最新伦敦经济学院高微讲义-企业理论(1)教学讲义ppt.ppt

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1、伦敦经济学院高微讲义-企业理论(1)ProductionOptimisationTheFirmComparativeStaticsTheFirmandtheMarketComparativeStaticsTheFirmandtheMarketProductionOverviewObjectivesConstraintsMethod-Profitmaximisation?-Technology;other-2-stageoptimisationLet'smakeaquicklistofthecompon

2、entsofastandardoptimisationproblem.Let'salsolookaheadtothewaywewilldoitforthefirm...TheoptimisationproblemChooseQandztomaximiseP:=PQ-Swizimi=1Q£G(z)...subjecttotheproductionconstraint...Q³0z³0...andsomeprettyobviousconditions:Optimisation:thestandardapp

3、roachYoucan’thavenegativeinputsYoucan’thavenegativeoutputSetupaLagrangeantotakecareoftheconstraintsBangouttheFirstOrderConditions(FOC)Checkoutsecond-orderconditionssufficiencynecessityUsingstandardmethods...FOC:theFirst-OrderConditionsL(...)¶¶zFirstorde

4、rconditionsareusedoverandoverinoptimisationproblemsaswewillsee...L(...)=0TheLagrangeanDifferentiateTheFirmProductionCostminimisationOptimisationComparativeStaticsTheFirmandtheMarketProfitmaximisationProfitmaximisationTwostagesofoptimisationSwizimi=1Pick

5、atargetoutputlevelQTakeasgiventhemarketpricesofinputsw(andofoutputP)Maximiseprofits......byminimisingcostsStage1optimisationForagivensetofinputpricesw......thisisthesetofpointszininputspace......thatyieldagivenleveloffactorcost.Theseformahyperplane(stra

6、ightline)......becauseofthesimpleexpressionforfactorcostWeintroducetheisocostSwizimi=1Swizimi=1z2z1increasingcostw1z1+w2z2=c(constant)w1z1+w2z2=c'w1z1+w2z2=c"Iso-costlinesz2z1warning-infeasible!!z*Whatconditionholdsatexactlythispoint??Cost-minimisation_

7、______=Gi(z)wiGj(z)wjinputMRTS=priceratioIfbothiandjareinuseandMRTSisdefined...Whatifwechangedtheassumptionsabouttechnology?implicitprice=marketpricez2z1{Whatwouldhappeniftheinput-requirementsetlookedlikethis?Anyz-valueinthissetofpointsiscost-minimising

8、z2z1z*…orthis?Therecouldbemultiplesolutions.z**Butnotethatthere’snosolutionpointbetweenz*andz**.z2z1z*…orthis?MRTS21isundefinedexactlyatz*.Butz*iscost-minimisingpointforgivenQandallfinitevaluesofw1/w2z2z1z*Andwhathappenshere?Here