伦敦经济学院高微讲义-企业理论(1).ppt

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1、TheFirm:OptimisationMicroEconomics2001/2ProductionOptimisationTheFirmComparativeStaticsTheFirmandtheMarketComparativeStaticsTheFirmandtheMarketProductionOverviewObjectivesConstraintsMethod-Profitmaximisation?-Technology;other-2-stageoptimisationLet'smakeaquicklistofthecomponentso

2、fastandardoptimisationproblem.Let'salsolookaheadtothewaywewilldoitforthefirm...Theoptimisationproblem...andquantitieswiPpriceofinputipriceofoutputziQamountofinputiamountofoutputUsetheinformationonprices...PQ-Swizimi=1Profits:PQRevenue:Swizimi=1Costofinputs:Soweget...Tosetup...…th

3、eobjectiveofthefirmPQ-Swizimi=1-=+Swizimi=1PQTheobjectiveofthefirmAsimpledefinitionofprofitsChooseQandztomaximiseP:=PQ-Swizimi=1Q£G(z)...subjecttotheproductionconstraint...Q³0z³0...andsomeprettyobviousconditions:Optimisation:thestandardapproachYoucan’thavenegativeinputsYoucan’tha

4、venegativeoutputSetupaLagrangeantotakecareoftheconstraintsBangouttheFirstOrderConditions(FOC)Checkoutsecond-orderconditionssufficiencynecessityUsingstandardmethods...FOC:theFirst-OrderConditionsL(...)¶¶zFirstorderconditionsareusedoverandoverinoptimisationproblemsaswewillsee...L(.

5、..)=0TheLagrangeanDifferentiateTheFirmProductionCostminimisationOptimisationComparativeStaticsTheFirmandtheMarketProfitmaximisationProfitmaximisationTwostagesofoptimisationSwizimi=1PickatargetoutputlevelQTakeasgiventhemarketpricesofinputsw(andofoutputP)Maximiseprofits......bymini

6、misingcostsStage1optimisationForagivensetofinputpricesw......thisisthesetofpointszininputspace......thatyieldagivenleveloffactorcost.Theseformahyperplane(straightline)......becauseofthesimpleexpressionforfactorcostWeintroducetheisocostSwizimi=1Swizimi=1z2z1increasingcostw1z1+w2z2

7、=c(constant)w1z1+w2z2=c'w1z1+w2z2=c"Iso-costlinesz2z1warning-infeasible!!z*Whatconditionholdsatexactlythispoint??Cost-minimisation_______=Gi(z)wiGj(z)wjinputMRTS=priceratioIfbothiandjareinuseandMRTSisdefined...Whatifwechangedtheassumptionsabouttechnology?implicitprice=marketprice

8、z2z1{Whatwouldhappeniftheinput-requireme