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# Introduction

DOI link for Introduction

Introduction book

# Introduction

DOI link for Introduction

Introduction book

## ABSTRACT

Our aim in this research monograph is to identify realistic dynamic models of the growth of wealth of nations. The dynamics are then examined for stability, controllability, and optimality when either time or effort (some time integral of the control) is to be minimized. The key fundamental idea in this book is controllability: from any initial state of Gross Domestic (National) Product, interest rate, employment, value of capital stock, prices and cumulative balance of payment, is it possible to attain another desirable target state? For example, is it possible to attain a state of paradise-high growth rate, low interest rate, full employment, high value of capital stock, low inflation, and zero, surplus or small value of cumulative balance of payment? It is important first of all to derive a credible economic model from accepted time series of economic variables and economic laws. The model of ordinary differential equations is considered in Chapters 1-5, and the hereditary dynamic models are treated in Chapter 6. Chapter 1 is an introductory mathematical theory of com petition and cooperation: the social environment for economic activity. The dynamic is either ordinary differential equation, functional differential equation, or parabolic partial differential equation when (density of) wealth is given a general definition in (1. 3. 1). It is discovered from our studies of existing mathematical research that competitive systems have either (at best) bounded dynamics or tend to extinction in finite time. For coop erative systems, Mierczynski [13] has proved that every solution converges to a positive equilibrium or leaves any compact set. Some generalizations exist through the work of Tang, Kuang, and Smith [21]. Solution of cooperative systems can either grow unbounded or (at worst) if bounded will converge to a positive equilibrium. There is no extinction; there is the possibility of a “stupendous orgy of mutuality, ” an unbounded growth for all concerned. The computer analysis of both the ordinary and the reaction diffusion equa tion are presented in Chapter 1. The philosophical and moral implications of Chapter 1 are explored in a book in preparation by the author: The Moral Basis o f Sustained Eco nomic Growth o f Nations. From the mathematics alone cooperative systems are prefer able. But there are limits placed by “individual’s initiative. ” This is taken up in Chapter 3.