Applications of numerical computation methods in microeconomic theory

Abstract

The solution of mathematical problems by numerical analysis is a large, intricate subject in its own right, and the substance-of many Ph. D. theses in mathematics. The advancement of numerical analysis and computer technology are clearly not mutually exclusive. Moreover this combination through the growth in computer software facilities is' easily within reach of a researcher with no expertise in either numerical analysis or computer programming. In particular the Numerical Algorithms Group (NAG) based in Oxford provides a library of subroutines for incorporation into source programmes across a broad spectrum of mathematics. The relevance of this development for the economist lies with the considerable scope for providing quantitative evaluations of microeconomic models outside of traditional statistical methods. To justify such a claim the thesis develops a number of applications from microeconomic theory: imperfect information in a non-sequential search framework; optimum tax with endogenous wages; a two sector general equilibrium model of union and non-union wage rate determination; Chamberlin's welfare ideal; and a quantity setting duopoly analysis of the structure conduct performance paradigm. It is hoped that the insights gained from such diverse topics will convince the reader as to the appropriateness of applying numerical computing to microeconomic questions in general, and the usefulness of the NAG software in particular