经济数学和金融数学

内容简介

[

片断：
WeshallrefertothisasthedemandsetDfortheparticulargood.Ineconomics
youwilllearnreasonswhyitoughttolookratherlikeitdoesinourdiagram,
asmooth,downwardslopingcurve.
SupposethedemandsetDcontainsthepoint(30,5).Thismeansthatwhen:
thepricep=5isgiven,thenthecorrespondingdemandwillbeforq=30
units.Ingeneral.providedDhasthe’right’shape,asinFigure1.1,thenfor
eachvalueofptherewillbeauniquelydeterminedvalueofq.Inthissituation
wesaythatDdeterminesademandfunction,qD.ThevaluewrittenqD(p)is
thequantitywhichwouldbesoldifthepricewerep,sothatqD(5)=30,for
example.
Thereisanotherwayoflookingattherelationshipbetweenqandp.Ifwe
supposethatthequantityqisgiven,thenthevalueofpforwhich(q,p)is
inthedemandsetDisthepricethatconsumerswouldbepreparedtopay
ifqisthequantityavailable.Fromthisviewpointweareexpressingpin
termsofq,insteadoftheotherwayround.WewritepD(q)forthevalueofp
correspondingtoagivenq,andwecallpDtheinversedemandfunction.
Example(continued)TakingthesamesetDasbefore,wecannowrearrange
theequationofthelineintheformp=(125-6q)/8.Sotheinversedemand
functionis
Nextweturntothesupplyside.WeassumethatthereisasupplysetS
consistingofthosepairs(q,p)forwhichqwouldbetheamountsuppliedto
themarketifthepncewerep.Therearegoodeconomicreasonsforsupposing
thatShasthegeneralformshowninFigure1.2.

]

目录

Contents1.Mathematicalmodelsineconomics1.1Introduction1.2Amodelofthemarket1.3Marketequilibrium1.4Excisetax1.5CommentsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises2.Mathematicaltermsandnotations2.1Sets2.2Functions2.3Compositefunctions2.4GraphsandequationsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises3.Sequences,recurrences,limits3.1Sequences3.2Thefirst-orderrecurrence3.3Limits3.4SpecialcasesWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises4.Theelementsoffinance4.1Interestandcapitalgrowth4.2Incomegeneration4.3TheintervalofcompoundingWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises5.Thecobwebmodel5.1Howstableismarketequilibrium?5.2Anexample5.3Thegenerallinearcase5.4EconomicimerpretationWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises6.Introductiontocalculus6.1Therateofchangeofafunction6.2Rulesforfindingthederivative6.3Marginalcostasaderivative6.4Thederivativeofacompositefunction6.5Thederivativeot’aninversefunctionWorkedexamplesMaintopics/KeytermsnotationsandtbrmulaeExercises7.Somespecialfunctions7.1Powers7.2Theexponentialfunctionanditsproperties7.3Continuouscompoundingofinterest7.4Thelogarithmfunction7.5Trigonometricalt’unctionsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises8.Introductiontooptimisation8.1Profitmaximisation8.2Criticalpoints8.3Optimisationinaninterval8.4Infiniteintervals.WorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises9.Thederivativeineconomics-19.1Elasticityofdemand9.2Profitmaximisationagain9.3CompetitionversusmonopolyWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises10.Thederivativeineconomics–1110.1Theefficientsmallfirm10.2StartupandbreakevenpointsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises11.Partialderivatives11.1Functionsofseveralvariables11.2Partialderivatives11.3ThechainruleWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises12Applicationsofpartialderivatives12.1Functionsdefinedimplicitly12.2Thederivativeofanimplicitfunction12.3Contoursandisoquants12.4ScaleeffectsandhomogeneousfunctionsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises13Optimisationintwovariables13.1Profitmaximisationagain13.2Howpricesarerelatedtoquantities13.3Criticalpoints13.4Maxima,minima,andsaddlepoints13.5Classificationofcriticalpoints-introduction13.6TheclassificationofcriticalpointsingeneralWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises14.Vectorspreferencesandconvexity14.1Vectorsandbundles14.2Pricesandbudgets14.3Preferences,utility,andindifferencecurves14.4Linearandconvexcombinations14.5ChoosingoptimalbundlesWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises15.Matrixalgebra15.1Whatisamatrix?15.2Matrixmultiplication15.3HowtomakemoneywithmatricesWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises16.Linearequations-116.1Atwo-industry’economy16.2Linearequationsinmatrixform16.3Solutionsoflinearequationsbyrowoperations16.4TheechelonformingeneralWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises17.Linearequations-1117.1Consistentandinconsistentsystems17.2Therankofaconsistentsystem17.3Thegeneralsolutioninvectornotation17.4ArbitrageportfoliosandstatepricesWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises18.Inversematrices18.1Thesquarelinearsystem18.2Theinverseofasquarematrix18.3Calculationoftheinverse18.4Theinverseofa2x2matrix18.5IS-LManalysisWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises19.Theinput-outputmodel19.1Aneconomywithmanyindustries19.2Thetechnologymatrix,19.3Whyisthereasolution?.WorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises20.Determinants20.1Determinants20.2Thedeterminantasatestforinvertibility20.3Cramer’sruleWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises21.Constrainedoptimisacion21.1Theelementarytheoryofthefirm21.2ThemethodofLagrangemultipliers21.3Thecostfunction21.4Theefficientsmallfirmagain21.5TheCobb-DouglasfirmWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises22.Lagrangeansandtheconsumer22.1Lagrangeans:amoregeneralformulation22.2Theelementarytheoryoftheconsumer22.3Thepriceratioandthetangencycondition22.4Theconsumer’sdemandfunctions22.5TheindirectutilityfunctionWorkedexamplesMaintopics/Keyterms,notationsandformulaeExercises23.Second-orderrecurrenceequations23.1Asimplifiednationaleconomy23.2Dynamicsoftheeconomy23.3Linearhomogeneousrecurrences23.4Non-homogeneousrecurrencesWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises24.Macroeconomicapplications24.1Recurrenceequationsinpractice24.2Oscillatorysolutions24.3Businesscycles24.4ImprovedmodelsoftheeconomyWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises25Areasandintegrals25.1Theconsumersurplus25.2Theconceptofarea25.3Anti-derivativesandintegrals25.4Definiteintegrals25.4StandardintegralsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises26.Techniquesofintegration26.1Integrationbysubstitution26.2Definiteintegralsbysubstitution26.3Integrationbyparts26.4PartialfractionsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises27.First-orderdifferentialequations27.1Continuous-timemodels27.2Sometypesofdifferentialequations27.3Separabledifferentialequations27.4Acontinuous-timemodelofpriceadjustmentWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercises28.Second-orderdifferentialequations28.1Markettrendsandconsumerdemand28.2Linearequationswithconstantcoefficients28.3Solutionofhomogeneousequations28.4Non-homogeneousequations28.5BehaviourofsolutionsWorkedexamplesMaintopics/KeytermsnotationsandformulaeExercisesSolutionstoselectedexercisesIndex

封面

书名:经济数学和金融数学

作者:M.Anthony/等

页数:394

定价:¥65.0

出版社:世界图书出版公司

出版日期:1998-08-01

ISBN:9787506239233

PDF电子书大小:97MB 高清扫描完整版