The organic composition of capital

In Capital, Marx introduces the idea of the organic composition of capital. In the LTV, a capitalist can achieve profit only by expropriating surplus labor from the workers who actually work for him. The labor embodied in machines and raw materials is "dead" labor: the surplus value has already been expropriated by the capitalist who sold him the machines or raw materials. A capitalist has to pay for capital, raw materials and directly employed labor up front*; he realizes a profit only after he has created, marketed, delivered, and sold his commodity. From the capitalists perspective, his rate of return $r={l_s}/{l_p+c}$, where $l_p$ is the cost of labor power, $l_s$ is the surplus value of labor (total labor minus cost of labor power), and $c$ is the constant capital, the cost of raw materials and the amortized cost of capital equipment.

*Wages are usually paid for in arrears, but labor is still usually paid for before the product is sold.

This model leads to two problems, one which Marx addresses and the other a puzzle Marx was not able to solve.

The first problem is why a capitalist would invest in capital: the more value a capitalist invests in capital, the lower her overall rate of return ($c$ is in the denominator, so as $c$ goes up, $r$ goes down). Marx answers this problem in two ways. First, as the value of wage goods falls, $l_p\/l_t$ falls, which means that more surplus labor can be extracted from workers, increasing the rate of profit. Second, Marx invokes competition. The value of a commodity is the socially necessary labor time. If a firm can produce a commodity for less that the socially necessary labor time, it can capture a producer surplus in addition to the surplus value of the labor it employs. (Essentially, the firm is exploiting its customers, getting them to give more embodied labor than they receive.) In the short term, a firm can make more money by investing in capital and become more efficient than its competitors; in the long term, absent monopoly, what one capitalist can figure out another can copy, and efficiency just leads to a lower rate of profit overall. Thus capitalism must constantly innovate to keep going in the short term, but this constant innovation leads to the constantly falling rate of profit.

The second problem is more severe. Firms in an economy create many different commodities. Some of these commodities will use more capital relative to labor, some less: they will have different organic compositions of capital. However, capitalists want to equalize profit. To make the typing simpler, I'll use $w$ to represent labor power ($l_p$) and $s$ to represent surplus labor ($l_s$). We'll keep the corn-corn model from my earlier post.

$v={w+s}/{1-a}$
$p=(1+r){w}/{1-(1+r)a}$

If the labor theory of value holds, we would expect that the values and prices of two commodities with different organic compositions of capital would be in the same proportion: $v_1/v_2=p_1/p_2$. However, unlike the previous model, adding an extra degree of freedom by separating labor into cost of labor power and surplus labor doesn't help us. We see that, holding the quantity of labor and the rate of profit constant, and letting the proportion of constant capital ($a$) vary,

$v_1/v_2=p_1/p_2→{{w+s}/{1-a_1}}/{{w+s}/{1-a_2}}={(1+r){w}/{1-(1+r)a_1}}/{(1+r){w}/{1-(1+r)a_2}}$

therefore,

${1-a_2}/{1-a_1}={1-(1+r)a_2}/{1-(1+r)a_1}$

which can be true if and only if $r=0$. Labor just divides out, no matter how it's expressed.

There are several ways of interpreting this equation. One way, which is not illegitimate, is that the LTV is just internally contradictory. But there are other ways. The LTV is, like most traditional economic theories, an equilibrium model; it does not talk about how or why an economy might not be in equilibrium, or how it achieves equilibrium. Thus we might conclude that in equilibrium all firms must have the same organic composition of capital; alternatively, we might conclude that in equilibrium the rate of profit is zero.

Another way of looking at this equation is that differences in the organic composition of capital is a source of fundamental instability in a capitalist economy. (A growing economy, protestations of traditional economists notwithstanding, is not in equilibrium.) It does not have an economic solution; instead, it requires an exogenous political solution: to stabilize the economy, capitalists can redistribute profits among themselves to equalize the rate of profit. It's not common, bu capitalists can work together, especially when their main tool, control of capital, cannot be used to gain short-term advantage.

Modeling the labor theory of value

In The Demise of Marx’s Labour Theory of Value and the ‘New Interpretation’ [pdf] Ernesto Screpanti uses a simple one-commodity model to show the theoretical incoherence in the Labor Theory of Value (LTV). (I don't think the model Screpanti's own invention; I've seen the model, and variants of it, for many years.) You can look at the article for the details of the model and the definitions.

The model states that value (exchange-value) is equal to the labor used in current production, plus a fraction $0<a<1$ of value from previous production. Price is equal to the cost of labor plus a fraction of the price of previous production, with the latter receiving a return on investment, $0<r<1$.

(1)	$v=l+av$
(2)	$p=l+(1+r)ap$
therefore
(3)	$v=l/{1-a}$
(4)	$p=l/{1-(1+r)a}$

A little algebra shows that value = price if and only if the rate of return on capital is zero.

There are some problems with this model, and not because it's simplified. First of all, it assumes that value and price are constant over time, i.e. that production is not growing. Otherwise, we would have to say $v_n=l+av_{n-1}$ and $p_n=l+(1-r)ap_{n-1}$, and have to worry about changing values over time. If production is not growing, then it is perhaps legitimate to say that the rate of profit really must be zero. However, this objection doesn't matter, because it is not a model of Marx's LTV. Absolutely central to Marx's theory is that capitalists do not pay workers for all their labor; capitalists only pay the cost of labor power, the amount of Socially Necessary Abstract Labor Time (SNLT) to produce the goods the workers must consume to continue working and reproduce the working class. Thus, a more accurate model is that value represents the total labor, whereas price represents the cost of labor power plus the cost of capital. Furthermore, capitalists want a return on their total investment, which includes both capital used and advance wages. Therefore, a more accurate model would be:

(1)	$v=l_p+l_s+av$
(2)	$p=(1+r)(l_p+ap)$
therefore
(3)	$v={l_p+l_s}/{1-a}$
(4)	$p=l_p/{1/{1-r}-a$

with $l_p$ the cost of labor power (in SNLT) and $l_s$ being the surplus labor. Therefore total labor $l_t=l_p+l_s$, and the rate of exploitation $l_e=l_s/l_t$

Because we're introducing the extra term, we can set value = price and just get a relation between the rate of exploitation and the rate of profit.

$l_e=l_s/{l_p+l_s}=1-{1/{1+r}-a}/{1-a}=r/{(1+r)(1-a)}$
$r=1/{1-(1-a)l_e}-1$

Both of these equations are well-behaved in the relevant ranges ($0<l_e,a<1;r>0$). They also show that holding the exploitation rate constant, as capital requirements increase (as $a$ gets larger), the rate of profit must decrease.

The labor theory of value as philosophy

The Labor Theory of Value is not itself a scientific theory. It is, instead, a "philosophical" or "historical" theory about more-or-less scientific theories of political economy. The LTV does not by itself predict the world; it is, instead, a way of making our economic predictions intelligible and meaningful. It asks the question, what do we mean when we're talking about economics? What is a "price"? What is "money"?

The LTV is not an "unscientific" theory: it does not (like many theologies) make covert scientific predictions that the real world does not bear out. It is, instead, a "metaphysical" theory, but only in Popper's sense; there's nothing transcendental or mystical about the LTV. It's about that most ordinary and material activity: real material human beings doing real material work producing real material goods and services. Indeed, the LTV denies transcendent or immaterial elements in economics.

