Goodness through optimal dynamics of the wealth of nations

Abstract

In this paper, we survey the mathematical theory of competitive an co-operative systems that monitor national interactions and economic systems. The dynamics are described by ordinary differential equations, functional differential equations and coupled partial differential equations. Conditions are given which guarantee finite time extinction, finite time unbounded growth, and persistence. These conditions are already available in the literature (Proceedings of the First World Congress of Nonlinear Analysis, 1992 Vol I–IV 359–368 Gruyler, Berlin; Appl. Anal. 57 (1995) 3–4, pp. 309–323; Math. Biosci. 118 (1993) 197; In: T.G. Hallam, S.A. Levin (Eds.), Mathematical Ecology, Biomathematics, Vol. 17, Biomathematics, Springer, Berlin, Heidelberg, 1986; Convex Structures and Economic Theory, Academic Press, New York, 1968; SIAM J. Math. Anal. 18 (1987) 642; Introduction to Differential Equation, Prentice-Hall, Englewood Cliffs, NJ, 1987; SIAM J. Appl. Math. 36 (1979) 421; Proc. Nat. Acad. Sci. USA 68 (1971) 980; SIAM J. Math. Anal. 24 (1993) 1331; The Passionate God, Paulist Press, New York, 1981; Nonlinear Parabolic and Elliptic Equation, Plenum Press, New York, 1992; Economic Theory and Social Justice, MacMillan, London, UK, 1999; Extinction in finite time of solutions to nonlinear absorption–diffusion equations, personal communication). The theory is applied to national wealth that is carefully defined. It is shown that the wealth of co-operating nations can grow unbounded and competing ones become extinct. Using the principle of “trickle down of wealth” and incorporating a strategy of internally generated wealth due to improved health and education, we derive the dynamics of wealth.