Marx's theory of value doesn't explain equilibrium prices, or at least, it doesn't explain them directly. As per Volume III equilibrium prices are equal to the cost-price (c+V) of the commodity plus the average rate of profit. Price and value are only really equal at the level of society as a whole.
This arises from competition between capitals. Competition tends to establish an average rate of profit, since a higher rate of profit in one branch of industry will lead to more capital investment in that industry, increasing production relative to demand, and a lower than average rate of profit will lead to the opposite. This is a problem for the theory of value, because a strict relationship between price and value would mean that, given a constant rate of surplus-value, industries with a lower than average capital composition (that is to say, a lower rate of constant to variable capital) would have higher rates of profit, which obviously isn't the case. If it was, it would produce some weird phenomena, capitalists would probably tend to invest in industries with lower organic compositions of capital, which contradicts the tendency stated by Marx for the organic composition to rise (which is a thing that actually happens) bringing about a fall in the rate of profit.
This leads to the problem of 'transforming' values into prices of production. The problem is not just a mathematical but a theoretical one. If long run prices can be adequately explained by cost-price plus the average rate of profit, the question arises as why we even need a theory of a value which needs to be 'transformed' into real prices in the first place. A lot of commentators, starting from Bohm-Bawerk onwards, have claimed that there is a contradiction between the model of capitalism Marx gives in Volume I (where prices are for the most part equal to value) and the model he gives in Volume III (where prices are equal to their 'price of production'), and that the theoretical constructs of Volume I are basically useless - a product of Marx's naive enthusiasm for the classical economists perhaps, or of a certain moral and sentimental belief in the value of human labour, or perhaps a conscious recognition that the theory of value must somehow be maintained in order to maintain the theory of exploitation, which was his real concern.
The important thing to bear in mind is that fundamentally, Marx's value theory is not a theory of prices but a theory of the social relationships of capitalist production. There's even a letter where he weighs in on the value controversy, claiming that even if you skipped the first chapter, his description of the social relationships of capitalist production should be enough to help you understand the meaning of the theory. Marx was aware of the transformation problem as early as 1847 in his Poverty of Philosophy, and describes the essential procedure of transformation in the Grundrisse, ten years before the publication of Volume I. It is not a case of a Marx who elaborated a theory in Volume I which he then later ran up against difficulties with, but a case of the fundamental difference between the Marxist and Ricardian understanding of value.
The movement of classical political economy up to Ricardo was a move towards an ever more rigorous reduction of the various categories of economics to value, the substance of which is human labour in the abstract. But classical political economy never examined what Marx calls the 'value-form'. Commodities don't just walk around with the labour time it took to produce them marked on them, they walk around with a price, their value is always expressed in the form of the relationship of one commodity to another.
But this is a circumstance that is utterly peculiar. It is evident that commodities, as inanimate objects, cannot really have relationships with one another, only human beings can. What Marx the undertakes is to examine the historically specific form of society in which the products of human labour take the form of value, and the relationships between people take on the fantastic, but prosaically real appearance of relationships between things.
In every form of society, it is a requirement that human labour time is apportioned between various activities. Even Robinson Crusoe on his island has to divide his time between foraging for food, hunting, building a shelter and so on, for example. In capitalist society, this division of human labour is accomplished through market exchange, "The effect is the same as if the different individuals had amalgamated their labour-time and allocated different portions of the labour-time at their joint disposal to the various use-values."
Or as he expresses it in the Grundrisse:
The reciprocal and all-sided dependance of individuals who are indifferent to one another forms their social connection. This social bond is expressed in exchange value, by means of which alone each individual's own activity or his product becomes an activity or a product for him.
Gavin Hughes
Time rules man. "Time is everything, man is nothing; he is, at the most, time's carcass." (Poverty of Philosophy) In a society of mutually indifferent individuals, all producing in isolation from one another, the social character of their labour can only express itself in the form of value relations. The form of appearance of value, as a relationship between commodities, is a necessary form of appearance. Exchange is not a process in which the producers relate to one another as real individuals, it is a process in which they relate to one another as owners of commodities, and each commodity represents for its owner nothing other than human labour in the abstract.
Because Ricardo and Smith could never step outside bourgeois society to see it's historically specific nature, and the conditions in which the products of human labour become 'values' in the first place, they could never solve the problems that the theory of value throws up with regards to the discrepancy between value and price (a discrepancy which is more than just a question of oscillation around a point of equilibrium, but has to do with the fundamental nature of competition under capitalism, which always reduces profit down to an average rate).
Marx was not a Ricardian. His theory of value is, in some sense, essentially the same as his theory of fetishism or alienated labour.
As someone who has not quite finished their reading of Capital, this is my view. Marx was opposed to exploitation first, and then came up with the theory of value in order to argue within the context of economic discourse at the time, that workers are exploited.
To the capitalist, workers and machines are just inputs to production. I reject the idea that only labor creates value - both labor and capital inputs create value. My objection to capitalism is that I don't like being treated like a machine where you input A and are expected to output B, meanwhile being disciplined to make sure I am an efficient machine.
Doesn't this solve the transformation problem? If both workers and capital/machine inputs create value, then there is no contradiction where more labor-intensive firms would have to have higher profit. In my understanding, labor is just another machine input, and which particular inputs will depend on the nature of the good being produced.
Of course if we take this strategy then that means giving up on a lot of the technical details of Marx's argument, and resorting to a more humanistic critique of exploitation. Which is fine by me, because I think that there is a lot of Scientism present in Marx and he needs to be re-read and reinterpreted to fit the present day conditions of capitalism.
