This book about mathematics and methodology for economics is the result of the lifelong experience of the authors. It is written for university students as well as for students of applied sciences. This self-contained book does not assume any previous knowledge of high school mathematics and helps understanding the basics of economic theory-building. Starting from set theory it thoroughly discusses linear and non-linear functions, differential equations, difference equations, and all necessary theoretical constructs for building sound economic models. The authors also present a solid introduction to linear optimisation and game theory using production systems. A detailed discussion on market equilibrium, in particular on Nash Equilibrium, and on non-linear optimisation is also provided. Throughout the book the student is well supplied with numerous examples, some 2000 problems and their solutions to apply the knowledge to economic theories and models.

First discussions on several topics of this book took place at a symposium held at the University of Karlsruhe (July 14 - 21, 1985). The book is divided into nine parts with the headings "Methodology and Methods" (4 papers), "Prices" (9), "Efficiency" (5), "Preferences" (7), "Quality" (2), "Inequality" (6), "Taxation" (6), "Aggregation" (6), and "Econometrics" (6). The topics range from the "equation of measurement", a functional equation which plays an important role in the subject, through various approaches to price, efficiency, inequality and tax progression measurement to results on consistency, efficiency and separability in aggregation, productivity measurement, cost functions, allocation inefficiencies, key sector indices, and testing of integrability conditions in econometrics. There are applications to the economies of the U.S.A., Japan and Germany. It contains also papers which deal with preferences, environmental quality and with noxiousness of substances.

The literature on economic problems connected with measuring and modelling of welfare and inequality has grown rapidly within the last decade. Since this literature is scattered throughout a great number of journals on economics, economic theory, econometrics, and statisties, it is difficult to get an adequate picture of the present state of the art. Therefore books should appear from time to time, which offer a representative cross-section of the latest results of research on: the subject. This book offers such material. It contains 54 articles by 84 authors from four of the five continents. Each paper has been reviewed by two referees. As a conse quence, the contributions of this book are revised versions, or, in many cases, revised revisions of the original papers. The book is divided into four parts. Part I: Measurement of Inequality and Poverty This part contains eleven papers on theory and empirical applications of inequa lity and/or poverty measures. Two contributions deal with, among other things, experimental findings on questions concerning the acceptance of distributional axioms. Part II: Taxation and Redistribution Distributional or, rather, redistributional aspects play an important role in Part II. The topics of the 14 papers included in this part range from tax progressivity and redistribution, allocative consequences of splitting under income taxation, and connections between income tax and cost-of-living indices to merit goods and welfarism as well as to welfare aspects of tax reforms."

This book about mathematics and methodology for economics is the result of the lifelong experience of the authors. It is written for university students as well as for students of applied sciences. This self-contained book does not assume any previous knowledge of high school mathematics and helps understanding the basics of economic theory-building. Starting from set theory it thoroughly discusses linear and non-linear functions, differential equations, difference equations, and all necessary theoretical constructs for building sound economic models. The authors also present a solid introduction to linear optimisation and game theory using production systems. A detailed discussion on market equilibrium, in particular on Nash Equilibrium, and on non-linear optimisation is also provided. Throughout the book the student is well supplied with numerous examples, some 2000 problems and their solutions to apply the knowledge to economic theories and models.