Basic Mathematics for Economists

536 Pages·2003·3.042 MB·English

by  Mike Rosser

Basic Mathematics for Economists
Economicsstudentswillwelcometheneweditionofthisexcellenttextbook.Given
thatmanystudentscomeintoeconomicscourseswithouthavingstudiedmathematics
foranumberofyears,thisclearlywrittenbookwillhelptodevelopquantitativeskills
ineventheleastnumeratestudentuptotherequiredlevelforageneralEconomics
orBusinessStudiescourse.Allexplanationsofmathematicalconceptsaresetoutin
thecontextofapplicationsineconomics.
Thisneweditionincorporatesseveralnewfeatures,includingnewsectionson:
• financialmathematics
• continuousgrowth
• matrixalgebra
Improvedpedagogicalfeatures,suchaslearningobjectivesandendofchapterques-
tions, along with an overall example-led format and the use of Microsoft Excel for
relevantapplicationsmeanthatthistextbookwillcontinuetobeapopularchoicefor
bothstudentsandtheirlecturers.
MikeRosserisPrincipalLecturerinEconomicsintheBusinessSchoolatCoventry
University.
© 1993, 2003 Mike Rosser
Basic Mathematics for
Economists
Second Edition
Mike Rosser
© 1993, 2003 Mike Rosser
Firsteditionpublished1993
byRoutledge
Thiseditionpublished2003
byRoutledge
11NewFetterLane,LondonEC4P4EE
SimultaneouslypublishedintheUSAandCanada
byRoutledge
29West35thStreet,NewYork,NY10001
RoutledgeisanimprintoftheTaylor&FrancisGroup
This edition published in the Taylor & Francis e-Library, 2003.
©1993,2003MikeRosser
Allrightsreserved.Nopartofthisbookmaybereprintedorreproducedor
utilisedinanyformorbyanyelectronic,mechanical,orothermeans,now
knownorhereafterinvented,includingphotocopyingandrecording,orinany
informationstorageorretrievalsystem,withoutpermissioninwritingfrom
thepublishers.
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationData
Acatalogrecordforthisbookhasbeenrequested
ISBN 0-203-42263-5 Master e-book ISBN
ISBN 0-203-42439-5 (Adobe eReader Format)
ISBN0–415–26783–8(hbk)
ISBN0–415–26784–6(pbk)
© 1993, 2003 Mike Rosser
Contents
Preface
PrefacetoSecondEdition
Acknowledgements
1 Introduction
1.1 Whystudymathematics?
1.2 Calculatorsandcomputers
1.3 Usingthebook
2 Arithmetic
2.1 Revisionofbasicconcepts
2.2 Multipleoperations
2.3 Brackets
2.4 Fractions
2.5 Elasticityofdemand
2.6 Decimals
2.7 Negativenumbers
2.8 Powers
2.9 Rootsandfractionalpowers
2.10 Logarithms
3 Introductiontoalgebra
3.1 Representation
3.2 Evaluation
3.3 Simplification:additionandsubtraction
3.4 Simplification:multiplication
3.5 Simplification:factorizing
3.6 Simplification:division
3.7 Solvingsimpleequations
(cid:1)
3.8 Thesummationsign
3.9 Inequalitysigns
© 1993, 2003 Mike Rosser
4 Graphsandfunctions
4.1 Functions
4.2 Inversefunctions
4.3 Graphsoflinearfunctions
4.4 Fittinglinearfunctions
4.5 Slope
4.6 Budgetconstraints
4.7 Non-linearfunctions
4.8 Compositefunctions
4.9 UsingExceltoplotfunctions
4.10 Functionswithtwoindependentvariables
4.11 Summingfunctionshorizontally
5 Linearequations
5.1 Simultaneouslinearequationsystems
5.2 Solvingsimultaneouslinearequations
5.3 Graphicalsolution
5.4 Equatingtosamevariable
5.5 Substitution
5.6 Rowoperations
5.7 Morethantwounknowns
5.8 Whichmethod?
5.9 Comparativestaticsandthereducedformof
aneconomicmodel
5.10 Pricediscrimination
5.11 Multiplantmonopoly
