It does no such thing. The Marxist labour theory of value says much more than this.
In volume 1 of Capital, the “law of value” expounded there was later described by Marx in these terms:
“The assumption that the commodities of the various spheres of production are sold at their value implies, of course, only that their value is the center of gravity around which prices fluctuate, and around which their rise and fall tends to an equilibrium.” (Marx 1909: 208–210).This is something very much more than the simple claim that prices are correlated with labour costs.
In fact, Eugen von Böhm-Bawerk gave the right response to the latter view made by Marxists over a century ago:
“In various parts of the third volume Marx claims for the law of value that it ‘governs the movement of prices,’ and he considers that this is proved by the fact that where the working time necessary for the production of the commodities decreases, there also prices fall; and that where it increases prices also rise, other circumstances remaining equal.The mere citation of empirical studies that show a correlation between hours worked/wage-bill data of workers and prices of commodities does not vindicate Marx.
This conclusion also rests on an error of logic so obvious that one wonders Marx did not perceive it himself. That in the case of ‘other circumstances remaining equal’ prices rise and fall according to the amount of labor expended proves clearly neither more nor less than that labor is one factor in determining prices. It proves, therefore, a fact upon which all the world is agreed, an opinion not peculiar to Marx, but one acknowledged and taught by the classical and ‘vulgar economists.’ But by his law of value Marx had asserted much more.” (Böhm-Bawerk 1949: 39).
Prices are correlated with labour costs because labour costs are often a very important component of prices. No sensible person denies this.
But so are energy costs for many industries. And so are non-labour factor input costs. You’d find a correlation there too, especially in capital/energy-intensive industries. Furthermore, if workers demand wage rises without their hours changing we would also find a correlation with prices.
Böhm-Bawerk, Eugen von. 1949. “Karl Marx and the Close of His System,” in Paul. M. Sweezy (ed.), Karl Marx and the Close of His System and Böhm-Bawerk’s Criticism of Marx. August M. Kelley, New York. 3–120.
Marx, Karl. 1909. Capital. A Critique of Political Economy (vol. 3; trans. Ernst Untermann from 1st German edn.). Charles H. Kerr & Co., Chicago.