The LTV starts from the premise that the only thing human beings have that we can trade is our labor. Our labor is (collectively and individually) the only thing that's ours. We must, of course, work upon nature; without a natural world, our labor would have nothing to work on, but nature itself is not ours; only our own labor is truly ours. Even Locke agrees: what fixes a part of nature as someone's property is precisely her labor operating on that part of nature, and she may expropriate a part of nature only so long as there is enough of nature sufficient so that others can expropriate their own part of nature. If nature is freely available, one cannot trade it, just as no one can trade air; all we have left to trade is our own labor.

The only free trade is a trade of equivalent exchange-values: one unit of labor embodied in a commodity for one unit of labor embodied in another commodity. The entire reason that trade actually does occur is because of the division of labor, the use-values of the two commodities are asymmetric: first, my commodity is of more use to you than to me, and your commodity is of more use to me than to you; second, my commodity is of more use to you than your own commodity, and your commodity is of more use to me than my own commodity. The asymmetry of use-values makes trade possible; the equivalence of exchange-values is what makes trade fair.

Marx did not invent this idea. Adam Smith and David Ricardo invented the LTV, and in Capital, Marx credits Benjamin Franklin with the idea that all we can do is trade our own labor. Marx's innovation is the distinction between labor power and actual labor: the ability to work for a period (i.e. a day), and the amount of work that can be actually done in a day. Labor power is (under capitalism) a commodity: it has an exchange-value, the Socially Necessary Abstract Labor Time (SNLT) required to create a working day, and a use-value, the total amount of Abstract Labor Time (LT) actually created. Marx labels the difference between the cost (in SNLT) of labor power and the amount of labor expended as "profit".

There are several objections to the LTV, most of which Marx addresses in Capital.

The first objection is that that if two people (or firms) create a commodity, and the first person expends half as much labor (in total, including labor used to produce raw materials, intermediate goods, amortized capital and administration) than the second, then the second person's commodity is absurdly worth twice as much as the first person's. To overcome this objection, Marx introduces the modifier, "socially necessary." If for example, in the material social and technological context of a society, the demand for coats can be satisfied by people working at most two hours per coat, then the exchange-value of a coat is two hours. If your firm takes four hours to make a coat, well, too bad for you. There are enough coats being produced using two hours of labor per coat that no one is forced by the scarcity of coats to pay you four hours. If, on the other hand, your firm can create a coat in only one hour, well, good for you. Because there are not enough coats that can be produced using only one hour of labor, people are forced to pay two hours of labor for a coat. Your firm will make an "economic profit" of an hour of labor per coat. (The capitalist who can capture such an economic profit is thus exploiting not only his workers, but his customers as well.) Economic profit is different from profit; even a producer who requires two hours of labor per coat, and exchanges them for two hours, will make a profit, because she will pay her own workers only for the cost of their labor power, which will be less than the total amount of labor they actually expend making coats.

The second objection is that actual labor (like use-value, as Marx argues elsewhere in Capital) is radically heterogeneous. The actual tasks performed by one individual laborer making one commodity are qualitatively different from those performed by another laborer making another commodity. Marx admits this, but what is still equivalent is the time a laborer expends, abstracted from the specific tasks he performs. (Of course, the worker still has to actually perform those tasks, and perform them efficiently, but the specific nature of the tasks does not enter into exchange value).

Related to the second objection that even labor abstracted from the heterogeneity of specific tasks is still heterogeneous. People differ in relative skill, talent, the intensity of their labor, etc., again, even abstracted from the specific tasks. Marx himself mostly handwaves this objection away, talking about averages and aggregates. However, this objection does not seem that important. First, Adam Smith argues that there is actually little difference in inherent ability; the difference between a philosopher and a laborer arises because of education and social situation, not inherent ability. Second, what matters is the socially necessary (marginal) labor time. If the "last" person hired to make a commodity were an inefficient slacker who takes twice as much time to produce the commodity as his most efficient co-worker, well, then that sets the socially necessary labor time. If the firm could hire someone more efficient, they would do so; if they could not sell the commodity for the price implied by the slacker's time, they would not hire him. Even if there really are innate differences in ability, we're still interested only in ability at the margin, which is measurable.

A third objection is that firms do not actually account for labor and labor power in the way corresponding to the LTV. Marx argues that this discrepancy is by design. If our accounting were honest, then no one would stand for capitalist exploitation; instead, the exploitation has to be carefully hidden for a capitalist society to work at all. Marx argues that this obfuscation is discernable: he argues that we (absurdly) think we have a social relationship with objects, when in reality producers of different commodities have a social relationship with each other.

There are other, deeper objections to the Labor Theory of Value, which I will (might) discuss in a further post,

Definitions

According to Marx's theory then:

• Socially Necessary Labor Time (SNLT): The total amount of human labor (abstracted from the specific tasks) embedded in a product, that is necessary to create a commodity (including capital creation, raw material/intermediate goods supply, and administration) in a particular social/technological context. Marx uses an average of all producers, but the average is not the correct statistic (otherwise some producers would operate at a loss). Instead, the marginal time is used: the labor time of the last, least efficiently produced instance of the commodity (amortizing capital and administration over all instances produced), which should equal the marginal demand for that last, least satisfying instance actually consumed.
• Exchange Value: The total amount of Socially Necessary Abstract Labor Time (SNLT) embodied in a commodity. The exchange value includes all the SNLT, including the SNLT necessary to create the capital and create the raw materials.
• Labor Power: The ability to work for a full period (e.g. a day).
• Cost of Labor Power: The SNLT required to create another period (day) of Labor Power, i.e. the SNLT required to supply a worker with the necessary food, shelter, clothing, medical care, leisure, etc. to work another period (day) and to reproduce the labor force. Because workers are human, the Cost of Labor Power may be more than bare subsistence.
• Labor Time: The actual amount of time a worker works in a period when he expends his or her labor power. The Labor Time worked will be less than the SNTL used to purchase his or her Labor Power.
• Profit: The difference between the Labor Time and the Cost of Labor Power employed by a firm

Labor and labor power

A question that puzzled Marx's predecessors was, where does profit come from? When a business makes a profit, what precisely are they making? Yes, they can make a money profit, but money does not have intrinsic use-value (by definition: if you actually consume a money-thing, such as salt, it ceases to be money and becomes an ordinary commodity). What does that money represent? If a capitalist pays full value for labor and capital (ignoring land), and exchange value is just the value of the labor and capital, then where does the profit come from? Neither Smith nor Ricardo were happy with their answers to this question.

What Marx does is posit that "labor" is really composed of two things: actual labor, the amount of work that's actually done, and labor power, the amount of work necessary to keep a worker alive, able to work another day, and reproduce the next generation of laborers. So, it might take six hours of labor to grow the food, build the houses, manufacture the clothes, etc. to keep a worker alive, and this cost of labor power will allow the worker to work twelve hours the next day. Thus, the capitalist does not pay full value for labor: he pays only for labor power, which costs "six hours", and receives "twelve hours" of actual labor; his profit is thus "six hours" of labor, i.e. the surplus value of labor. Although the capitalist is obtaining six hours of "free" labor from the worker, this exchange of wages for labor power is, in capitalist terms, a "free" exchange that satisfies the Labor Theory of Value: the worker is exchanging a commodity, his labor power, which costs "six hours" of labor, for wages (representing goods) worth "six hours" of labor.

