On the controllability of nonlinear economic systems with delay: The Italian example

Abstract

The dynamic model of some key economic indicators – the gross national product, GNP, interest rate, R, employment, L, value of capital stock, k, prices, p, and cumulative balance of payment, E – are derived here from mathematical and economic principles. The model is described by a hereditary ordinary differential equation, a nonlinear delay differential pursuit game of neutral type. The quarry control-solidarity or government intervention consists of money supply, M, government budget, net expenditure, taxation, T, exchange rate, e, tariffs, foreign credit fo, distance between trading partners or trading arrangements d, or preferential arrangement. The pursuer control (private initiative) consists of autonomous private consumption, investment, net export, labor productivity, money wage rate w, autonomous money demand m, income autonomous consumption y 10. Conditions are established for the variables of the economic indicators to be controllable from one initial function to a terminal function, in particular, employment, national income and prices can be controlled from one arbitrary vector function to another when the controls of the system are subject to scarcity, i.e., to constraints. Conditions for controllability are presented. Our model is tested with data on Italian economy. This paper opens up the hope that full employment, high income growth is compatible with low prices and low inflation, provided the control matrix has full rank, i.e., the existing controls are fully effectively used.