microeconomic theory production functions

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1、CHAPTERNINEProductionFunctionsTheprincipalactivityofanyfirmistoturninputsintooutputs.Becauseeconomistsareinterestedinthechoicesthefirmmakesinaccomplishingthisgoal,butwishtoavoiddis-cussingmanyoftheengineeringintricaciesinvolved,theyhavechosentoconstructanabstractmodelofproduction.Inthismodeltherelatio

2、nshipbetweeninputsandoutputsisformalizedbyaproductionfunctionoftheformq¼fðk,l,m,...Þ,(9:1)1whereqrepresentsthefirm’soutputofaparticulargoodduringaperiod,krepresentsthemachine(i.e.,capital)usageduringtheperiod,lrepresentshoursoflaborinput,m2representsrawmaterialsused,andthenotationindicatesthepossibil

3、ityofothervaria-blesaffectingtheproductionprocess.Equation9.1isassumedtoprovide,foranycon-ceivablesetofinputs,theengineer’ssolutiontotheproblemofhowbesttocombinethoseinputstogetoutput.MarginalProductivityInthissectionwelookatthechangeinoutputbroughtaboutbyachangeinoneoftheproductiveinputs.Forthepurp

4、osesofthisexamination(andindeedformostofthepur-posesofthisbook),itwillbemoreconvenienttouseasimplifiedproductionfunctiondefinedasfollows.DEFINITIONProductionfunction.Thefirm’sproductionfunctionforaparticulargood,q,q¼fðk,lÞ,(9:2)showsthemaximumamountofthegoodthatcanbeproducedusingalternativecombinations

5、ofcapital(k)andlabor(l).Ofcourse,mostofouranalysiswillholdforanytwoinputstotheproductionprocesswemightwishtoexamine.Thetermscapitalandlaborareusedonlyforconvenience.Similarly,itwouldbeasimplemattertogeneralizeourdiscussiontocasesinvolving1Hereweusealowercaseqtorepresentonefirm’soutput.Wereservetheupp

6、ercaseQtorepresenttotaloutputinamarket.Generally,weassumethatafirmproducesonlyoneoutput.Issuesthatariseinmultiproductfirmsarediscussedinafewfoot-notesandproblems.2Inempiricalwork,rawmaterialinputsoftenaredisregarded,andoutput,q,ismeasuredintermsof‘‘valueadded.’’303304Part4:ProductionandSupplymorethant

7、woinputs;occasionally,wewilldoso.Forthemostpart,however,limitingthediscussiontotwoinputswillbehelpfulbecausewecanshowtheseinputsontwo-dimensionalgraphs.MarginalphysicalproductTostudyvariationinasingle