Von Neumann’s Model of Economic Growth

Abstract

In the present chapter we shall discuss the known dynamical model of the economic growth and few problems which can be formulated within the framework of von Neumann’s classical model [33,16]. These problems are the problem of maximizing technological and minimizing economic growth rates, the problem of exit to the path of a balanced growth and the problem of minimizing transition time taken by the economy to reach a given set of terminal states from a given initial state. The state of economy at a given instant t will be defined as the vector X(t) = (X₁ (t),...,X_m(t)) whose components are the amounts of goods imparted to the economy at a given instant. The intensity with which technological processes are used should naturally be considered as a parameter controlling the growth rate of the economy. The change in state X(t) will be considered in discreet time, that is, we shall consider a sequence of states X(0) ,X(1),... and call the transformation X(t) → X(t+1) a production cycle. We shall see that an analogue of von Neumann’s model is a chain of successively connected physical models for systems of linear equalities and inequalities.