Monday, April 06, 2015

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.

2 comments:

  1. I've been reading your series of posts on the attempted formalization of the Marxian LTV, and I'm finding them problematic. Some of them are just fairly elementary mistakes, like defining Profit as "The difference between the Labor Time and the Cost of Labor Power employed by a firm," which I'm sure a lot of Marxists are going to tear their hair out because that's actually the definition of surplus value.

    It's also not true that the LTV as presented in Marx's Capital is an equilibrium theory at all. Or so the Marxists associated with the TSSI hold, and as far as I can tell, they don't seem to be mistaken on the interpretative issue in question.

    I'm not sure that the corn model proves anything against the LTV, since the idea that a general rate of profit contradicts the LTV seems obvious on the one hand, but once one realises that the nature of capital is to flow wherever there is a higher profit rate, and that this will average out the profit rate, the problem is revealed to be a pseudo-problem and that were holding tacit assumptions that were question-begging in nature.

    There's also something a little bit suspicious about using corn models of any kind in discussing the LTV, because if we're careful enough to remember what value is, the idea of a one-commodity model makes little sense, since value and markets have a division of labour and hence numerous types of commodity as their presupposition.

    Finally, to go back to your post on definitions again, the justification for SNLT as marginal cost relies on an equivocation of "producers operating at a loss." To be sure, if the average labour-time needed to produce a commodity is 3 hours and a given capitalist can only produce it in 4 hours, he's losing out on one hour of labour-time. But as long as he is not losing all of the labour-time embodied in the surplus-value, he is not operating at a loss in the normal capitalist sense. Though, it must be remarked, that in Volume 3 Marx DOES discuss conditions under which the market value is determined by the labour-time of the least efficient producers.

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  2. I've been reading your series of posts on the attempted formalization of the Marxian LTV, and I'm finding them problematic. Some of them are just fairly elementary mistakes, like defining Profit as "The difference between the Labor Time and the Cost of Labor Power employed by a firm," which I'm sure a lot of Marxists are going to tear their hair out because that's actually the definition of surplus value.

    So what is Marx's definition of profit? I do not have an encyclopedic command of Marx's work.

    It's also not true that the LTV as presented in Marx's Capital is an equilibrium theory at all. Or so the Marxists associated with the TSSI hold, and as far as I can tell, they don't seem to be mistaken on the interpretative issue in question.

    No? Why do you think not?

    I'm not sure that the corn model proves anything against the LTV...

    No model proves anything.

    ... once one realises that the nature of capital is to flow wherever there is a higher profit rate, and that this will average out the profit rate, the problem is revealed to be a pseudo-problem and that were holding tacit assumptions that were question-begging in nature.

    Is it a pseudo-problem? Why do you think so? What are the question-begging assumptions?

    There's also something a little bit suspicious about using corn models of any kind in discussing the LTV, because if we're careful enough to remember what value is, the idea of a one-commodity model makes little sense, since value and markets have a division of labour and hence numerous types of commodity as their presupposition.

    [Terry Gilliam voice] "It's only a model."

    Can you make a better model?

    To be sure, if the average labour-time needed to produce a commodity is 3 hours and a given capitalist can only produce it in 4 hours, he's losing out on one hour of labour-time. But as long as he is not losing all of the labour-time embodied in the surplus-value, he is not operating at a loss in the normal capitalist sense.

    It is perhaps more accurate to say the marginal producer is making the minimum amount of profit, i.e. (although you might object) extracting the minimum acceptable amount of surplus labor.

    Is this an important point?

    Though, it must be remarked, that in Volume 3 Marx DOES discuss conditions under which the market value is determined by the labour-time of the least efficient producers.

    Indeed? In all sincerity, I invite you to share your interpretation of Marx's thoughts in this matter; I have not read vols. 2 and 3 of Capital with any rigor.

    ReplyDelete

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