(Marx makes the point that workers are not mindless objects. A chair cannot object that someone exchanges it for its cost, but workers can and do object, sometimes violently. Therefore, workers can politically demand a price for their labor power, with a lower bound set by bare subsistence, and an upper bound set by their total amount of labor. And different categories of workers can have different political power, so the price of labor power can differ by category or sector.)

This analysis is the point of the Labor Theory of Value. It is not to predict actual market prices on a day to day basis. There are many things that can change market prices in the short term and medium term. If you're interested in price arbitrage, trying to calculate the "true" price (and arbitrage "distorted" prices), the LTV is not a particularly good tool. The LTV is a conceptual tool for understanding what capitalism is all about. Marx notes that Ricardo, Smith, and Benjamin Franklin observed that all human beings have to trade that is our own is labor; the fruits of nature are given to us for "free": we do not have to work to make the sun shine, the rain fall, plants and animals grow. Yes, people can "own" things like land or capital, and while they themselves do nothing directly productive, they can still charge people to work on it. However, what they are obtaining is the surplus labor of the people who are actually productive.

Assume my land can use a certain amount of direct labor (ignoring for the moment labor indirectly embedded in some capital) to produce a certain amount of corn. The cost of labor power, what I must give to the workers, is less than the total amount of corn I can grow. I keep the extra corn. The exchange-value of the corn I have left is precisely the difference between what the labor produces and what the labor costs. (And, in fact, the amount of labor I hire is precisely the amount at which the "last" laborer produces just the cost of labor power.)

I can exchange the extra corn I grow for an equal amount of labor embedded in other goods. If I could trade it for more labor embedded in some other good, then people would stop using labor to make the other good and start growing corn; similarly, if I could trade it only for less labor embedded in other good, then I would stop using labor to grow corn and start making the other good, and trade with other (more foolish or more efficient) producers of corn.

Previous: Marx's project: Introduction and commodities (and Measuring socially necessary abstract labor time
Next: The organic composition of capital

Measuring socially necessary abstract labor time

In his comment (and on his excellent blog, Social Democracy for the 21st Century) LK argues that it's impossible to define, much less measure, socially necessary abstract labor time (SNALT).

First, the "abstract" in SNALT refers to labor abstracted from the specific things that laborers do. Marx argues that because the specific tasks are incommensurable (how do compare sewing a seam to gluing a sole to a shoe?) the specific tasks used to create different commodities cannot be a basis of a consistent exchange value. In this sense, abstract labor time is just the fact that someone has worked for a specific period of time, without regard to the specific tasks that person has performed.

But there are definitely factors other than time that affect productivity. LK asks, "How do you take an average of a heterogeneous factor like labour, when there is so much difference in profession, skill, competence, experience, and skills to be 'averaged'?"

To get average abstract labor time per unit, first count the number of objects produced, count the total number of raw person-hours used to create those products, including the time necessary to create all the capital, all the skill training, and all externalities, and divide by the number of objects. If you want marginal SNALT, find the least efficient producer who is still in business, and do the same thing just for the last unit they produce. Standard economic theory predicts that the marginal cost of the last unit should equal the minimum average total cost and the price. (LK challenges this aspect of standard economic theory, and it might be incorrect, but marginal cost is not exactly a novel economic concept.) Any effects other than time, skill, competence, experience, etc. should all be normally distributed and should cancel out in the aggregate. This is not rocket science.

Of course, the Labor Theory of Value (LTV) is not the only thing affecting actual money prices. You would want to look for shocks (the price of gas just after the beginning of the Iraq war, for example, would probably not reflect SNALT), monopoly and monopolistic competition (SNALT is a valid predictor of prices only under perfect competition), hidden positive and negative externalities, imperfect or asymmetric information, network effects, etc.

Remember, Marx never intends the LTV to be a tool for predicting prices that hedge funds can use to make a lot of money in arbitrage. The LTV is a conceptual tool to explain what it means to say that the capitalist exploits the working class: the capitalist class expropriates labor time without compensation from the working class.

Marx's project: Introduction and commodities

I think that to understand Marx, it is necessary to understand what his project was. I'm writing quickly, so I'm not going to cite, and this is my personal interpretation of my (rather limited) reading of Marx. As I mention below, all theories are false, but some are useful; I'm describing here why I think Marx's theories about capitalism are useful. I am not a truth relativist; I'm saying only that our theories about the world are always limited and approximate.

Marx starts with two observations: first, by the middle of the 19th century, capitalism had increased the forces of human production by at least a couple of orders of magnitude relative to feudalism; second, most people in industrialized economies were living in abject misery, far worse than under feudalism. Why? Smith (and perhaps Ricardo) were convinced that greater economic activity would lead to increased happiness for everyone, including the working class. By the mid 1800's, almost a century after Smith published The Wealth of Nations in 1776, the condition of the working class had actually declined. Why?

Marx rejected the hypothesis that the rulers of capitalist society are just especially bad people. Indeed, although Marx's seething rage at the suffering of the workers is apparent, in his economic writing, Marx rarely (if ever) employs a moral critique of anyone or anything, even capitalism. (Marx did not exhibit the same reserve in his personal relationships.) Marx was enraged, to be sure, but he knows that the fact that he is enraged is of no value; he wants to understand why he's enraged, and what precisely he's enraged about. Even before writing Capital, Marx was already convinced that not individual "evil" capitalists, but rather the fundamental structure of capitalism was responsible for human misery. Thus, Unlike his predecessors and other economists, Marx was completely uninterested in a descriptive, positivist account of how capitalism works. Instead, Marx's analysis of capitalism was geared towards locating precisely what it is about the structural relations of capitalism that causes the misery of the working class.

Marx was a theoretician, not a scientist, and he was trying to solve a problem, not simply describe the world as it is. It is important to understand that, like every scientific theory, Marx's theory is a model. All models, scientific and economic, cut away, i.e. abstract, important parts of reality. In much the same sense, theories of gravity abstract away things like air resistance. Looking only at gravity will not explain why aircraft fly, but to make an aircraft fly, we still have to understand gravity on its own terms. Because all models abstract away important parts of reality, all models are wrong; some models, however, are useful. Because a theory of gravity, neglecting air resistance, is useful for making aircraft fly, we continue to use it, in addition, of course, to theories of aerodynamics.

So, Marx begins Capital with a theoretical analysis of the commodity. Marx defines a commodity as:

1. A physical object that
2. by virtue of its physical properties has some use-value (i.e. its consumption satisfies some human want),
3. can and must be created using directed, willful human effort (i.e. labor), and
4. is created for the purpose of exchanging it for other commodities.

If something does not fulfill any of the above conditions, Marx is no more interested in it than he is in the speed of light or aesthetic appeal of the Mona Lisa. (Not that such things aren't interesting — they are interesting — but they're not part of Marx's project. Marx also tacitly assumes (at first; later in Capital he makes the assumption explicit), that people are actually exchanging commodities in free, uncoerced competition with each other. So, if someone creates something without use-value, it is not a commodity, no matter how much directed, willful human effort went into it. If something has use-value, but is not created by human labor, it is not a commodity. If someone uses human labor to create something they themselves will consume, it is not a commodity. (Marx focuses on the "goods" part of "goods and services", but the argument for services is virtually identical.) Marx then asks the question: what determines the quantity of one commodity that will exchange for some quantity of another commodity?

