The Quantity Equations and Duality

Abstract

So far, I have considered productive economies in a stationary state. At the end of each production period, the value of the physical surplus (over and above inter-industry requirements to maintain next period’s outputs at this period’s levels) is allocated between wages and profits, all of which is consumed. That is, the level of new investments (in the form of advances of means of production) is zero. Retain all the assumptions made in the stationary state analysis except that referring to a constant labour force or population; instead, assume that the labour force grows at rate ϱ in each period. Hitherto, the net outputs, F₁ and F₂ (which, in a stationary state, can be thought of as consumption) have been taken as exogenous; I now assume not only exogeneity but also constancy of consumption, the latter in the sense of consumption per head. Thus, I shall concentrate on those features resulting solely from the introduction of a growing labour force with a constant technology and constant consumption per head. To maintain constant consumption per head with a growing labour force, production of each commodity must be expanded at rate ϱ. If next period’s production has to be (1+ϱ) times this period’s, it follows that the advances of means of production made at the end of this period (for inter-industry uses next period) must be (1+ϱ) times the advances made at the end of last period (for uses this period).