Value Conservation with Effective Demand: Resolution of the Transformation Problem in a Dynamic Framework[La conservation de la valeur sous contrainte de demande effective : une résolution dynamique du problème de la transformation Innovation et Baisse tendancielle du Taux de Profit]

We revisit the classical transformation problem by showing that Marx's aggregate equalities— that total value equals total price, and total surplus value equals total profit—are not mere accounting identities but express conservation laws central to the labor theory of value. These laws can hold if values are defined as socially necessary labor constrained by effective demand. We develop a multi-sector model where price formation is underdetermined, and market dynamics (e.g., competition, marketing, trends) resolve the indeterminacy among possible price configurations. Simulating capital reallocation following a cost-reducing innovation, we find that the average profit rate may decline due to rising organic composition—even under constant or slightly increasing real wages—seemingly contradicting Okishio's theorem. This contradiction stems not from a flaw in the theorem's logic, but from its static assumptions, particularly the neglect of transitional dynamics and demand constraints. In all simulations, the rate of exploitation rises, yet this is not always sufficient to prevent a falling profit rate. In a two-sector version of the model, we derive a structural identity: the ratio of capital allocations (W₁/W₂) equals the ratio of constant to variable capital (C/V). This highlights the rigid interdependence between Departments I and II in Marx's reproduction schemes, offering a new perspective on classical debates about accumulation and sectoral imbalance, notably those between Luxemburg and Bauer (1913). Our results provide a consistent, dynamic, and demand-constrained resolution to the transformation problem—one that remains faithful to the core of Marx's value theory.