.

Marx's numerical examples in volume I of Das Kapital never "prove" that capitalism always involves exploitation, i.e., that L always exceeds v. Instead, this relationship involves class struggle over the length of the working day, the intensity of labor, the use of machinery, etc. The existence of exploitation reflects the capitalists' victory (so far) in the struggle.

Instead, the "proof" that capitalism typically involves exploitation comes from his institutional and historical analysis of capitalism as a whole. One way to get L > v is to use force against the workers. But unlike other systems (such as feudalism or slavery), under capitalism the direct use of force to get workers to produce a surplus is the exception rather than the rule. To Marx, under capitalism workers are free to quit their jobs, while they are rarely beaten.

To explain the normality of L > v, Marx instead pointed to capitalism's institutional framework, in which a small minority (the capitalists) monopolize the means of production, in which the workers cannnot survive except by working for capitalists, and in which the state preserves this inequality of power. In this explanation, the normal role of force is structural, part of the usual workings of the system: the reserve army of unemployed workers continually threatens employed workers, pushing them to work hard to produce for the capitalists.

2.3 Böhm-Bawerk's critique

The Austrian economist, Eugen von Böhm-Bawerk argued against both the Ricardian labor theory of price and Marx's theory of exploitation. On the former, he contended that return on capital arises from the roundabout nature of production. A steel ladder, for example, will be produced and brought to market only if the demand supports the digging of iron ore, the smelting of steel, the machines that press that steel into ladder shape, the machines that make and help maintain those machines, etc. Advocates of the labor theory will point out that every step in that process, however roundabout, involves labor. But Böhm-Bawerk said that what they missed was the process itself, the roundaboutness, which necessarily involves the passage of time.

Roundabout processes, Böhm-Bawerk maintained, lead to a price that pays for more than labor value, even the labor value of all the process involved added together statically, and given any empirical standard for the latter. This makes it unnecessary to postulate exploitation in order to understand the return on capital.

Marx might respond that this did not contradict his understanding of prices, in which sectors of the economy which have higher " capital intensity" (greater roundaboutness) have higher prices (see below). The difference, it seems, between Marx and Böhm-Bawerk concerns perspective: for Böhm-Bawerk, roundaboutness explains entrepreneurial profits on the microeconomic level, whereas for Marx, a society-wide institutional explanation is needed. To him, roundaboutness explains only those profits of the more capital-intensive operations relative to less capital-intensive ones.

Furthermore, in Böhm-Bawerk's development of a positive theory of interest he said that workers trade in their share of the end price for the more certain and soon wages paid by the entrepreneur. In other words, he claimed that profits compensated the entrepreneur for the willingness to bear risk and to wait to receive income.

Critics of Böhm-Bawerk's theory argue that workers are often exposed to risks such as injury on the job, a more profound kind of risk than the merely financial risk that the entrepreneur takes. A capitalist entrepreneur also has a greater ability to diversify (to minimize risk) than does the laborer because the latter has only one main asset, i.e., labor-power. Further, when the entrepreneurs' risk-taking does not pay off, this cost can be shifted to workers as wage cuts and/or layoffs. The existence of the " reserve army of the unemployed" means that even if they are aware of these risks, they often have little choice but to take them. In the Marxian view, this argument means that entrepreneurs have no right to compensation for bearing entrepreneurial risk.

Böhm-Bawerk and other Austrian economists replied to such critics by claiming that they played upon the ambiguities of the term "risk," that specifically financial risk must be isolated in order to understand the production process. Furthermore, the fact that capital markets lead to the control and minimization of financial risk is a valuable development in itself -- an argument for, not against, the overall social efficacy of capitalism.

Some critics take another tack, observing that not all risk-taking seems worth rewarding: for example, the invention and promotion of "crack" cocaine or e-mail spam were clearly a matter of risk-taking entrepreneurship, yet both seem to have more social costs than benefits. This is the problem of external costs, a form of market failure which (if serious enough) encourages people to seek non-market solutions.

3 The transformation problem

The most common interpretation of the LTV is as a theory of price determination, which makes Marx's theory roughly correspond to that of Ricardo. In this view, a commodity's price derives neither from its utility to the consumer (Marx's " use value") nor from supply and demand but from the labor that society has expended on its production. Early in volume III of Capital, Marx presents an analysis of the relationship between values and prices. Most read this as describing how prices can be calculated from given values.

The problems with Marx's "solution" to this mathematical problem have spawned a long debate concerning the " transformation problem." This problem of finding (or rejecting) mathematical formulae linking individual prices to individual values is central to the dominant interpretation of the Marxian LTV.

