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Mathematical controllability theory of the growth of wealth of nations

  • Ethelbert N. Chukwu
Article

Abstract

Inspired on one hand, by a full Keynesian model and its IS-LM representation in equilibrium [28], [18, p.72], and on the other by the Kalecki [23], Goodwin [13] dynamics of income and capital stock, we derive a nonlinear functional differential equation of neutral type as the dynamics of the growth of wealth of nations. The functions which monitor an individual firm’s initiative or government interventions are carefully identified as control instruments in a differential game of pursuit. This is a reasonable setting [29, pp.79–91]. The nonlinear equations derived are generalizations of ordinary differential systems studied by Takayama [33, pp.685–706], Arrow [2, p.184], Knowles [26, p.3] and Isaacs [20], and the delay systems studied by Kalecki [23], Allen [1, p.254], and Cooke and Yorke [12]. Given an initial (capital/income) fluctuating endowment ϕ we investigate conditions on the systems parameters and on the private and public policy instruments which will guarantee that ϕ can be steered to some fixed (growing trend) target in some finite time. From the controllability theorems proved for hereditary systems, we derive universal laws for the control of growth of wealth of nations. These laws provide broad, starting, but obvious policy prescription for the growth of companies and for national economies. For example, it describes how big government interventions on the firms (in the form of monetary policy, public expenditure and taxation) must be relative to the firms autonomous consumption, export, investment, and real money demand (private initiative) to ensure the growth of capital stock to the given target. It also states when this growth is impossible. Fixed point theorems and argument from the theory of games of pursuit [16] are used.

Key words

firms solidarity strategy capital growth 

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Copyright information

© JJIAM Publishing Committee 1994

Authors and Affiliations

  • Ethelbert N. Chukwu
    • 1
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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