Using this definition, Marx comes to the surprising conclusion: the exchange-value of commodities, i.e. the quantity of a commodity that will be freely exchanged for a quantity of another commodity, depends only on the total quantity of socially necessary abstract labor time (SNLT) used to create the commodity. Marx first argues that for a free exchange to take place, there must be something equivalent in the commodities exchanged. If there were nothing at all equivalent, then exchanges would be arbitrary and highly variable: one person would exchange a coat for ten pairs of shoes, others would exchange ten coats for one pair of shoes, and everywhere in between. But, given competition, even if someone really wanted a coat, and had more shoes than he knew what to do with, if one person with a coat will take two pairs of shoes and another demands ten pairs, he will still buy from the cheaper seller, and vice-versa. There are some price variations, but I don't see a gallon of gas selling for \$0.10 at one station and \$10.00 at another.

Marx rejects the idea that use-value has anything to do with exchange-value. Marx argues that use-values are incommensurable. We cannot quantitatively compare the use-value of keeping one's body dry with the use-value of a good meal. No one, Marx argues, would exchange comparable use-values, i.e. exchange a coat for a coat. Since use-values are incommensurable, they cannot be equal. And this position makes sense, even if we could numerically compare use-value. I need a certain amount of food every day to survive — a hamburger has infinite use-value to me — but I don't sell myself into slavery for a meal. Similarly, my local restaurant has more hamburgers than the owners could possibly eat — they have zero use-value to the owners — but they don't just give them to me for free. Furthermore, my computer is far more useful to me than my car (if you forced me to choose, I would give my car without hesitation), but I paid twenty times more for my car than for my computer. The whole point of trade is that both parties gain more use-value than they give up; there can be nothing directly equivalent about a positive-sum game.

Marx argues that what can be, and is, equal about two commodities is the socially necessary abstract labor time used to create them. If, counting all the labor time, including the labor time necessary to create the physical capital, it takes one hour of labor time to create a pair of shoes and two hours to create a coat, then two pairs of shoes will have the same exchange-value as a coat; in a money economy, then a coat will have double the money price of a pair of shoes. Again, this makes sense: if I someone is selling a coat for three times the price of a pair of shoes, then I will just work and create the coat myself, giving up the time I could use to create only two pairs of shoes. More precisely, if a company can make identical coats for two-thirds the price their competitors charge, they will do so, and sell all the coats they make.

The qualifiers "socially necessary" and "abstract" are important. "Socially necessary" means that inefficient producers relative to the technical and social state of production do not get to charge more for their commodities than efficient producers. "Abstract" means that the details of precisely how some commodity is produced is irrelevant; what matters is only the actual time (and perhaps other factors, such as intensity and agreeableness/disagreeableness of the labor) involved.

Again, I will reiterate: the Labor Theory of (Exchange-)Value is a model. Marx does not argue that if you go out and measure the money price and socially necessary abstract labor time of every product on the market, you will get a nice neat regression line with only random errors. In much the same sense, if you drop a hammer and a feather, the hammer will hit the ground well before the feather. But Marx does say that if there really is free competition, and if labor really can create more of a commodity, then yes, there will be a direct correlation between the prices and socially necessary abstract labor time. Similarly, if there is a substantial discrepancy between prices and socially necessary abstract labor time, then there will be a violation of the assumption of free competition.

Sidebar: Measuring socially necessary abstract labor time
Next: Labor and labor power

The Labor Theory of Value

This essay was first submitted to Economics 201-400, at the Community College of Denver, on 6 Dec. 2010.

What determines what quantity of one thing will fetch some quantity of another thing? Why is the price of a pair of ordinary shoes, a shirt, or a loaf of bread the same in every store? Why should bread be $2.50 a loaf and shoes $25 a pair and not vice-versa? Philosophers since Aristotle have inquired into economic value and prices. Beginning with Adam Smith and David Ricardo, economists have tried to understand the exchange value of commodities in terms of the embodied human labor, the Labor Theory of Value. Karl Marx improved the Labor Theory of Value, identifying the source of non-wage factors in surplus labor, and making explicit the fundamentally statistical character of the theory. There are issues with Marx’s theory, however. The most serious issue, the transformation problem, demonstrates that Marx’s theory conflicts with the assumption that capitalists will allocate their capital to achieve a uniform rate of return across all industries, including those that produce both final and intermediate goods. The transformation problem, however, itself requires assumptions that are at best suspect, especially under global equilibrium conditions. While these issues render Marx’s theory insufficient to predict money prices in the short term, we can look at the Labor Theory of Value in a paradigmatic sense, to make issues of political economy explicit and inform normative economics.

Marx himself did not first propose the Labor Theory of Value. In The Wealth of Nations, Adam Smith connects labor to price. According to Smith, “The value of any commodity, therefore, to the person who possesses it, and who means not to use or consume it himself, but to exchange it for other commodities, is equal to the quantity of labour which it enables him to purchase or command. Labour, therefore, is the real measure of the exchangeable value of all commodities” (par. 1). Although Smith identifies labor as the source of value, he fails to identify the historical labor indirectly embodied in commodities, such as the labor necessary to make a worker’s tools and equipment. To Smith the exchange value of a commodity is the immediate labor saved by the exchange; if buying a commodity will save one person two hours of labor, the exchange value would be two hours of labor, or the equivalent in money. While a useful approximation, the immediate exchange value becomes too imprecise and variable to construct a quantitative theory.

David Ricardo performs a more thorough accounting in Principles of Political Economy: “The exchangeable value of the commodities produced [is] in proportion to the labour bestowed on their production; not on their immediate production only, but on all those implements or machines required to give effect to the particular labour to which they were applied” (par. 19). But Engels still observes that traditional economics fails to give a satisfactory explanation for the distinction between wages and actual labor: If the exchange value of an hour of labor is an hour of labor, then how can wages – just the value of labor in money form – afford the owner of capital any opportunity for profit? If wages are less than the actual value of labor, why are they less? How do we calculate how much less?

In Capital, Karl Marx improves the Labor Theory of Value by formally separating the notions of labor and labor power. Labor is the actual labor performed by a worker; labor power is the cost to make that labor available, essentially the cost to feed, clothe, house, and entertain the worker, as well as providing for the next generation of workers. In any economy generating a surplus, the cost of labor power, i.e. the labor necessary to feed a worker, will be less than the labor made available by that labor power. Wages are therefore a function of labor power, but the exchange value of a commodity is a function of the actual labor required to produce that commodity (ch. 6). We can conclude then that the difference between labor and labor power, the surplus value of labor, is the ultimate source of profit.

