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This volume presents mathematical formulas and theorems commonly used in economics. It offers the first grouping of this material for a specifically economist audience, and it includes formulas like Roy’s identity and Leibniz's rule.
The practice of economics requires a wide ranging knowledge of formulas from math ematics and mathematical economics. The selection of results from mathematics included in handbooks for chemistry and physics ill suits economists. There is no concise reporting of results in economics. With this volume, we hope to present a formulary, targeted to the needs of students as weIl as the working economist. It grew out of a collection of mathematical formulas for economists originally made by Professor B. Thalberg and used for many years by Scandinavian students and economists. The formulary has 32 chapters, covering calculus and other often used mathemat ics; programming and optimization theory; economic theory of the consumer and the firm; risk, finance, and growth theory; non-cooperative game theory; and elementary statistical theory. The book contains just the formulas and the minimum commcntary needed to re-learn the mathematics involved. We have endeavored to state theorems at the level of generality economists might find useful. By and large, we state results for n-dimensional Euclidean space, even when the results are more generally true. In contrast to thc economic maxim, "everything is twice more continuously differentiable than it needs to be", we have listed the regularity conditions for theorems to be true. We hope that we have achieved a level of explication that is accurate and useful without being pedantic.
A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.
This highly-successful manual is the first to present in one volume all of the mathematical formulas and theorems commonly used by economists. It will thus be indispensable to economists, researchers, and students who are in need of exact statements of mathematical results. The third edition has been extensively revised and contains more than 250 new formulas, as well as many new figures.
This text offers a presentation of the mathematics required to tackle problems in economic analysis. After a review of the fundamentals of sets, numbers, and functions, it covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics.
The use of Mathematica in performing computations takes the tediousness out of solving mathematical problems. The book is self-contained, and provides the material to learn the mathematics as well as programming skills to learn the Mathematica language.
Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory
Mathematical Statistics for Economics and Business, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics. The selection of topics in this textbook is designed to provide students with a conceptual foundation that will facilitate a substantial understanding of statistical applications in these subjects. This new edition has been updated throughout and now also includes a downloadable Student Answer Manual containing detailed solutions to half of the over 300 end-of-chapter problems. After introducing the concepts of probability, random variables, and probability density functions, the author develops the key concepts of mathematical statistics, most notably: expectation, sampling, asymptotics, and the main families of distributions. The latter half of the book is then devoted to the theories of estimation and hypothesis testing with associated examples and problems that indicate their wide applicability in economics and business. Features of the new edition include: a reorganization of topic flow and presentation to facilitate reading and understanding; inclusion of additional topics of relevance to statistics and econometric applications; a more streamlined and simple-to-understand notation for multiple integration and multiple summation over general sets or vector arguments; updated examples; new end-of-chapter problems; a solution manual for students; a comprehensive answer manual for instructors; and a theorem and definition map. This book has evolved from numerous graduate courses in mathematical statistics and econometrics taught by the author, and will be ideal for students beginning graduate study as well as for advanced undergraduates.
Presents mathematical furmulas and theorems common to economics and applied mathematics. It serves as an excellent reference for students and professionals.
MATHEMATICAL ANALYSIS FOR ECONOMISTS by R. G. D. ALLEN. Originally published in 1937. FOREWORD; THIS book, which is based on a series of lectures given at the London School of Economics annually since 1931, aims at providing a course of pure mathematics developed in the directions most useful to students of economics. At each stage the mathematical methods described are used in the elucidation of problems of economic theory. Illustrative examples are added to all chapters and it is hoped that the reader, in solving them, will become familiar with the mathematical tools and with their applications to concrete economic problems. The method of treatment rules out any attempt at a systematic development of mathematical economic theory but the essentials of such a theory are to be found either in the text or in the examples. I hope that the book will be useful to readers of different types. The earlier chapters are intended primarily for the student with no mathematical equipment other than that obtained, possibly many years ago, from a matriculation course. Such a student may need to accustom himself to the application of the elementary methods before proceeding to the more powerful processes described in the later chapters. The more advanced reader may use the early sections for purposes of revision and pass on quickly to the later work. The experienced mathematical economist may find the book as a whole of service for reference and discover new points in some of the chapters. I have received helpful advice and criticism from many mathe maticians and economists. I am particularly indebted to Professor A. L. Bowley and to Dr. J. Marschak and the book includes numerous modifications made as a result of their suggestions on reading the original manuscript. I am also indebted to Mr. G. J. Nash who has read the proofs and has detected a number of slips in my construction of the examples. R. G. D. ALLEN THE LONDON SCHOOL OF ECONOMICS October, 1937. Contents include: FOREWORD ----------v A SHORT BIBLIOGRAPHY - ..... xiv THE USE OF GREEK LETTERS IN MATHEMATICAL ANALYSIS - - ...... xvi I. NUMBERS AND VARIABLES -------1 1.1 Introduction ---------1 1.2 Numbers of various types ------3 1.3 The real number system -------6 1.4 Continuous and discontinuous variables ... - 7 1.5 Quantities and their measurement ..... 9 1.0 Units of measurement - - - - - - - 13 1.7 Derived quantities - - - - - - - - 14 1.8 The location of points in space - - - - - 1G 1.9 Va viable points and their co-ordinates 20 EXAMPLES 1 The measurement of quantities graphical methods ---------23 . JpOJ ACTIONS AND THEIR DIAGRAMMATIC REPRESENTATION 28 2.1 Definition and examples of functions 28 2.2 The graphs of functions - - - - - - - 32 2.3 Functions and curves - - - - - - - 3 5 2.4 Classification of functions - - - - - - 38 2.5 Function types - - - - - - - - 41 2.6 The symbolic representation of functions of any form - 45 2.7 The diagrammatic method - - - - - - 48 2.8 The solution of equations in one variable 50 2.9 Simultaneous equations in two variables 54 EXAMPLES II Functions and graphs the solutionjof equa- tions ......... 57 III. ELEMENTARY ANALYTICAL GEOMETRY 61 3.1 Introduction ......... 61 3.2 The gradient of a straight line ..... 03 3.3 The equation of a straight line - - - 66 viii CONTENTS CHAP. 3.4 The parabola 09 3.5 The rectangular hyperbola - - - - - - 72 3.6 The circle 75 3.7 Curve classes and curve systems . - ... 76 3.8 An economic problem in analytical geometry 80 EXAMPLES III--The straight line curves and curve systems 82 IV...
