On dynamic price formation in the course of capital reallocation driven by differential rates of profit: strict conservation of value supports Karl Marx's theory

Abstract

We develop a dynamic three-sector model in which Marx's aggregate equalities (total price equals total value and total profit equals total surplus value) are treated as strict conservation constraints throughout capital reallocation and technical diffusion. Three price-value coefficients are determined by the two aggregate equalities and a closure that sets one sector's price-based profit rate equal to the contemporaneous value-based average (the anchor). Before innovation, capital inflow expands the receiving sector's output and, under both anchors, lowers its unit price and excess profitability. This endogenous fall in price as output rises supports a two-timescale reading: demand-related price movements may precede slower adjustment through capital mobility. A labour-saving, capital-intensifying innovation generates temporary extra surplus value, revalues committed capital, and changes the economy-wide profit rate. At constant real wages, the final uniform rate rises, consistent with Okishio's theorem. When real wages rise sufficiently to keep aggregate exploitation approximately constant, the organic composition increases and the final rate falls. Strict aggregate conservation is computationally coherent and yields distinct transitional predictions under explicit closure and wage assumptions.