Some Properties of a Dynamic Leontief System with a Spectrum of Techniques

Abstract

Tlis article was written independently of Solow's [13] but is closely related to it. Under some plausible assumptions the author discusses various stability properties of a dynamic input-output system wNith a spectrum of techniques. Those economists who are interested in game theory, linear programming and input-output analysis may be charmed by Mrs. Robinson's model [9], a bor(derline model between von Neumann's theory of growth [8] and Marx's theory of reproduction. It is shown that her solution of a golden age is a particular solution of the dynamic Leontief model. INTERINDUSTRY ANALYSIS of the Leontief type is concerned with systems in whiclh the products of economic factors (materials, machines, labour, etc.) are themselves used as factors to produce further goods. Dynamic Leontief models include at least one good entering production repeatedly in more than one period (capital good), whereas static models comprise only goods which cease to exist once they are used up in further production (current goods). This paper deals with a dynamic Leontief model, i.e., the length of life of at least one good is assumed to be greater than unit time. In Sections 1 and 2 we discuss the time paths of prices and outputs, and we reach the following main results: (1) the long-run equilibrium prices have global stability; (2) the stationary solutions for outputs are necessarily unstable; (3) there is a balanced growth solution for the deviations of outputs from the stationary state; and (4) this balanced growth solution is unstable