simultaneous differential equations and difference equations

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1、ChapterSimultaneousDifferentialEquationsandDifferenceEquationsHeretofore,ourdis..:ussionofeconomicdynamicsha~beenconfinedtotheanalysisofasingledynamic(differentialordifference)equation.Intheprescntchapter,methodsforanalyzingasystemofsimultaneousdynamicequationsareintroduced.Becausethiswouldentailt

2、hehandlingofsClcraJvariablesatthesametime,youmightanticipateagreatdealofncwcomplications.ButthetruthisthatmuchofwhatW(Jhavealreadylearnedaboutsingledynamiccquation~canbereadilyextendedto:.ystemsofsimultaneousdynamicequations.~)rimlancc,thesolutionofadynamicsystemwouldstillconsistofasetorparticul

3、arintegralSorparticularsolutions(intcrtempnraiequilibriumvaluesofthevariousvariables)andcomplemenfaryfunctions(deviationsfromequilibriums).Thecomplemcn•taryfunctionswouldstillbebasedonthereducedequations,i.e.,thehomogeneousversionsoftheequationsinthesystem.Andthedynamicstabilityofthesystemwouldsti

4、lldependonthesigns(ifdHrerentialequationsystem)OJ'theabsolutevalues(ifdifferenceequationsystem)oftheehilraetcristicrootsinthecomplementaryfunctions.Thustheproblemoradynamksy~temisonlyslightlym(lfecomplieatcdthanthatorasingledynamicequation.19.1TheGenesisofDynamicSystemsTherearetwOgeneralv"aysinwhi

5、chadynamicsystemcancomeintobeing.[tmaycm~anatefromaghensetorinternctingp

6、sthatofamultisec·tormodelwhereeachsector.asdctclibedbyaJynamicequation,impingesonatIcastoneoftheothersectors.Adynamicversionoftheinput-outputmodel.forexampk,cuuldin•olveflindustrieswhoseoutputchangesproducedynamicrepercussinnsontheotherin·592dustries.Thusitconstitute~auynamicsystem.Similarly,ady

7、namicgeneral-equilibriumChapter19Slmultal1eousPijfer<'l1tiulEqllallol1sandD(lfen.~nceEquations593marketmodelwouldinvolvefJcommoditiesthatarcinterrelatedintheirpriceadjustments.Thus,thereisagainadynamicsystem.Howe