Introduction

Michael Huemer has put up a Web page providing an overview of the (exploded) neoclassical theory of value. In asides, he asserts that Marx's critique of capitalism depended on the Labor Theory of Value, and he attempts to demonstrate that the LTV is mistaken. This page demonstrates that Huemer's history of economics is arguably mistaken in crucial propositions and that the grounds Huemer gives for rejecting the LTV are difficult to sustain. I do not here enter into why the neoclassical theory of value is mistaken; on those portions of Huemer's comments on Marx with which I agree; or on Huemer's confusion of the returns to capitalists, which tend towards a proportion with the capital value of investments, with a kind of wage for upper management.

Mistaken History of Economics

General Acceptance of Labor Theory of Value

Huemer asserts that "Marx embraced the Labor Theory of Value (LTV)". The claim that Marx accepted the LTV as a theory of price is problematic. In the first volume of Capital, Marx explicitly stated that relative prices do not bob up and down around labor values:
The continued 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 [labor] value of the commodities. I say 'ultimately,' because average prices do not directly coincide with the [labor] values of commodities, as Adam Smith, Ricardo, and others believe. (Marx, Capital, Volume 1, Chapter V)
Marx is unfair to Smith and Ricardo here. Marx treats Smith and Ricardo more fairly in Theories of Surplus Value. For example, Marx there recognizes that Ricardo understood that average prices cannot be expected to be proportional to labor values (Marx, Theories of Surplus Value, Part II, Chapter X, Section A.4.a).

This brings me to my second point of criticism of Huemer. His claim, that the LTV "was accepted at the time Marx was writing" is difficult to sustain. The LTV is arguably not central to Classical economics. For example, neither Adam Smith, Ricardo, nor John Stuart Mill accepted the LTV as applicable unmodified to capitalist societies.

Smith confined the LTV to an eigthteenth century fable of a primitive society:

In that early and rude state of society which precedes both the accumulation of stock and the appropriation of land, the proportion between the quantities of labour necessary for acquiring different objects seems to be the only circumstance which can afford any rule for exchanging them for one another. (A. Smith, Wealth of Nations, Book I, Chapter VI.)
(Smith does use a "labor commanded" measure in analyzing capitalist economies, for example, in Wealth of Nations, Book I, Chapter V. I think that Smith uses "labor commanded" for measuring welfare, not as a theory of value.)

David Ricardo put forth, in his Principles of Political Economy, the central objection to the LTV:

Suppose I employ twenty men at an expense of 1000 pounds for a year in the production of a commodity, and at the end of the year I employ twenty men again for another year, at a further expense of 1000 pounds in finishing or perfecting the same commodity, and that I bring it to market at the end of two years, if profits be 10 per cent., my commodity must sell for 2,310 pounds.; for I have employed 1000 pounds capital for one year, and 2,100 pounds capital for one year more. Another man employs precisely the same quantity of labour, but he employs it all in the first year; he employs forty men at an expense of 2000 pounds, and at the end of the first year he sells it with 10 per cent. profit, or for 2,200 pounds. Here then are two commodities having precisely the same quantity of labour bestowed on them, one of which sells for 2,310 pounds - the other for 2,200 pounds. (Ricardo Principles, Chapter I, Section IV)
In other words, Ricardo noted that as long as the proportion of the expenses of production required for wages varies among industries, the LTV cannot be totally true. It is true that Ricardo emphasized the variation of relative prices with wages (in the chapter from which I selected the above quote), instead of this simple divergence between prices and labor values. Furthermore, one can argue about how much Ricardo's epigones understood this point.

But the most prominent mainstream nineteenth century follower of Ricardo did. I refer to John Stuart Mill:

From the unequal proportion in which, in different employments, profits enter into the advances of the capitalist, and therefore into the returns required by him, two consequences follow in regard to value. One is, that commodities do not exchange in the ratio simply of the quantities of labour required to produce them; not even if we allow for the unequal rates at which different kinds of labour are permanently renumerated...

A second consequence is, that every rise or fall of general profits will have an effect on values. Not indeed by raising or lowering them generally, (which, as we have so often said, is a contradiction and an impossibility): but by altering the proportion in which the values of things are affected by the unequal lengths of time for which profit is due...

