Marx and Engels explicitly denied that in reality total product-value would be equal to the total of production prices (see prices of production). Such an "accounting identity" was ruled out in the real world by continual variations in labour productivity and because, at any time, no competitive force existed that could exactly cancel out the difference between goods sold above value and goods sold below value.See e.g. chapter 49 in Capital Vol. 3, p. 972. See also Engels's letter to Conrad Schmidt dated March 12, 1895. It was also ruled out by the imperfections of the price-form itself, which, the fetishization of price statistics notwithstanding, permitted the expression of product-values only in an approximate way (see real prices and ideal prices). At best—Marx assumed—there was a reasonably close correspondence between total product-value and total production prices.Marx, Capital, Volume III, Penguin ed., p. 261. He believed economic fluctuations implied that if some products were sold below their value, this necessarily meant that other products were sold above their value, and vice versa.Karl Marx, Notes on Adolph Wagner's “Lehrbuch der politischen Ökonomie” (Second Edition), Volume I, 1879.
