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1、ChapterEconomicDynamicsandIntegralCalculusThetermdynamics.asappliedtoeconomicanalysis,hashaddifferentmeaningsatdiffer•enttimesandfordifferenteconomisb,tInstandardusagetoday,hnwe'cr,thetermreferstothetypeofanalysisinwhichtheobjectiseithertotraceandstudyth.:spel~ifictimepathsoft
2、hevari,lhlcsortodeterminewhether,givensufficienttirne.thci:.Cvariableswilltendtoconvergetocertain(equilibrium)values.Thistypeofinformationisimportantbecauseitfillsamajorgapthatmarredourstudyofstaticsandcomparativestatics.[11thelatter,wealwaysmakethearbitraryassumptionthatthepro
3、cc$i)ofeconomicadjustmentinevitablyleadstoanequilibrium.Inadynamicanalysis,thequestionof"attainability"istlbesquarelyfaced,ratherthanas~u1TIedaway.Onesalientfeatureofdynamicanalysisisthedatingofthevariables,whichintroducesthccxplicitconsiderationoftimeintothepicture.Thiscanbed
4、oneintwoways:timel~anbeconsiden::deitherasacontinuOllsvariableorasadiscretevariable.Intheformercase,somethingiHhappeningtothevariableateaehpoinroftime(slichasincontinuousiotl:rel>tcompounding);whereasinthelatter,thevariableundergoesach~mgeonlyoncewithinaperiodoftime(e.g.,intere
5、stisaddedonlyattheendofevery6months).Oneofthesetimec~mecptsmaybemoreappropriatethantheotherincertaincontcxts.Weshalldiscussfirstthecontinuous~timecase,towhichthemathematicaltechnlquc~ofintegralcalculusanddifferentialequuliunsarepertincnt.Later,inChaps.17and1R,weshallturntothedi
6、screte-timecase,whichutilize~themethodsofdifferenccequaliof/s.14.1DynamicsandIntegrationInastaticmodel,generallyspeaking,theproblemistofindthc-aluesoftheendogenousvariablesthatsatisfysomespecifiedequilibriumcondition(s),Appliedtothecontextofoptimizationmodels,thetaskbecomesone
7、offindingthevaluesofthechoicevariablesthatmaximize(orminimize)aspecificobjectivefunctionwiththefirst-ordercondi•tionservingastheeqUJlil:mumcondition.Inadynamicmodel,bycontrast,theproblemIFrittMachlup,"StaticsandDynamics:Kaleidosr;:opir;:Words,"SouthernEwnomicjournal,October1959
8、,pp_91-110;reprintedinMIlChlup,EssaysonEconomicSemanti