It follows from this, that even a general rise of wages, when it involves a real increase in the cost of labour, does in some degree influence values. It does not affect them in the manner vulgarly supposed, by raising them universally. But an increase in the cost of labour lowers profits; and therefore lowers in natural value the things into which profits enter in a greater proportion than the average, and raises those into which they enter in a less proportion than the average. (J. S. Mill, Principles, Book III, Chapter IV, Section 5.)

Dependence of Marx's Critique of Capitalism On LTV

Huemer asserts:
the LTV ... is crucial to [Marx's] critique of capitalism. Central to that critique is his claim that, in a capitalist system, the workers are 'exploited' by the capitalists (businessmen). If one accepts the LTV, then Marx's argument for the theory of exploitation is persuasive. But if one rejects the LTV, then the argument collapses. (Huemer)
Since Marx rejected the LTV as an accurate theory of price, Huemer's claims are arguably mistaken. Marx did indeed use the LTV at the high level of abstraction of the first volume of Capital. And this use was for demonstrating that the returns to capital have their source in the exploitation of workers. It is not clear that this demonstration is the basis for Marx's attack on capitalism:
Marx, therefore, never based his communist demands upon [the exploitation of workers], but upon the inevitable collapse of the capitalist mode of production which is daily taking place before our eyes to an ever greater degree; he says only that surplus value consists of unpaid labour, which is a simple fact. (Engels, Poverty of Philosophy, First German edition, Preface.)

Even so, it is not clear that the account of the source of profits in value added by workers not paid out in wages depends on the LTV. For example, we have seen that Adam Smith rejected the LTV as a theory of price for capitalist economies. Nevertheless, he put forth a similar theory of surplus value:

As soon as stock has accumulated in the hands of particular persons, some of them will naturally employ it in setting to work industrious people, whom they will supply with materials and subsistence, in order to make a profit by the sale of their work, or by what their labour adds to the value of the materials.. The value which the workmen add to the materials, therefore, resolves itself in this case into two parts, of which one pays their wages, the other the profits of their employer upon the whole stock of materials and wages which he advanced. (Smith, Wealth of Nations, Book I, Chapter VI.)
This understanding of Smith was a commonplace among the so-called Ricardian Socialists predating Marx.

Furthermore, it is a mathematical theorem that the rate of profits is positive in certain contemporary models of prices of production if and only if workers are exploited. The meaning of "exploitation" in the so-called Fundamental Theorem of Marxism (Michio Morishima, Marx's Economics: A Dual Theory of Value and Growth, Cambridge University Press, 1973) seems to be formally defined in a manner consistent with Marx's approach.

