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Basic Mathematics for Economists

Basic Mathematics for EconomistsEconomics students will welcome the new edition of this excellent textbook. Giventhatmanystudentscomeintoeconomicsco urseswithouthavingstudiedmathematicsfora numberofyears, thisclearlywrittenbookwillhelptodevelopq uantitativeskillsin even the least numerate student up to the required level for a general Economicsor Business Studies course. All explanations of mathematical concepts are set out inthe context of applications in new edition incorporates several new features, including new sections on: financial Mathematics continuous growth matrix algebraImproved pedagogical features, such as learning objectives and end of chapter ques-tions, along with an overall example-led format and the use of Microsoft Excel forrelevant applications mean that this textbook will continue to be a popul

4 Graphsandfunctions 4.1 Functions 4.2 Inversefunctions 4.3 Graphsoflinearfunctions 4.4 Fittinglinearfunctions 4.5 Slope 4.6 Budgetconstraints 4.7 Non-linearfunctions

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Transcription of Basic Mathematics for Economists

1 Basic Mathematics for EconomistsEconomics students will welcome the new edition of this excellent textbook. Giventhatmanystudentscomeintoeconomicsco urseswithouthavingstudiedmathematicsfora numberofyears, thisclearlywrittenbookwillhelptodevelopq uantitativeskillsin even the least numerate student up to the required level for a general Economicsor Business Studies course. All explanations of mathematical concepts are set out inthe context of applications in new edition incorporates several new features, including new sections on: financial Mathematics continuous growth matrix algebraImproved pedagogical features, such as learning objectives and end of chapter ques-tions, along with an overall example-led format and the use of Microsoft Excel forrelevant applications mean that this textbook will continue to be a popular choice forboth students and their Rosseris Principal Lecturer in Economics in the Business School at CoventryUniversity.

2 1993, 2003 Mike RosserBasic Mathematics forEconomistsSecond EditionMike Rosser 1993, 2003 Mike RosserFirst edition published 1993by RoutledgeThis edition published 2003by Routledge11 New Fetter Lane, London EC4 P4 EESimultaneously published in the USA and Canadaby Routledge29 West 35th Street, New York, NY 10001 RoutledgeisanimprintoftheTaylor&FrancisG roup 1993, 2003 Mike RosserAll rights reserved. No part of this book may be reprinted or reproduced orutilised in any form or by any electronic, mechanical, or other means, nowknown or hereafter invented, including photocopying and recording, or in anyinformation storage or retrieval system, without permission in writing fromthe catalogue record for this book is available from the British LibraryLibraryofCongressCataloginginPubl icationDataA catalog record for this book has been requestedISBN 0 415 26783 8 (hbk)ISBN 0 415 26784 6(pbk)

3 This edition published in the Taylor & Francis e-Library, 0-203-42263-5 Master e-book ISBNISBN 0-203-42439-5 (Adobe eReader Format) 1993, 2003 Mike RosserContentsPrefacePreface to Second EditionAcknowledgements1 Why study Mathematics ? Calculators and Using the book2 Revision of Basic Multiple Elasticity of Negative Roots and fractional Logarithms3 Introduction to Simplification: addition and Simplification: Simplification: Simplification: Solving simple The summation sign Inequality signs 1993, 2003 Mike Rosser4 Graphs and Inverse Graphs of linear Fitting linear Budget Non-linear Composite Using Excel to plot Functions with two independent Summing functions horizontally 5 Linear Simultaneous linear equation Solving simultaneous linear Graphical Equating to same Row More than two Which method?

4 Comparative statics and the reduced form ofan economic Price Multiplant monopolyAppendix: linear programming6 Quadratic Solving quadratic Graphical The quadratic Quadratic simultaneous Polynomials7 Financial Mathematics : series, time and Discrete and continuous Part year investment and the annual equivalent Time periods, initial amounts and interest Investment appraisal: net present The internal rate of Geometric series and annuities 1993, 2003 Mike Perpetual Loan Other applications of growth and decline8 Introduction to The differential Rules for Marginal revenue and total Marginal cost and total Profit Respecifying Point elasticity of Tax The Keynesian multiplier9 Unconstrained First-order conditions for a Second-order condition for a Second-order condition for a Summary of second-order Profit Inventory Comparative static effects of taxes10 Partial Partial differentiation and the marginal

5 Further applications of partial Second-order partial Unconstrained optimization: functions with two Total differentials and total derivatives11 Constrained Constrained optimization and resource Constrained optimization by The Lagrange multiplier: constrained maximizationwith two The Lagrange multiplier: second-order Constrained minimization using the Lagrange Constrained optimization with more than two variables12 Further topics in The chain The product The quotient rule 1993, 2003 Mike Individual labour Definite integrals13 Dynamics and difference Dynamic economic The cobweb: iterative The cobweb.

6 Difference equation The lagged Keynesian macroeconomic Duopoly price adjustment14 Exponential functions, continuous growth anddifferential Continuous growth and the exponential Accumulated final values after continuous Continuous growth rates and initial Natural Differentiation of logarithmic Continuous time and differential Solution of homogeneous differential Solution of non-homogeneous differential Continuous adjustment of market Continuous adjustment in a Keynesian macroeconomic model1 5 Matrix Introduction to matrices and Basic principles of matrix Matrix multiplication the general

7 The matrix inverse and the solution ofsimultaneous Minors, cofactors and the Laplace The transpose matrix, the cofactor matrix, the adjointand the matrix inverse Application of the matrix inverse to the solution oflinear simultaneous Cramer s Second-order conditions and the Hessian Constrained optimization and the bordered HessianAnswersSymbols and terminology 1993, 2003 Mike RosserPrefaceOver half of the students who enrol on economics degree courses have not studied mathe-matics beyond GCSE or an equivalent level. These include many mature students whose lastencounter with algebra, or any other Mathematics beyond Basic arithmetic, is now a dim anddistant memory.

8 It is mainly for these students that this book is intended. It aims to developtheir mathematical ability up to the level required for a general economics degree course ( )orforamodulardegreecourseineconomicsand related subjects, such as business studies. To achieve this aim it has several , it provides a revision of arithmetical and algebraic methods that students probablystudied at school but have now largely forgotten. It is a misconception to assume that, justbecause a GCSE Mathematics syllabus includes certain topics, students who passed exami-nations on that syllabus two or more years ago are all still familiar with the material.

9 Theyusually require some revision exercises to jog their memories and to get into the habit ofusing the different mathematical techniques again. The first few chapters are mainly devotedto this revision, set out where possible in the context of applications in , this book introduces mathematical techniques that will be new to most problems in economics using these techniques as soon as possible so that they cansee how useful they are. Students are not required to work through unnecessary proofs, orwrestle with complicated special cases that they are unlikely ever to encounter again.

10 Forexample, when covering the topic of calculus, some other textbooks require students toplough through abstract theoretical applications of the technique of differentiation to everyconceivable type of function and special case before any mention of its uses in economicsis made. In this book, however, we introduce the Basic concept of differentiation ,such as the second-order conditions for optimization, partial differentiation, and the rulesfor differentiation of composite functions, are then gradually brought in over the next fewchapters, again in the context of economics , this book tries to cover those mathematical techniques that will be relevant to stu-dents economics degree programmes.


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