Okishio's theorem

Okishio's theorem states that cost-reducing technical change raises the equilibrium rate of profit when the real wage remains unchanged. It is a challenge to Marx’s account of a tendency for profit rates to fall.

Connect

Input–output model: A mathematical representation of production that tracks goods used as inputs to produce other goods. Okishio's theorem models production techniques as input requirements across industries.
Nobuo Okishio: A Japanese Marxian economist who formulated the theorem in 1961. His formal result gives the theorem its name.
Marx's law of the tendency of the rate of profit to fall: Marx's argument that capitalist development tends to reduce the rate of profit despite counteracting influences. The theorem challenges a specific interpretation of this tendency, not every account of declining profitability.
Temporal equilibrium: An economic framework in which prices and quantities adjust through time rather than being fixed simultaneously. It changes how technical change and profit-rate movements are compared with the theorem's equilibrium result.
Production price: A price that allows a commodity's producer to earn the general rate of profit on invested capital. Competition establishes these prices after the new technique is adopted.
Marxian economics: An economic tradition that develops and critiques Karl Marx's analysis of capitalism. Okishio formulated the theorem within debates over Marx's account of capitalist accumulation.
Temporal single-system interpretation: An interpretation of Marx that determines prices and values over time within one interconnected system. Its defenders argue that Okishio's equilibrium price comparison does not refute Marx's temporal account.
Joint production: Production in which one process yields multiple outputs or by-products. Allowing joint products can complicate the conditions under which the theorem's result holds.
General rate of profit: The economy-wide rate of return that competition tends to equalize across industries. The theorem's conclusion concerns how this rate changes after technical innovation.
Capital (Marx): Karl Marx's critique of political economy, published in three volumes between 1867 and 1894. Marx's analysis of profit-rate decline supplied the claim Okishio's result challenged.