Wages At Level Of Physical Subsistence

Huemer writes that the "wages of the workers will naturally fall to the bare subsistence level (the minimum needed for the workers to live)." This is a fallacious description of the Classical and Marxian account of "natural" wages or the value of labor-power. The classical theory of value depends on the value of labor-power as being given or determined in another part of the theory (for example, Malthus' theory of population or Marx's account of the "General Law of Capitalist Accumulation"). As a matter of fact, the Classical economists did not describe the "natural" wage as a minimum for bare subsistence. They thought the "natural" wage included a conventional or moral element:
By necessaries I understand, not only the commodities that are indispensably necessary for the support of life, but whatever the custom of the country renders it indecent for creditable people, even of the lowest order, to be without. A linen shirt, for example, is, strictly speaking, not a necessary of life. The Greeks and Romans lived, I suppose, very comfortably, though they had no linen. But in the present times, through the greater part of Europe, a creditable day-labourer would be ashamed to appear in public without a linen shirt, the want of which would be supposed to denote that disgraceful degree of poverty, which, it is presumed, no body can well fall into without extreme bad conduct. (Adam Smith, Wealth of Nations, Book V, Chapter II, Article 4.)
It is not to be understood that the natural price of labour, estimated even in food and necessaries, is absolutely fixed and constant. It varies at different times in the same country, and very materially differs in different countries. It essentially depends on the habits and customs of the people. An English labourer would consider his wages under their natural rate, and too scanty to support a family, if they enabled him to purchase no other food than potatoes, and to live in no better habitation than a mud cabin; yet these moderate demands of nature are often deemed sufficient in countries where 'man's life is cheap' and his wants are easily satisfied. Many of the conveniences now enjoyed in an English cottage, would have been thought luxuries at an earlier period of our history. (Ricardo, Principles, Chapter V.)
But the permanent renumeration of the labourers essentially depends on what we have called their habitual standard; the extent of the requirements which, as a class, they insist on satisfying before they choose to have children. If their tastes and requirements receive a durable impress from the sudden improvement in their condition, the benefits to the class will be permanent. (J. S. Mill, Principles, Book IV, Chapter III, Section 4.)
Marx included this moral element in his understanding of the value of labor-power.
Therefore, the foundation of modern political economy, whose business is the analysis of capitalist production, is the conception of the value of labour-power as something fixed, as a given magnitude - as indeed it is in practice in each particular case. The minimum of wages therefore correctly forms the pivotal point of Physiocratic theory. They were able to establish this although they had not yet recognized the nature of valuee itself, because this value of labour-power is manifested in the price of the necessary means of subsistence, hence in a sum of definite use-values. Consequently, without being in any way clear as to the nature of value, they could conceive the value of labour-power, so far as it was necessary to their inquiry, as a definite magnitude. If moreover they made the mistake of conceiving this minimum as an unchangeable magnitude - which in their view is determined entirely by nature and not by the stage of historical development, which is itself a magnitude subject to fluctuations - that in no way affects the abstract correctness of their conclusions, since the difference between the value of labour-power and the value it creates does not at all depend on whether the value is assumed to be great or small. (Marx, Theories of Surplus Value, Part I, Chapter II, Section 1.)

Huemer's Three Objections

Given these flaws and misconceptions in Huemer's understanding of Marx's economics, it is hardly surprising that his objections to the LTV are not well-taken.

Some Jobs Are More Desirable Than Others

First, the argument for LTV assumes that the cost, or disutility, of production Is determined solely by the quantity of labor. But what if chocolate workers just enjoy 6 hours of making chocolate more than they enjoy 6 hours of making a shirt? ...However, this problem can be fixed by simply replacing 'quantity of labor' in the theory with 'disutility of labor' (the decrease in utility that one experiences as a result of having to work). (Huemer)
The bit about the "disutility of labor" is Huemer imposing his own paradigm on the quite different texts of the Classical economists and of Marx. Those economists did not use a quantitative notion of utility, even if only attaining an ordinal measurement scale, thereby reducing every commodity, including labor, to a single measure of utility.

However, it has been long been recognized that Classical value theory took account of heterogeneous labor. For example, here are some of Edwin Cannan's comments in the margin in his edition of Smith's Wealth of Nations:

Advantages and disadvantages tend to equality where there is perfect liberty. Actual differences of pecuniary wages and profits are due partly to counterbalancing circumstances and partly to want of perfect liberty. There are five counterbalancing circumstances: (1) Wages vary with the agreeableness of the employment. Some very agreeable employments are exceedingly ill paid. The same thing is true of profits. (2) Wages vary with the cost of learning the business. The cost of apprenticeship accounts for the wages of manufacturers being higher than those of country laborers. Education for liberal professions is more costly and the pecuniary recompense consequently higher. Profits are not much affected by this circumstance. (3) Wages vary with constancy of employment. Constancy does not affect profits. (4) Wages vary with the trust to be reposed. Profits are unaffected by trust. (5) Wages vary with the probability of success. Law and similar professions are nevertheless crowded. Public admiration makes a part of the reward of superior abilities, except in the peculiar case of players, opera singers, &c. The greater part of men have an overweening conceit of their own abilities: lotteries show that the chance of gain is overvalued, and the moderate profit of insurers shows that the chance of loss is undervalued. Young people are particularly prone to overvalue the chance of gain and undervalue the risk of loss. For this reason soldiers are poorly paid, and sailors not much better. Dangers which can be surmounted attract, though mere unwholesomeness repels. Profits vary with certainty of return. Profits are less unequal than wages, and their inequality is often only due to the inclusion of wages, as in the case of an apothecary, or country grocer. The greater difference between retail and wholesale profits in town than country is due to the same cause. The lesser rate of profits in towns yields larger fortunes, but these mostly arise from speculation.

