A Dynamic Analysis of Structural Change in a Leontief Model

Abstract

1. The so-called Leontief model, originally static in character, is usually dynamized by introducing consumptionand productionlags, accelerators, growth of final demand, structural changes due to technological invention, and so on. In this article we are not concerned with consumption-lags, the acceleration principle, or the growth of final demand. Instead, we shall concentrate on structural changes due to technological invention on the assumption that the period of production of each good is one unit time. Since my analysis is dynamic, it will depart from the comparative statics approach to structural change as used by Professors Leontief, Simon and Rasmussen.2 The original version of this paper was written in mathematical form, but following the editor's suggestion, I have removed the armour of mathematics and attempted to explain my problems in plain language. All the propositions stated in the theorems below can be rigorously proved, but the mathematical demonstration is omitted. 2. The Leontief system consists of two sets of equations, the first describing the balance of input and output for all products, and the second the equality of costs and prices. Solving the first and the second sets, we obtain equilibrium outputs and equilibrium prices respectively. We assume that a national economy is divided into n industries each of which produces a single commodity. It is further assumed that the i-th industry can choose between ml different manufacturing processes or activities in producing commodity i. An activity is defined by a vector (with n + 1 components) stating the inputs of n commodities and of labour per unit output ;3 labour is indispensable, and