Marx also makes clear that the exchange value of a particular instance of a commodity is not related to the total amount of labor embodied in that instance. “Some people might think that if the value of a commodity is determined by the quantity of labour spent on it, the more idle and unskilful the labourer, the more valuable would his commodity be, because more time would be required in its production” (“Capital” pt. 1 ch. 1 par. 14). The exchange value is instead related to the socially necessary labor embodied in the commodity as a class, which Marx clearly describes as a statistical property: The individual unit of labor “is the same as any other, so far as it has the character of the average labour-power of society, and takes effect as such; that is, so far as it requires for producing a commodity, no more time than is needed on an average, no more than is socially necessary” (“Capital” pt. 1 ch. 1 par. 14). For example, 

The introduction of power-looms into England probably reduced by one-half the labour required to weave a given quantity of yarn into cloth. The hand-loom weavers, as a matter of fact, continued to require the same time as before; but for all that, the product of one hour of their labour represented after the change only half an hour’s social labour, and consequently fell to one-half its former value. (“Capital” pt. 1 ch. 1 par. 14)

It is thus clear that the exchange value derives from some statistical property of the actual labor embodied in all the instances of a commodity as a class.

            Finally, Marx introduces the two distinct notions of abstract labor. The first notion is human labor abstracted from the particular task a worker performs. “Neither can [a commodity] any longer be regarded as the product of the labour of the joiner, the mason, the spinner, or of any other definite kind of productive labour. . . . All are reduced to one and the same sort of labour, human labour in the abstract” (“Capital” pt. 1 ch. 1 par. 10). But Marx also realizes that even in this sense of abstraction, not all labor is created equal. “One man is superior to another physically, or mentally, and supplies more labor in the same time, or can labor for a longer time; and labor, to serve as a measure, must be defined by its duration or intensity, otherwise it ceases to be a standard of measurement” (“Gotha” pt. 1). Environmental factors also affect intensity. It seems obvious that ceteris paribus an hour doing physical labor standing in a sewer would be more “intense” than an hour sitting in an air-conditioned office.

The Labor Theory of Value has considerable philosophical appeal. Smith and Ricardo seem to treat other factors of production – profit, rent and interest – as sui generis, having their own distinct character and contribution to exchange value unrelated to human labor. While these factors contribute to immediate prices, it is difficult to understand how mere ownership – distinct from the administrative or supervisory labor the capitalist, landlord or banker might perform – can itself create value in the same sense that labor creates value. In a society without a class structure, without a distinct class or group of owners, the same competitive forces that equalize prices would ensure that no individual as owner of the equipment, land or money he used directly in his own production could say that the ownership by itself contributed more than just his own labor to the exchange value of the product. All individuals have to trade is their individual time and effort, either directly (“I scratch your back; you scratch mine”) or indirectly by embodying their labor in commodities. The non-wage factors of production would seem, philosophically, to be just social constructions to allocate the surplus value of labor.

As philosophically appealing as Marx’s Labor Theory of Value might be, it suffers from considerable problems as a descriptive theory. A good descriptive theory, especially a reductive theory, requires that the reduced elements be independently determinable. Marx’s Labor Theory of Value fails to the extent that it purports to reduce the competitive market price of a commodity – including labor power as a commodity – to any independently determinable quantity of embodied labor. In this sense the Labor Theory of Value predicts that the market “discovers” the exchange value of a commodity, the socially necessary abstract labor embodied in that commodity. However, the market itself directly affects the socially necessary abstract labor embodied in the commodity in a number of ways.

            Unlike any other commodity, labor power is instantiated in human beings. A shoe or a steel girder as a commodity has no preferences, needs or wants of its own; it thus cannot object to being sold at cost. Human beings, on the other hand, do indeed have preferences, needs and wants; they are strongly motivated to act on those subjective properties. Hence the cost of labor power feels a “force” tending towards disequilibrium not present in any other commodity. As Marx notes:

The number and extent of [the labourer’s] so-called necessary wants, as also the modes of satisfying them, are themselves the product of historical development, and depend therefore to a great extent on the degree of civilisation of a country, more particularly on the conditions under which, and consequently on the habits and degree of comfort in which, the class of free labourers has been formed. In contradistinction therefore to the case of other commodities, there enters into the determination of the value of labour-power a historical and moral element. (“Capital” pt. 2 ch. 6 par. 10)

Although Marx does go on to say, “In a given country, at a given period, the average quantity of the means of subsistence necessary for the labourer is practically known” (“Capital” pt. 2 ch. 6 par. 10), we cannot expect the price of labor power to move toward equilibrium with the same alacrity as other commodities.

Another problem is that market prices do not just emerge from the socially necessary abstract labor time embodied in a commodity; market forces directly affect the labor embodied in a commodity. Marx’s simplistic formulation, “The labour-time socially necessary is that required to produce an article under the normal conditions of production” (“Capital” pt. 1 ch. 1 par. 14), requires substantive revision. Even absent non-wage factors, we see that a shift in just the demand curve, with no changes to technology, individual efficiency, or any other specific characteristics of supply, still changes the statistical properties of the cost of supply, and therefore changes the socially necessary labor time necessary to supply the commodity. When demand falls, the incentive is not to arbitrarily eliminate suppliers of a commodity, but rather to eliminate the suppliers with the highest marginal cost. Similarly, when demand rises, we do not add “average” suppliers; we must add new suppliers with a higher marginal cost. Thus while the socially necessary labor time is still strictly meaningful – regardless of the demand, the marginal cost of supply at equilibrium and the average cost of supply are real costs – we cannot determine the socially necessary labor time independently of market forces.

            This characteristic means that the efficiency of labor, a component of abstract labor, is also dependent on demand. The only way to compare efficiency across different forms of labor is to compare an individual laborer’s productivity to the socially necessary labor time for the commodity as a class. If the socially necessary labor time for producing a widget is 10 hours, and a particular laborer can produce a widget in 8 hours, then her productivity is 10/8 x 100% = 125%. But if the socially necessary labor time falls to 9 hours, then her productivity falls to 10/9 x 100% ~ 11% even though nothing about the quality of her own work has changed.

             

Furthermore, while it’s intuitively appealing that the environmental conditions of some labor can affect the intensity or desirability of the labor, it is difficult to independently measure these factors quantitatively. Yes, working in a sewer might obviously be less desirable than working in an air-conditioned office, but by how much? One tenth as desirable? One half? Ten percent? We have to rely on market forces to quantify these subjective factors. We cannot predict the market price based on the environmental conditions; we must, rather, infer the environment’s effect from the market prices.

             

The transformation problem is perhaps the most serious problem affecting the Labor Theory of Value. Succinctly, the capitalist mode of production consists of using the production of commodities to convert money into commodities, and commodities into more money. The capitalist wants to realize a profit on the total amount of money he invests in an enterprise, regardless of what that money is spent on. If the surplus value of labor is the only “true” source of profit, then the capitalist could realize a profit only from the direct labor inputs to production; the surplus value of labor embodied in the rest of the inputs, especially physical capital and intermediate goods, has already been extracted by the suppliers of those inputs. Samuelson notes that Marx’s Labor Theory of Value predicts that profit should act like a value-added tax; the “added value” consists of the surplus labor at each stage of production. But in the capitalist mode of production profit actually acts like a turnover tax, where each stage of the production process incurs a “tax” on the entire value transmitted, not just the value added. Samuelson shows that these different ways of looking at profit result in different slopes for the wage component of the production possibility frontier (p. 409). It is mathematically impossible to model a constant turnover tax as a constant value-added tax; they might have the same total cost, but their allocation cannot be transformed to individual industries. The transformation problem alone thus decisively renders the Labor Theory of Value insufficient as a short-run predictor of market prices in a capitalist economy.