The five circumstances thus countervalance differance of pecuniary gains, but three things are necessary as well as perfect freedom: (1) the employments must be well known and long established, since new trades yield higher wages, and higher profits: (2) the employments must be in their natural state, since the demand for labour in each employment varies from time to time and profits fluctuate with the price of the commodity produced: and (3) the employments must be the principal employment of those who occupy them, since people maintained by one employment will work cheap at another, like the Scotch cotters, Shetland knitters, Scotch linen spinners, and London lodging house keepers. (Cannan's marginal summary of the first part of Smith's Wealth of Nations, Book I, Chapter X.)

Chapter X, although the most detailed, is not the only place that Smith took heterogeneous labor into account:
But though labour be the real measure of the exchangeable value of all commodities, it is not that by which their value is commonly estimated. It is often difficult to ascertain the proportion between two different quantities of labour. The time spent in two different sorts of work will not alone determine this proportion. The different degrees of hardship endured, and of ingenuity exercised, must likewise be taken into account. There may be more labour in an hour's hard work, than in two hours easy business; or, an hour's application to a trade which it costs ten years' labour to learn, than in a month's industry at an ordinary and obvious employment. But it is not easy to find any accurate measure, either of hardship or ingenuity. In exchanging, indeed, the different productions of different sorts of labour for one another, some allowance is commonly made for both. It is adjusted, however, not by any accurate measure, but by the higgling and bargaining of the market, according to that sort of rough equality, which though not exact, is sufficient for carrying on the business of common life. (Smith, Wealth of Nations, Book I, Chapter V)
Ricardo looked back to Smith's account:
In speaking, however, of labour, as being the foundation of all value, and the relative quantity of labour as almost exclusively determining the relative value of commodities, I must not be supposed to be inattentive to the different qualities of labour, and the difficulty of comparing an hour's or a day's labour, in one employment, with the same duration of labour in another. The estimation in which different qualities of labour are held, comes soon to be adjusted in the market with sufficient precision for all practical purposes, and depends much on the comparative skill of the labourer, and intensity of the labour performed. The scale, when once formed, is liable to little variation. If a day's labour of a working jeweller be more valuable than a day's labour of a common labourer, it has long ago been adjusted, and placed in its proper position in the scale of value. (Ricardo Principles, Chapter I, Section IV)
Notice Ricardo's claim that relative wages tend to be stable. Marx, typically, expressed the same theory in a manner influenced by Hegel's turns of phrase:
Just as, therefore, in viewing the coat and linen as values, we abstract from their different use-values, so it is with the labour represented by these values: we disregard the difference between its useful forms, weaving and tailoring. As the use-values, coat and linen, are combinations of special productive activities with cloth and yarn, while the the values, coat and linen, are, on the other hand, mere homogeneous congelations of undifferentiated labour, so the labour embodied in the latter values does not count by virtue of its productive relation to cloth and yarn, but only as being expenditure of human labor-power. Tailoring and weaving are necessary factors in the creation of the use-values, coat and linen, precisely because these two kinds of labor are of different qualities; but only in so far as abstraction is made from their special qualities, only in so far as both possess the same quality of being human labor, do tailoring and weaving form the substance of the values of the same articles. (Marx Capital, Volume 1, Chapter I, Section 2).
I find the following from Marx more clear in some ways:
Does labour time, as the measure of value, suppose at least that the days are equivalent, and that one man's day is worth as much as another's? No.

Let us suppose for a moment that a jeweller's day is equivalent to three days of a weaver; the fact remains that any change in the value of jewels relative to that of woven materials, unless it be the transitory result of the fluctuation of demand and supply, must have as its cause a reduction or an increase in the labour time expended in the production of one or the other. If three working days of different workers be related to one another in the ratio 1:2:3, then a change in the relative value of their products will be a change in the same proportion of 1:2:3. Thus values can be measured by labour time, in spite of the inequality of value of different working days; but to apply such a measure we must have a comparative scale of the different working days: it is competition that sets up this scale.

