微观经济学讲义(黄有光)6

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1、AdvancedMicroeconomicsTopic5:Production&CostPrimaryReadings:DL–Chapter2&JR–Chapter5Inthislecture,wewillpresentageneralframeworkofproductiontechnology.Wewillfocusonwhatchoicescouldbemade;andtheissueofwhatchoiceswouldbemadewillbedeferredtothenextlecturewhenwelookintothefirm’sbehaviour.Th

2、efirstpartwilldescribeproductionpossibilitiesinphysicalterms;whilethesecondpartwillrecastthisdescriptionintoacostfunctionframework.Thetreatmentinthislectureisabitabstractandquitegeneral.Youarerequiredtounderstandtherelevanceofthisabstractframeworkintermsofparticulartechnologicalprocess

3、es.5.1ProductionPossibilitySetsTherearemanywaystodescribethetechnologyofafirm,suchas,productionfunctions,graphs,orsystemsofinequalities.Butinmathematicalterm,theserepresentationscanallbeexpressedasaset.·Thefirmusesandproducesatotalofmcommodities.·AparticularproductionplanisyinRm:·yi>0i

4、mpliesthatanetamountyiofi-thcommodityisproduced;·yj<0impliesthatanetamount–yjofj-thcommodityisused;·yiscalledanetputvector.·ProductionpossibilitysetofafirmisasubsetYÌRm.AfirmmayselectanyvectoryÎYasitsproductionplan.PropertiesofProductionPossibilitySet·Closed:Ifthelimitofanyconvergingse

5、quenceofvectorsinYisinY.·Convex:Convexcombinationsofitselementsremaintobeinside.·Freedisposal:IfyÎYimpliesthaty’ÎYforally’£y.·Meaningthat:commodities(inputsoroutputs)canbethrownaway.InputRequirementSet:V(q)={z:(-z,q)ÎY}z2V(q)Q(q)z19Isoquant:Q(q)={z:(-z,q)ÎY,(-z,q’)ÏY"q’³q,q’¹q}·Theisoq

6、uantQ(q)isusuallytheboundaryclosesttotheoriginofV(q).Proposition:IfYisconvex,soisV(q).·Wenormallydonotrequirethattheproductionpossibilitysetisconvex.Ifso,itwillruleout"start-upcosts"andothersortsofreturnstoscale.(Doyouseewhy?)5.2ProductionFunctionsTransformationFunctionoftheProductionP

7、ossibilitySetFormostproductionpossibilitysets,itispossibletodescribetheminitemofsingleinequalityoftheformT(y)£0.Thatis,Y={y:T(y)£0}AfunctionTthatdescribesYthiswayiscalledatransformationfunction.EfficientProduction·AproductionpointyÎYisefficientisthereisnoy’ÎY,y’¹y,withy’³y.·Anefficie