Even as "a simple theory of price" in which prices are directly determined by values, Marx's LTV does not deny the role of demand. Not only must each commodity have a use-value to its buyer, but demand and short-term supply determine its "market price" (p). Following the classical-school perspective, Marx saw each p as tending toward the "price of production" (Smith's "natural price") due to market forces. Prices of production (p*) are long-term average prices, seen as totally determined by costs. It was thus only in the long run that Marx denied the role of demand in determining relative prices (under competitive markets, with no land-rent).

A simple example shows that on the micro level, the p* cannot be proportional to values, even when pure competition prevails. Even before Marx presented his numerical examples exploring price/value relationships, David Ricardo had presented a numerical example of this fact.

1. Again measure values and prices in the same units, labor hours. Thus, the value/price contrast corresponds to Smith's distinction between labor-embodied values and labor-commanded values and Marx's distinction between "values" and " exchange values."

2. Assume that each p initially equals value so that for any given commodity, total profits are proportional to unpaid labor-time (surplus-value, S), total wages are proportional to paid labor-time (W), and the total amount of money invested by the capitalist is proportional to the value of the capital invested (K). This is the "simple labor theory of price" referred to above.

3. Suppose the ratio of unpaid labor-time to paid labor-time is the same for all commodities. This assumption reflects the tendency (when workers are not slaves or serfs and labor-power markets are competitive) for workers to move away from sectors with more exploitation, toward those with less. Thus, the rate of exploitation tends toward equality between sectors. This ratio is measured here by s = S/W (unpaid labor-time/paid labor-time).

4. But there is no reason why technical conditions of production will be the same for all commodities. Different proportions of labor and means of production are used in distinct production processes and for different commodities. To Marx, the " organic composition of capital" or OCC differs between sectors. For any commodity, measure this as k = K/W, the ratio of the total amount invested in "capital" to the total amount spent on paid labor. K includes raw materials and fixed capital purchased before a production process starts. An industry with high OCC is capital-intensive, i.e., is relatively roundabout.

5. If products were traded according to labor-values, different rates of profit will be received on the capital invested in different industries. The rate of profit, r, equals the total amount of profit divided by the capital advanced, or S/K. This implies that the profit rate equals

r = (S/W)/(K/W) = s/k

If s is the same for all commodities, while k varies, r differs between commodities.

6. This situation makes no sense in the real world of capitalism, even as conceived by Marx, in which firms and sectors are competing with each other, with capitalists seeking profits everywhere. Competition among industries should remove differences in profit rates. When able to do so, capitalists earning low r move their capital out of their industries, reducing supply and raising p there. They enter high-r sectors, raising supply and reducing p there.

7. Thus, market prices tend toward being equal to the p* which are proportional to long-term average costs and r is equalized between sectors. Since, according to the equation above, it is high k – or a high degree of roundaboutness – that depresses the rate of profit, the mobility of capital raises p in the high-k sectors, assuring capitalists a r equal to that of low k sectors. To Marx, this represents a redistribution of value and surplus-value between sectors.

This means that the commodities produced in high-k sectors command more labor than it took to produce them. This is Marx's take on the issue of capital intensity that Böhm-Bawerk stressed (see above ).

This in turn implies that the p cannot equal values. In the long run, they equal p*, but these latter differ from values — because they reflect profit-rate equalization. That is, the simple labor theory of price cannot be true while "equal exchange" is not the norm.

The above consequence of varying capital intensity has been central to critiques of Marx's LTV. Some see this as its reductio ad absurdum. However, Ricardo himself employed a "93 percent labor theory of value," believing that most of the time labor-values were a good guide for guessing relative prices and (after correcting for inflation) the progress of prices over time.

In general, the above shows that the simple "labor theory of price" cannot work exactly (100 percent) unless

• the organic composition of capital (k) is the same in each industry;
• there is no capital invested (k = 0, as in Smith's "early and rude state of society");
• the rate of surplus-value (s) equals zero (as in Marx's hypothetical " simple commodity production");
• differences in the rate of surplus-value between sectors are perfectly correlated with those of the organic composition; or
• there is no tendency for the rate of profit to equalize between sectors, so there is no tendency for prices to move away from proportionality to values (again as in Marx's simple commodity production).

Even if one or more of the conditions above applies, price/value deviations will arise if monopolies exist or if land has been appropriated as private property, so that land-rent income is received (beyond "normal" profits). In either of these cases, demand plays a role in determining long-term prices.

More complex labor theories of price (more complex mathematical relationships between values and prices of production) have been proposed — but then most, if not all, of them have been criticized severely and rejected. In 1969, Amit Bhaduri pointed out that the "transformation" problem of finding a mathematical relationship between individual prices and individual values has intractable difficulties that are mathematically identical to those seen in the famous "Cambridge" critique of Robert Solow's aggregate production function. Whereas the problem with Solow's model is aggregation from micro- to macroeconomics, one interpretation is that the problem with Marx's theory is disaggregation: in Capital, Marx starts from the whole of capitalism (values) and moves to the parts (prices). In neither case can one level of analysis be explained by the other by a mathematical relationship except under unrealistic assumptions. Instead, Marx might say that there is a dialectical connection between the two levels (whole and parts).