It is not clear, however, that the transformation problem decisively rebuts the fundamental premise of the Labor Theory of Value.

            Wikipedia attempts an analysis of the transformation problem using the Deer-Beaver-Arrow model, but the analysis has several flaws; it simply assumes a constant rate of return on capital, with no deeper justification. A more careful analysis is required.

            Let us first consider a very simple two-product economy, consisting of the production of Deer and Beavers, each of which require only direct labor. We can assume that all labor is homogenous: Any person may turn her hand equally effectively to the production of Deer or Beavers, and she is free to do so. We can also assume that supply curves are horizontal, perfectly elastic; the marginal cost remains constant and demand determines only the quantity supplied. We can make these assumptions without loss of generality: All the properties that complicate microeconomic analysis – comparative advantage, rising marginal cost of supply, land allocation – affect the equilibrium price, a real labor cost that (absent non-wage factors) determines the socially necessary labor time for the production of a commodity. We can assume that to reach some equilibrium, the individuals have made all available Pareto optimizations, and we have settled on some definite socially necessary labor time necessary to meet demand. It is clear in this case that the relative price of Deer and Beavers is the relative socially necessary labor time embodied in their production. Changes in demand curves will change only the relative quantities of Deer and Beaver produced at that relative price.

            To this model, we will add a “capital” good, Arrows, which make the production of both Deer and Beavers more efficient. As a capital good, we might conjecture that Arrows would earn a rate of return, over and above their labor cost. But where does this rate of return come from? If we hold to our original assumption, that labor is homogenous and each individual can freely allocate her labor, then a rate of return implies that labor spent making Arrows returns more than labor spent hunting Deer and Beavers, even using Arrows. In this case everyone will “bid” for the privilege of making Arrows until each individual becomes indifferent to how she spends her time, implying a zero rate of return over and above the labor cost. Far from disproving the Labor Theory of Value, simple equilibrium analysis under free market assumptions seems to disprove the capitalist mode of production!

Samuelson concludes from a more sophisticated analysis of the Labor Theory of Value and the transformation problem that the Labor Theory of Value is essentially a restatement of “bourgeois” money-based economics: 

Although Capital’s total findings need not have been developed in dependence on Volume I’s digression into surplus values, its essential insight does depend crucially on comparison of the subsistence goods needed to produce and reproduce labor with what the undiluted labor theory of value calculates to be the amount of goods producible for all classes in view of the embodied labor requirements of the goods. The tools of bourgeois analysis could have been used to discover and expound this notion of exploitation if only those economists had been motivated to use the tools for this purpose. (p. 422)

Even though the Labor Theory of Value fails as a short-term predictor of prices in a growing capitalist economy, it does put at the forefront the fundamental dependence of economics on the particular characteristics of labor and labor power. By making labor central, the Labor Theory of Value actually does discover what Samuelson implies traditional analysis could have discovered but did not. Taking a labor-centric view of economics thus has significant implications for not only how economics affects our political decision-making, but also how we should actually conduct economic analysis.

            An important consequence of a labor-centric view of economics is that profitability is not intrinsically good. Profit is not “real”; it is, rather, a disguised form of surplus labor. To determine whether some profit is good, we have to look at where it comes from and where it goes. Profit that comes from a real increase in labor productivity is better than profit that comes from a reduction in the price of labor power. Profit that goes to expanding our physical, human and technological capital is better than profit that goes to the extravagant consumption of the capital-owning class. A money-centric view of economics does not make clear the source, destination or justification of profit; a labor-centric view puts these characteristics in plain sight.

            Although labor power has unique historical and moral characteristics, it is still in many important senses a commodity, one that workers exchange with capitalists in a competitive market. As a commodity, labor power is subject to the same market forces as any other commodity, forces that tend to move the price of any commodity to its socially necessary cost. Thus we cannot count on the “invisible hand” to raise the price of labor power and distribute the productivity of society to those who do the actual work; raising the price of labor power – if we choose to do so – must therefore be a social decision. In just the same sense allowing the invisible hand to lower the price of labor power is just as much a social decision. Money-centric economics, however, allows us to obscure the social nature of this decision, making it seem the outcome of “inexorable” economic forces.

            Finally, the Labor Theory of Value argues that the principal efforts of economists should be turned to understanding and measuring the role of labor in the economy. Statistics about the labor embedded in individual products, the labor available to the economy as a whole, as well as the price of labor power should receive as much or more attention as the Dow Jones Industrial Average and nominal Gross Domestic Product. The Labor Theory of Value implies that every measurement of real economic activity should be stated somehow in terms of labor and labor power. Indeed the Labor Theory of Value suggests that money itself, i.e. nominal economic measurement, should explicitly refer to some property of labor.

The tools are there; we need a shift in emphasis. In 1845, Marx wrote, “The philosophers have only interpreted the world, in various ways; the point is to change it” (“Feuerbach”). What we do not measure, we cannot optimize; what we do not discuss, we cannot change. We must explicitly discuss and make central the role of labor and labor power in our economy if we want to improve the conditions of the billions of people who spend their time working.

Works Cited

Engels, Frederick. Introduction. Trans. Frederick Engels. Wage Labour and Capital. By Karl Marx. Ed. Frederick Engels. 1849. Marx/Engels Internet Archive (marxists.org). Web. 6 Dec. 2010. 

Marx, Karl. Capital: A Critique of Political Economy. Ed. Frederick Engels. Trans. Samuel Moore and Edward Aveling. First English Edition ed. Vol. 1. Moscow: Progress, 1887. Marx/Engels Internet Archive (marxists.org). Web. 6 Dec. 2010. 

Marx, Karl. "Theses on Feuerbach." Marx/Engels Selected Works. Trans. W. Lough. Vol. 1. Moscow: Progress, 1969. 13-15. Marx/Engels Internet Archive (marxists.org). Web. 6 Dec. 2010. 

Ricardo, David. "On Value." On The Principles of Political Economy, and Taxation. 1821. Project Gutenberg, 31 July 2010. Web. 6 Dec. 2010. 

Samuelson, Paul A. "Understanding the Marxian Notion of Exploitation: A Summary of the So-Called Transformation Problem Between Marxian Values and Competitive Prices." Journal of Economic Literature 9.2 (1971): 399-431. EconLit. Web. 2 Nov. 2010. 

Smith, Adam. "Of the Real and Nominal Price of Commodities, or of Their Price in Labour, and Their Price in Money." An Inquiry into the Nature and Causes of the Wealth of Nations. 1776. Project Gutenberg, 1 June 2002. Web. 6 Dec. 2010. 

"Transformation Problem." Wikipedia, the Free Encyclopedia. n.d. Web. 6 Dec. 2010. .

The transformation problem

Intuitively (and I don't yet have the tools to analyze the problem mathematically) I suspect that the transformation problem might be "unsolvable", but the unsolvability might actually be evidence for a labor theory of value as a semi-normative theory, i.e. as a means to the end (or a way of measuring progress towards the end) of an efficient economy.

