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1、ChapterTheNatureofMathematicalEconomicsMathematicaleconomicsisnotadistinctbranchofeC(loomicsinthesensethatpublicfi•nanceorinternationaltradeis.Rather,itisanapproachtoeconomicanalysis,inwhichthecconomi~tmakesuseofmathematicalsymbolsinthestatementoj'theproblemandalsodrawsUpl111knownmathematicalthe
2、oremstoaidinreasoning.Asfarastilespecificsub•jectmattaofanalysisgoes,itcanbemicro-ormacroeconomictheory,publicfillJ.ncc,urbaneconomies,orwhatnot.Usingthetermmathematicaleconomicsinthebroadestpossiblesense,onemayVCT)'wellsaythateveryelementarytcxtb(lOkofeconomicstoday~xemplifiesmathematicaleco•no
3、micsin~otarasgeometricalmethod~arefrequentlyutilizedLaderivetheoreticalresults.:viorecommonly,however,mathematicaleconomicsisreservedtodescribecasesempl(lY•iogmathematicaltechniqllesbeyond~implegeometry,sllchasmatrixalgebra,differentialandintegralcalculws,differentialeqllation~!diHerenceequation
4、s,etc.Itisthepurpose()fthisbooktointroducethereadertothemostfundamentalaspc:ctsofthesemathematicalmetbods·thoseencountereddailyinthecurrenteconomicliterature.1.1MathematicalversusNonmathematicalEconomicsSincemathematicaleconomicsismerelyanapproachtoeconomicanalysis,itshouldnotanddoesnotfundament
5、allydifferfromthennnmathematicalapproachtoeCllnOlTIlCanaly·sis.Thepurposeofanytheoreticalanalysis,regardlessoftheapproach,isalvaystodcrivcasetofconclusionsortheoremsfromagiven!-.ctofassumptionsorpostulat(:sviaaprocessofreasoning,Themujordifferencebetween"mathematica1economics"and"literaryeco·no
6、mies"istvofold:Fir~t,inthefiJTmer,theassumptionsandconclusionsarestatedinmathematicalsymbolHratherthanwordsandinequationsratherthansentences.Second,inplaceofliterarylogi.::,useismadeofmathematicaltheorems~ofwhiehtherecxi~t~anabundancetodrawupon-inthereasoningprocess,inasmuchassymbolsandwordsare
7、reallycquivalents(witnessthefactthatsymbolsareusuallydefinedinwords),itmatterslit•tlewhichischosenovertheother.Butitisperhapsbeyonddisputethatsymbolsaremoreconvenienttou~cindeductivereasoning,andcertainlyarcmoreconducivetoco