4 An alternative interpretation

Although the above interpretation dominates most discussions, there are other views. In fact, one accepts the transformation problem's demonstration that individual prices deviate from individual values as its starting point. In this alternative view, Marx rejected modern economists' concern with price theory (without denying a role for supply and demand) and in some ways returned to Locke's questions about the nature and origin of property rights and the orgins of unequal ownership of property under capitalism. That is, in this view, Marx was not interested in developing a labor theory of price.

Marx argued that price phenomena (markets, competition, supply and demand) create illusions that obscure the underlying social relations of a capitalist society. He called this distortion of appearances " commodity fetishism". If there were some easy-to-understand mathematical relationship between prices and values, then property income would clearly correspond to unpaid labor and the class nature of capitalism would be obvious to almost everyone. To Marx, such clarity would undermine capitalism's legitimacy. Commodity fetishism thus helps maintain social stability.

To Marx, social relations are best understood in terms of value: who works and who doesn't? And how do incomes received correspond to labor done? These questions can apply just as easily to non-capitalist societies as to capitalist ones: in volume III, ch. 47, of Capital, Marx suggests that the

"specific economic form in which unpaid surplus-labor is pumped out of direct producers" is the basis for the "entire formation of the economic community," revealing "the innermost secret, the hidden basis of the entire social structure ... the political form of the relation of sovereignty and dependence ... [and] the specific form of the state."

These questions form a transhistorical theory of different types of society (e.g., capitalism, feudalism, slavery, and the old U.S.S.R.). However, it is only in a commodity-producing society that these questions are stated in terms of values.

In this view, the LTV, as used in Capital, is a method for understanding the nature of social relationships for capitalism as a whole: the examples of workers producing value that Marx presents in volume I are microcosms representing the totality of society instead of being microeconomic analyses. They present the shared characteristics of a large number of different relationships between capitalists and workers.

In this view, the contrast between labor-values and prices is just as important as their unity or connection. Values correspond to the abstract labor-time socially necessary to produce commodities (the contributions by workers to commodity-producing society), while prices are set by supply, demand, and market institutions.

However, on the macro level, there is a clear relationship between price and value. All commodities are produced by labor (using means of production and technology); the commodity-producing segment of society is nothing but a community of producers working for each other through a complex division of labor mediated by markets. Thus, the total value of the product (the total amount of labor done) corresponds to the total price of the product (such as that measured by Gross Domestic Product). That is, labor embodied equals labor commanded (production equals demand) on the macro level.

In addition, the total surplus-value that workers produce limits total property income (profits, interest, and rent) that all of the individual capitalists together can receive. That is, to Marx, all property income — income received due to property ownership rather than from one's labor — is the result of exploitation.

Thus, there is redistribution of property income within the capitalist class: given the state of class relations and thus the amount of surplus-value produced, a capitalist who receives a high profit rate will be benefiting partly at the expense of capitalists who receive low profit rates. In this interpretation, markets and prices redistribute surplus-value between capitalists so some can command more labor than is embodied in the commodities they have had produced. Others can command less labor than is embodied in their commodities. But in the end, the total amount embodied is equal to the total amount commanded.

The contrast between the "macro" level of values and the "micro" level of prices corresponds to the contradiction that Friedrich Engels posited under capitalism, between the socialized production of wealth and the individual appropriation of it. Although society as a whole organizes production and exploitation, individuals are able to claim and use the individual results of this process. Engels saw this contradiction as resulting in class conflict and crises.

Even accepting this alternative understanding of Marx's LTV, a serious criticism remains: now that Marx has explained the nature of capitalist exploitation, why do we need the LTV? Why can't we explain exploitation in other terms, as say John Roemer does in his 1982 General Theory of Exploitation and Class (BooksEnthsiast.com)? Others argue that Roemer's neoclassical general equilibrium approach hides more than it reveals and is based on dubious assumptions. The debate continues.

5 External links and references

• The Marxists Internet Archive
• Capital, Volume One
• Marx's discussion of the form of value in Capital
• I.I.Rubin's accessible commentary on Marx's form and content of value
• Wage Labour and Capital
• Robert Vienneau's LTV FAQ
• Jim Devine's alternative view of Marx's LTV
• A critical explanation of LTV by Eugen von Böhm-Bawerk

• Bhaduri, Amit. 1969. "On the Significance of Recent Controversies on Capital Theory: A Marxian View." Economic Journal. 79(315) September: 532-9.

Economics Marxist theory

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