An efficient economy operates at the the production-possibility frontier, the trade-off between producing different combinations of various commodities. Any point on the frontier (the blue line in the graph to the right, e.g. points B, C and D) represents efficient aggregate production: we could not produce more of one commodity without sacrificing production of another. Any point "outside" the frontier (e.g. point X) is impossible to achieve given the current means of production. Any point "inside" the frontier (e.g. point A) represents real inefficiency: we could produce more of one commodity without sacrificing any production of the other.

The production-possibility frontier has direct implications on prices. The relative prices of the commodities when production is on the frontier should have some definite relationship to bind them to the line, but prices inside the frontier will not have that same relationship, since they are set inside an area, not on a line, giving them another degree of freedom.

Suppose, for example, we impose a "tax" on butter, and this tax is simply wasted. For every nine workers a butter manufacturer hires, he must hire another worker at the same wage to sit around watching TV and surfing the net. This "tax" then reduces whatever level of butter production we might achieve without achieving a corresponding increase in the number of guns produced. Since we could (by not paying 10% of our butter production workforce to sit around doing nothing) produce more guns without producing less butter, we must therefore be inside the production-possibility frontier, and our economy is not efficient.

The relative prices of guns and butter, however, will have some definite relationship that takes into account this wasted tax on butter. Having this relationship, however, based on inefficient production means that any relationship with the assumption of efficient production will not hold.

My speculation is that the requirement that capital receive a constant rate of return by itself introduces real economic inefficiency. Furthermore, because a capitalist economy typically measures total rate of return on capital, but the real rate of return is a rate on variable capital (the surplus value of the workers), the economic inefficiency is not just variable across industries with different organic compositions of capital, but it's also opaque.

To sum up: At the production-possibility frontier, the labor theory of value should more-or-less obviously hold. The requirement of a constant rate of return on total capital places us inside the production-possibility frontier. The inefficiencies introduced by the constant rate of return will vary according to the organic composition of capital. We could solve the transformation problem only by measuring the individual organic compositions; since these values are opaque, the transformation problem is unsolvable. Observing that the labor theory of value does not more-or-less obviously hold (and the transformation problem is unsolvable) is direct evidence that the economy is not efficient.

Is it true? I dunno. Ask me in a few years when this is my PhD thesis topic.

Why a labor theory of value?

A reader asks a number of good questions about a labor theory of value:

What good is an idealization? It seems to me that an idealization may serve two purposes: either it provides by itself a good enough approximation to reality for certain problems, or it can be easily combined with other idealizations to yield a useful picture of the world.

Indeed. all theories in economics are, to some extent, idealizations. And no economic theory is all that good at predicting reality, at least not nearly as good as theories in the physical sciences.

One method I've brought from my study of the physical sciences is to be extremely conscious of your units of measure. Not only do you want to be rigorously consistent about your units, you want to know what your units mean. The meaning of a unit has two components: the operational definition: how precisely do you measure things in that unit, and the physical definition: what actually existing physical property of the object being measured corresponds to that unit. There are cases where scientists operate with units and quantities that aren't physical (such as with the ideal gas law), but by and large it's Very Important to assign a physical meaning to your units of measure.

Most of economics use some currency as the direct unit of measure. But currency by itself does not have any sort of physical referent. Indeed, because currency defines a relationship between quantities that (presumably) have the same underlying units of measure, a quantity qualified by currency is a dimensionless quantity: it has no units of measure. Dimensionless quantities are important in and of themselves, but it's also important to be able to talk about real physical things using real physical units of measure.

A labor theory of value gets us at least closer to thinking about economics using units of measure that directly reference a physical quantity: human time and effort. It doesn't get us all the way there, because of the "abstract" (subjective) and "socially necessary" (statistical) components of the definition. And a labor theory of value seems at least intuitively better than referencing the prices of specific commodities to tie prices to objective physical reality.

As far as understanding market prices is concerned, the labour theory of value does neither, since there is no theory of 'frictions' that can be added on to the theory to make it more realistic.

Not all economists endorse the methodology of adding "frictions" to an ideal model to generate a predictive model.

But I'm not at all convinced that one can't add "frictions" to a labor theory of value. I haven't studied enough economics to offer a rigorous mathematical rebuttal, but in general replacing perfect rationality with an evolutionary model using uncorrelated heritable variation and natural selection seems to have considerable potential, giving us a mechanism that might result over time the equilibrium that perfectly rational people would figure out instantaneously.

To my mind the debate on the transformation problem shows that there is no meaningful connection between labour values and prices.

I'm not yet convinced* that the transformation problem is (a) unsolved, (b) important at all or (c) a problem specifically for a labor theory of value. Marx seems to consider the transformation problem to make very specific predictions about capitalism; he does not seem to treat it directly as a way of connecting the LTV to observed prices in general. It's also worth noting that according to the Wikipedia article cited by the commenter, the transformation problem assumes that the use of capital requires not just compensation for its creation, but a continuing rate of return. This assumption might constitute an externality, which would require a specific kind of mathematical treatment. As I noted earlier, my understanding of mathematical economics is not yet sufficiently sophisticated to address the problem more rigorously.

When I use this particular phrase, it should be noted that I'm equally unconvinced of the opposite; I'm truly agnostic.

On the other hand the standard micro discussion of prices (or Sraffa's prices of production for those so inclines) is no more complex than the labour theory of value and much more convincing empirically.

It would be nice to have a link to an authoritative description of these models; a superficial search of Wikipedia doesn't yield anything particularly illuminating.

The labor theory of value

Maxine Udall asks,

Could I get [an English PhD student] to explain coherently the labor theory of value, please? Or if not explain it, point me to a reliable way of identifying the value of labor as opposed to the value of capital across all the production processes that exist today (under my naive assumption that incentives matter so there probably has to be some return to capital if we're hoping to deploy it in a way that serves us all well)?

I'm not an English PhD student (and I probably won't be a Political Science/Economics PhD student for some years). And I don't know if I can explain the labor theory of value, or even Marx's theory. I think I can, however, explain a reasonably coherent labor theory of value.

As I see it, my labor theory of value is an ideal theory, in the sense of a partial explanation excluding certain distorting or complicating conditions. In much the same sense, the theory of gravity is — on the surface of the Earth — an ideal theory that ignores, however ubiquitous, the complicating conditions of aerodynamics. Even though it's obviously not the case that airplanes actually fall towards the surface of the Earth accelerating at 10m/s², gravity and gravity alone does indeed exert a force or the airplane that must somehow be counteracted.

The ideal theory is that absent complicating factors, commodities produced for exchange will trade according to the total amount of socially necessary abstract labor time consumed in their production.

The abstract labor time is actual physical human time spent creating the commodity modified by subjective and objective factors. The subjective factors discuss the "inherent undesirability" of a particular task: an hour spent cleaning a sewer or doing manual labor in the hot sun is generally considered more inherently undesirable than sitting in an air conditioned office typing at a keyboard. The objective factors discuss the "intensity" of the work: if everything else being equal Alice can create twice as many widgets as Bob in an hour's time, then Alice is putting in twice as many hours as Bob of abstract labor time.

It is typically the case (with notable exceptions) that many different firms (or individuals) act as suppliers of a commodity in a non-trivial market. These individuals will typically produce the same or similar goods by consuming different amounts of abstract labor time. The socially necessary labor time is a statistical property of the individual labor times, specifically the labor time actually used by the least efficient firm producing the commodity at the market clearing price. Firms which produce the commodity more efficiently receive something of a premium; firms which would produce the commodity less efficiently go bankrupt and are eliminated.