Appendix:linearprogramming
6 Quadraticequations
6.1 Solvingquadraticequations
6.2 Graphicalsolution
6.3 Factorization
6.4 Thequadraticformula
6.5 Quadraticsimultaneousequations
6.6 Polynomials
7 Financialmathematics:series,timeandinvestment
7.1 Discreteandcontinuousgrowth
7.2 Interest
7.3 Partyearinvestmentandtheannualequivalentrate
7.4 Timeperiods,initialamountsandinterestrates
7.5 Investmentappraisal:netpresentvalue
7.6 Theinternalrateofreturn
7.7 Geometricseriesandannuities
© 1993, 2003 Mike Rosser
7.8 Perpetualannuities
7.9 Loanrepayments
7.10 Otherapplicationsofgrowthanddecline
8 Introductiontocalculus
8.1 Thedifferentialcalculus
8.2 Rulesfordifferentiation
8.3 Marginalrevenueandtotalrevenue
8.4 Marginalcostandtotalcost
8.5 Profitmaximization
8.6 Respecifyingfunctions
8.7 Pointelasticityofdemand
8.8 Taxyield
8.9 TheKeynesianmultiplier
9 Unconstrainedoptimization
9.1 First-orderconditionsforamaximum
9.2 Second-orderconditionforamaximum
9.3 Second-orderconditionforaminimum
9.4 Summaryofsecond-orderconditions
9.5 Profitmaximization
9.6 Inventorycontrol
9.7 Comparativestaticeffectsoftaxes
10 Partialdifferentiation
10.1 Partialdifferentiationandthemarginalproduct
10.2 Furtherapplicationsofpartialdifferentiation
10.3 Second-orderpartialderivatives
10.4 Unconstrainedoptimization:functionswithtwovariables
10.5 Totaldifferentialsandtotalderivatives
11 Constrainedoptimization
11.1 Constrainedoptimizationandresourceallocation
11.2 Constrainedoptimizationbysubstitution
11.3 TheLagrangemultiplier:constrainedmaximization
withtwovariables
11.4 TheLagrangemultiplier:second-orderconditions
11.5 ConstrainedminimizationusingtheLagrangemultiplier
11.6 Constrainedoptimizationwithmorethantwovariables
12 Furthertopicsincalculus
12.1 Overview
12.2 Thechainrule
12.3 Theproductrule
12.4 Thequotientrule
© 1993, 2003 Mike Rosser
12.5 Individuallaboursupply
12.6 Integration
12.7 Definiteintegrals
13 Dynamicsanddifferenceequations
13.1 Dynamiceconomicanalysis
13.2 Thecobweb:iterativesolutions
13.3 Thecobweb:differenceequationsolutions
13.4 ThelaggedKeynesianmacroeconomicmodel
13.5 Duopolypriceadjustment
14 Exponentialfunctions,continuousgrowthand
differentialequations
14.1 Continuousgrowthandtheexponentialfunction
14.2 Accumulatedfinalvaluesaftercontinuousgrowth
14.3 Continuousgrowthratesandinitialamounts
14.4 Naturallogarithms
14.5 Differentiationoflogarithmicfunctions
14.6 Continuoustimeanddifferentialequations
14.7 Solutionofhomogeneousdifferentialequations
14.8 Solutionofnon-homogeneousdifferentialequations
14.9 Continuousadjustmentofmarketprice
14.10 ContinuousadjustmentinaKeynesianmacroeconomicmodel
15 Matrixalgebra
15.1 Introductiontomatricesandvectors
15.2 Basicprinciplesofmatrixmultiplication
15.3 Matrixmultiplication–thegeneralcase
15.4 Thematrixinverseandthesolutionof
simultaneousequations
15.5 Determinants
15.6 Minors,cofactorsandtheLaplaceexpansion
15.7 Thetransposematrix,thecofactormatrix,theadjoint
andthematrixinverseformula
15.8 Applicationofthematrixinversetothesolutionof
linearsimultaneousequations
15.9 Cramer’srule
15.10 Second-orderconditionsandtheHessianmatrix
15.11 ConstrainedoptimizationandtheborderedHessian
Answers
Symbolsandterminology
© 1993, 2003 Mike Rosser