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1、CHAPTERNINEProductionFunctionsTheprincipalactivityofany?rmistoturninputsintooutputs.Becauseeconomistsareinterestedinthechoicesthe?rmmakesinaccomplishingthisgoal,butwishtoavoiddis-cussingmanyoftheengineeringintricaciesinvolved,theyhavechosentoconstructanabstractmodelofproduction.Inthismodeltherelatio
2、nshipbetweeninputsandoutputsisformalizedbyaproductionfunctionoftheformq?fek,l,m,...T,(9:1)1whereqrepresentsthe?rm’soutputofaparticulargoodduringaperiod,krepresentsthemachine(i.e.,capital)usageduringtheperiod,lrepresentshoursoflaborinput,m2representsrawmaterialsused,andthenotationindicatesthepossibil
3、ityofothervaria-blesaffectingtheproductionprocess.Equation9.1isassumedtoprovide,foranycon-ceivablesetofinputs,theengineer’ssolutiontotheproblemofhowbesttocombinethoseinputstogetoutput.MarginalProductivityInthissectionwelookatthechangeinoutputbroughtaboutbyachangeinoneoftheproductiveinputs.Forthepurp
4、osesofthisexamination(andindeedformostofthepur-posesofthisbook),itwillbemoreconvenienttouseasimpli?edproductionfunctionde?nedasfollows.DEFINITIONProductionfunction.The?rm’sproductionfunctionforaparticulargood,q,q?fek,lT,(9:2)showsthemaximumamountofthegoodthatcanbeproducedusingalternativecombinations
5、ofcapital(k)andlabor(l).Ofcourse,mostofouranalysiswillholdforanytwoinputstotheproductionprocesswemightwishtoexamine.Thetermscapitalandlaborareusedonlyforconvenience.Similarly,itwouldbeasimplemattertogeneralizeourdiscussiontocasesinvolving1Hereweusealowercaseqtorepresentone?rm’soutput.Wereservetheupp
6、ercaseQtorepresenttotaloutputinamarket.Generally,weassumethata?rmproducesonlyoneoutput.Issuesthatariseinmultiproduct?rmsarediscussedinafewfoot-notesandproblems.2Inempiricalwork,rawmaterialinputsoftenaredisregarded,andoutput,q,ismeasuredintermsof‘‘valueadded.’’303304Part4:ProductionandSupplymorethant
7、woinputs;occasionally,wewilldoso.Forthemostpart,however,limitingthediscussiontotwoinputswillbehelpfulbecausewecanshowtheseinputsontwo-dimensionalgraphs.MarginalphysicalproductTostudyvariationinasingle