The total amount of socially necessary labor time is simply the sum of all the socially necessary abstract labor time consumed in producing the good, including all time spent creating capital and performing lower- or higher-level managerial and administrative tasks, including transaction costs. We consume labor time to create factories and equipment; we consume labor time to train and educate skilled workers, managers and administrators. It is not the case (at least under my labor theory of value) that we make a distinction between the value of capital and labor: capital requires labor to produce and has the value of the labor used to provide the capital. The distinction is more precisely captured by contrasting the value labor with the value of the ownership of capital, independently of its (labor) cost of creation.

The labor theory of value is most important, I think, when looking at the dichotomy between labor and labor power, i.e. the difference between the total amount of socially necessary labor time required to create a commodity vs. the total socially necessary labor time required to create labor time, i.e. the difference between the amount of labor necessary to create a commodity vs. the amount of labor necessary to feed, clothe, house, etc. a worker. We see a surplus economic growth when the cost of labor power is lower than the labor produced by that cost.

As I noted at the beginning, my labor theory of value is an ideal theory, and it might be the case that complicating factors are not merely ubiquitous but actually desirable — analogously, airplanes cannot fly without the "complicating factor" of aerodynamics.

Specifically, we must make decisions about how much labor to allocate directly to the production of commodities that will be directly consumed in the short term, and how much labor to allocate to investment and creation of capital to improve productivity in the medium and long term. I suspect that absent these complicating factors, a market based exclusively or ideally on the trade of socially necessary would "naturally" invest very little in future productivity.

The Labor Theory of Value

The Labor Theory of Value (LTV) holds that the price of a commodity is determined by the amount of actual labor required to produce that commodity.

There are a couple of quibbles that can easily be addressed.

The LTV talks explicitly about price, not use-value. A commodity that takes twice as much labor to produce as another is not necessarily twice as useful or inherently valuable the other commodity. The LTV says only that if some item is actually traded for some other item (i.e. presuming the use-value of the items justifies the trade, and therefore makes them commodities), the relative magnitude of the trade will be determined by the amount of labor necessary to produce the items. If it's worth trading hats for shoes, and it takes twice as long to make a pair of shoes as to make a hat, then one pair of shoes will be traded for two hats.

All the quantities in the LTV are not individual but statistical quantities, and they are all relative to the physical means of production actually in use. "The amount of labor necessary to produce a commodity" is a statistical property of how much labor is necessary to produce all the shoes in a particular economy. Hence Marx explicitly qualifies his version of the LTV by talking about the socially necessary labor time.

All labor is not the same, even restricting "labor" to time spent producing commodities of known price and use-value. Labor differs in intensity, desirability, training, education and marginal utility* (i.e. the time spent making the first widget creates more use-value than the time spent creating the last marginally useful widget). Again, Marx explicitly qualifies his version of the LTV by talking about the abstract labor time. If, for example, it were half as desirable to make hats as shoes (perhaps because of the obnoxious fumes), then the abstract labor time necessary to create a hat would be twice the actual labor time, and one hats would trade for one pair of shoes. Similarly, because it takes an additional seven to ten years (and a considerable amount of labor) to train a physician, the abstract labor time of an hour of a physician's actual labor is also magnified.

Also, the Marginal Utility Theory of Value (MUTV) does not contradict the LTV. The MUTV specifies which statistical properties of labor time constitute the price.

These quibbles notwithstanding, the LTV is, of course, not even close to being true, at least not by itself. For example, it's implausible to believe that in 2007 more than ten times more labor* was required to build a house in Sunnyvale, CA than in Youngstown, OH. It's implausible to believe that a Macintosh computer takes twice as much labor to build as a similarly configured Windows computer.

*National Association of Realtors

The best way, I think, to view the LTV is as a candidate "ideal" theory in the same sense as Newton's First Law of Motion. Neither bodies on Earth nor celestial bodies ever travel in straight lines at constant velocity. In a similar sense, the LTV can be recast with the proviso: In the absence of external economic forces, the price of a commodity is determined by the amount of socially necessary abstract labor time necessary to produce that commodity.

Of course, simply saying that the LTV is an "ideal" theory does not make it true, any more than calling Newton's First Law of Motion an ideal theory makes it true. There are specific scientific techniques that we can bring to bear on ideal theories to gain confidence in their truth.

It's important to understand that Newton never observed an object traveling in a straight line at constant velocity. The "net force" Newton was most interested in, of course, was gravity. Newton never actually observed one body exerting a net force on another body. The First Law of Motion (inertia) is explicitly contradicted by observation, and its primary modifier (which turns inertia into an complete* theory) was also not observable. (Worse yet, Newton had no clue how one body could actually exert a gravitational force on another.)

*At least regarding celestial bodies, which aren't affected by air resistance and aerodynamics, and leaving aside General Relativity for the time being.

We cannot justify inertia on "philosophical" grounds. The elegance and aesthetic appeal of the logical derivation from first principles is irrelevant. The "obvious" or intuitive appeal of those first principles is irrelevant. How can we empirically justify the FLM and the theory of gravity?

If we simply "induce" laws of motion from celestial bodies and bodies on the Earth, we end up with one law of motion for Mercury, one for Venus, one for the Sun, one for the Moon, etc., etc. and yet another for bodies on the surface of the Earth. (Curiously, we have (not counting aerodynamics) only one law of motion for all objects on the Earth's surface.) But if we hypothesize "unobservable" inertia and gravity, we end up with one law of motion which takes two independently observable* parameters: mass and distance. We cannot simplify all the motions of the celestial bodies without assuming inertia and gravity.

*More-or-less observable (and more directly observable than inertia and gravity). Density does not vary that much, and we can get a reasonable estimate of mass and distance from apparent size.

(It is a separate philosophical issue whether this sort of substantial simplification is at all epistemically relevant.)

If we consider LTV as an "ideal" partial theory, can we do the same sort of thing? There are a number of scientific tools available to us for testing the LTV.

The first tool is a general correlation. Correlation is not causation, but lack of correlation falsifies hypothetical causation. And there is indeed an apparent general correlation between actual labor time and price: jet airliners require more labor time per unit than houses, which require more labor time than cars, which require than computers, which require more than hamburgers, which require more than jellybeans, and the money prices show the same inequalities.

We can eliminate or control for "external" forces: Houses might vary in price between Sunnyvale and Youngstown without regard to labor time, but the difference in price of two houses in Sunnyvale or two houses in Youngstown will correlate more strongly to the difference in the amount of labor actually required to build the houses. A computer shipped by Amazon.com (i.e. a non-location-dependent commodity) to Sunnyvale will have almost exactly the same price as one shipped to Youngstown. (In a similar sense, inertia is more directly observable for bodies moving in nearly frictionless environments at right angles to the force of gravity.) The difference in price of two Windows computers will be more correlated to the difference in actual labor time, as will the difference in price of two Mac computers.

Better yet, we can independently observe "external" economic forces — geographical location, network effects, monopolies and monopsonies, etc. — and we can observe that two commodities with similar independently observable externalities will have similar "distortions" to the LTV.

Therefore we can conclude that the LTV + externalities has a similar empirical justification to inertia + gravity, and similar confidence is scientifically warranted in both.