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1、TheFirm:ComparativeStaticsMicroEconomicsProductionOptimisationTheFirmandtheMarketComparativeStaticsComparativeStaticsOptimisationTheFirmandtheMarketProductionTheFirmOverview......wederivethefirm'sreactionstochangesinitsenvironment.Thesearetheresponsefunctions.Wewillexam
2、inethreetypesofthem,treatingthefirmasa......BlackBoxthefirmMovingonfromtheoptimum...thefirmoutputlevel;inputdemandsmarketpricesHowitworks...UsethefactthatthefirmisanoptimiserBehaviourcanbepredictedbynecessaryandsufficientconditionsforoptimumTheFOCcanbesolvedtoyieldbehav
3、iouralresponsefunctions.TheirpropertiesderivefromthesolutionfunctionThefirmasa“blackbox”TheFirmProductionOutputSupplyOrdinaryInputDemandOptimisationComparativeStaticsTheFirmandtheMarketOutputSupplyConditionalInputDemandOrdinaryInputDemandblackboxproblemsChooseztominimis
4、eSwizimi=1Q￡G(z)...subjecttotheproductionconstraint...z30...andtheobviousnon-negativityconditionsThesolutiontothefirst-stageproblem...C(w,Q):=min?wizivectorofinputpricesSpecifiedoutputleveland,presumably...Yieldsminimisedcostasafunctionofexogenousvariables...oneforeacho
5、ftheminputsz1*=H1(w,Q)z2*=H2(w,Q)............zm*=Hm(w,Q)üyt...optimalinputdemandsasafunctionofexogenousvariablesdemandforinputi,conditionalonoutputQWeneedtoexaminethefirststageoftheoptimisationprocesszi*=Hi(w,Q)Afunctionofinputprices...andoutputlevelconditionalinputdema
6、ndfunction(ourfirstresponsefunction)ResultdependsonshapeofZz1z2z1z2z1z2z1z2z2z1Taketheconventionalcase...Maptheoptimuminto(z1,w1)-spacez2z1w1z1Startwithanarbitraryvalueofw1...Doitagainforalowervalueofw1......andagaintoget...H1(w,Q)theconditionaldemandcurveInthe"conventi
7、onal"case......theconstraintsetisconvex,withasmoothboundaryWefindthesolutionisacontinuousmap......thatissinglevalued.PointstonoteResultdependsonshapeofZz1z2z1z2z1z2z1z2Z(Q)_2z2z1Whataboutthenon-convexcase...?againmaptheoptimuminto(z1,w1)-spaceZ(Q)_2w1z2z1z1...nowtryaver
8、ylowvalueofw1Butwhathappensinbetween?ademandcorrespondenceNonconvexZ:jumpsinz*w1z1nopriceyieldsasolutionheremu