Is your hour's labour worth mine? That is a question which is decided by competition. (Marx, Poverty of Philosophy)

A modern classical economist can be more terse:
We suppose labour to be uniform in quality or, what amounts to the same thing, we suppose any difference in quality to have been previously reduced to equivalent differences in quantity so that each unit of labour receives the same wage. Sraffa, PoCbMoC, Section 10.
So Huemer's first objection, which he does not regard as unfixable, depends on failing to accurately describing the texts in which Classical economists and Marx examined the LTV. Labor values are defined only after qualitative differences in tasks have been reduced to quantitative differences in labor inputs.

Cost of Production Varies With Quantity

The second problem is more serious. The argument for LTV treats cost of production as if it were a constant (e.g., "6 hours' labor"). ...The cost of producing something is a function of the quantity produced. ...We have to ask which cost of production is going to determine the price of a good, and the LTV doesn't tell us this.
This objection, too, has already been addressed in the texts of the Classical economists and of Marx. Labor values are defined for production at the level of effectual demand:
The market price of every particular commodity is regulated by the proportion between the quantity which is actually brought to market, and the demand of those who are willing to pay the natural price of the commodity, or the whole value of the rent, labour, and profit, which must be paid in order to bring it thither. Such people may be called the effectual demanders, and their demand the effectual demand; since it may be sufficient to effectuate the bringing of the commodity to market. It is different from the absolute demand. A very poor man may be said in some sense to have a demand for a coach and six; he might like to have it; but his demand is not an effectual demand, as the commodity can never be brought to market in order to satisfy it. (Smith, Wealth of Nations, Book I, Chapter VII.)
Notice that the effectual demand for a commodity is a quantity, not a schedule relating quantities and prices.

I like to think of the structure of the Classical theory of value as follows. Gross quantities are taken as given, as determined in a theory of growth and accumulation upstream, so to speak, from the theory of value. Given real wages (including stable ratios of wages among different types of jobs), technology, and those quantities, relative prices follow. How market prices fluctuate around prices determined by the theory of value is determined by another part of Classical theory, downstream, so to speak, from the theory of value. Marxists refer to this question as the "realization problem".

No Role For Demand In LTV

A third problem is that LTV assigns no role to the demand for a good (how much people want it). But it is obvious intuitively that this must have something to do with the price for which a good will sell.
What is "obvious" need not be true. Given the real wage and the assumptions of the so-called non-substitution theorem, consumer tastes have no influence on equilibrium prices. Even when the assumptions of the theorem are violated, equilibrium prices do not behave in accordance with neoclassical intuitions on substitution, a point made a quarter century ago by Luigi Pasinetti.

I have already shown that, although the Labor Theory of Value has a different structure than neoclassical theory, demand does play a role in that theory. There is another aspect of the role of demand in that theory; Marx states that commodities have use values:

Every useful thing...is an assemblage of many properties, and may therefore be of use in various ways...The utility of a thing makes it a use-value...When treating of use-value, we always assume to be dealing with definite quantities, such as dozens of watches, yards of linen, or tons of iron. (Marx, Capital, Volume 1, Chapter I, Section 1)
I think Marx treats use-values as not reducible to a single dimension. In other words, Marx doesn't consider the nutrition of a loaf of bread, for example, and the warming and style properties of a specific coat to be commensurable. Marx is here echoing Ricardo:
Utility then is not the measure of exchangable value, although it is absolutely essential to it. If a commodity were in no way useful, - in other words, if it could in no way contribute to our gratification, - it would be destitute of exchangeable value, however scarce it might be, or whatever quantity of labor might be necessary to procure it. (Ricardo, Principles, Chapter I, Section I)

Conclusion

Somewhere Mark Blaug criticizes Fernando Viannello's New Palgrave entry on the LTV for concluding merely "that the only thing that can be said against the labour theory of value is that it cannot be defended in the way that Marx defended it." My point here is rather that the LTV cannot be successfully critiqued in the way that Michael Huemer attacks it.