What precisely is Marx’s argument in Das Kapital is subject to interpretation, for Das Kapital was a work pregnant with meaning. Which is why Marx has had manifold interpreters with very different views as to what “Marxism” constitutes. On the other hand, I think it is true that–even if (as I believe) the precise meaning of the labor theory of value depends on the interpretation of the dialectical movement of Das Kapital (whose movement is only founded upon but does not end with LTV)–we can nonetheless briefly parse out Marx’s elementary scientific use of LTV.
The use, roughly, is just this: The value of the commodity, on average, determines the price of the commodity. The value of the commodity is determined by two things: the value of the raw material used to produce the commodity (which includes also, e.g. the value of the machines that is “used up” in the production process) + the value of the labor. The value of the labor can therefore be empirically determined by comparing, in general, the average price of the material and the average price of the commodity.
Now, profit comes from the difference between what the worker is paid and the value of the labor. So, to sketch this out, roughly, in an equation as Marx had done (but, in this case, with different variables): C = V + L, and L = W + S. V is the raw materials (roughly speaking), L is labor, W is wages, and S is profit.
It was Marx’s argument that the worker was not remunerated L (the real value of his labor), but W, because the capitalist had obtained total domination over the means of production through a series of historical struggles (struggles which continue in the third world to the present day), forcing the laborer to work for W (rather than L) or starve. But this struggle was mystified through the ahistorical ideologies of bourgeois apologetic economics. (Now, marginalism is not such an economics; the ideological struggle has already been won, and economics is not any longer concerned with explaining the origins of wealth).
Now, the theory of surplus value (or: the theory of exploitation) was Marx’s theoretical contribution to economics, not the labor theory of value as such. And it was upon the theory of surplus value that his economic theory was based–which is why his discussion of the theory of surplus value comes at the beginning of Das Kapital and is not the conclusion. To any serious reading of the work, his central point in Das Kapital is not the injustice of exploitation: this is a fundamentally misreading of Marx’s work–and a violence, at that. There is no central point of Das Kapital as such–it is a scientific study of capitalism, a scientific study even of the possibility of bourgeois theories of capitalism, and a scientific study of the contradictions within capitalism.
To those who say that Marx’s theory is normative, and take this as a weakness: Tell me of a scientific theory that is not normative. For, does not even the most basic scientific statement, “All roses are red,” tell you to not to search for white roses, and that the search for white roses is perverse? Does not the notion that all men evolved from an ape-like ancestor circumscribe a whole constellation of possible values, or at the very least demand their reorientation? Does not the neo-mechanism of modern physics imply something about free will and responsibility? The charge of the value-ladenness of Marx’s theory is not a refutation of the theory, any less (or more) than it is for any other theory that has implications for human action. This move is a sleight of hand and a fallacy when serious engagement with the ideas is refused.
Last, to those who claim that Marx does not account for a difference between value and price: this is patently false. He devotes no small amount of space to discussing the discrepancy between value and price, and discusses a few circumstances when this could occur. But Marx’s point is that, except for very brief periods of time and for certain specific individuals–under normal conditions of capitalism (i.e. not under monopoly, etc.), value = price. And as far as the price of, say, a guitar played by Elvis or a da Vinci painting: this is an industry, with its advertisers, and its fervent devotees–a long, laborious history responsible for the production of a reputation–where communication produces value in images as industry produces value in automobiles; it is an industry in which, in a word, a lot of work is done on the commodities after the fact of their creation. It would indeed be more damning to the labor theory of value if the work that is done on behalf of art, or any other novel commodity, were not to affect its price.
But the power of the labor theory of value, while it can be used to predict prices, is the role it plays in understanding the dynamics of capitalism and the place of modern people within it. For everything else, I let you have your neo-marginalism; I am sure it is quite effective for what it does, but it is addressed to a whole different set of questions and is not therefore in principle exclusive to the labor theory of value, except as far as camps and polemics are concerned. But for all its power at predicting prices, it will never and can never give the full story of the real origin of those prices.