資源描述：
《經(jīng)典經(jīng)濟(jì)數(shù)學(xué)筆記》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在行業(yè)資料-天天文庫(kù)。
1、LectureNotesonMathematicsforEconomistsChien-FuCHOUSeptember2006ContentsLecture1StaticEconomicModelsandTheConceptofEquilibrium1Lecture2MatrixAlgebra5Lecture3VectorSpaceandLinearTransformation10Lecture4Determinant,InverseMatrix,andCramer’srule16Lecture5Di?erentialCalculusan
2、dComparativeStatics25Lecture6ComparativeStatics–Economicapplications36Lecture7Optimization44Lecture8Optimization–multivariatecase61Lecture9OptimizationwithequalityconstraintsandNonlinearProgramming74Lecture10GeneralEquilibriumandGameTheory8911StaticEconomicModelsandTheCon
3、ceptofEquilibriumHereweusethreeelementaryexamplestoillustratethegeneralstructureofaneco-nomicmodel.1.1PartialmarketequilibriummodelApartialmarketequilibriummodelisconstructedtoexplainthedeterminationofthepriceofacertaincommodity.Theabstractformofthemodelisasfollows.Qd=D(P
4、;a)Qs=S(P;a)Qd=Qs,Qd:quantitydemandedofthecommodityD(P;a):demandfunctionQs:quantitysuppliedtothemarketS(P;a):supplyfunctionP:marketpriceofthecommoditya:afactorthata?ectsdemandandsupplyEquilibrium:Aparticularstatethatcanbemaintained.Equilibriumconditions:Balanceofforcespre
5、vailinginthemodel.Substitutingthedemandandsupplyfunctions,wehaveD(P;a)=S(P;a).Foragivena,wecansolvethislastequationtoobtaintheequilibriumpriceP?asafunctionofa.Thenwecanstudyhowaa?ectsthemarketequilibriumpricebyinspectingthefunction.Example:D(P;a)=a2/P,S(P)=0.25P.a2/P?=0.2
6、5P??P?=2a,Q?=Q?=ds0.5a.1.2GeneralequilibriummodelUsually,marketsfordi?erentcommoditiesareinterrelated.Forexample,thepriceofpersonalcomputersisstronglyin?uencedbythesituationinthemarketofmicro-processors,thepriceofchickenmeatisrelatedtothesupplyofpork,etc.Therefore,wehavet
7、oanalyzeinterrelatedmarketswithinthesamemodeltobeabletocapturesuchinterrelationshipandthepartialequilibriummodelisextendedtothegeneralequilibriummodel.Inmicroeconomics,weevenattempttoincludeeverycommodity(includingmoney)inageneralequilibriummodel.Qd1=D1(P1,...,Pn;a)Qd2=D2
8、(P1,...,Pn;a)...Qdn=Dn(P1,...,Pn;a)Qs1=S1(P1,...,Pn;a)Qs2=S2(P1,...,Pn;a)Qsn=Sn(P1,...,Pn;a)Qd1=
