nicholson微观经济理论（答案+ppt+习题库）-120-03-033593-0

COSTSINTHISCHAPTERWEILLUSTRATETHECOSTSTHATARMINCURSINITSPRODUCTIVEACTIVITIESINCHAPTER13,WEWILLBEABLETOUSETHISINFORMATIONANDINFORMATIONABOUTREVENUESTOSHOWHOWMUCHTHERMWILLCHOOSETOPRODUCEHEREWEWILLBECONCERNEDONLYWITHQUESTIONSABOUTTHECOSTSASSOCIATEDWITHHIRINGTHEINPUTSTHATTHERMCHOOSESTOEMPLOY12CHAPTERDENITIONSOFCOSTSBEFOREWECANDISCUSSTHETHEORYOFCOSTS,SOMEDIFCULTIESABOUTTHEPROPERDENITIONOF“COSTS”MUSTBECLEANEDUPSPECICALLY,WEMUSTDIFFERENTIATEBETWEEN1ACCOUNTINGCOSTAND2ECONOMICCOSTTHEACCOUNTANTSVIEWOFCOSTSTRESSESOUTOFPOCKETEXPENSES,HISTORICALCOSTS,DEPRECIATION,ANDOTHERBOOKKEEPINGENTRIESTHEECONOMISTSDENITIONOFCOSTWHICHINOBVIOUSWAYSDRAWSONTHEFUNDAMENTALOPPORTUNITYCOSTNOTIONISTHATTHECOSTOFANYINPUTISGIVENBYTHESIZEOFTHEPAYMENTNECESSARYTOKEEPTHERESOURCEINITSPRESENTEMPLOYMENTALTERNATIVELY,THEECONOMICCOSTOFUSINGANINPUTISWHATTHATINPUTWOULDBEPAIDINITSNEXTBESTUSEONEWAYTODISTINGUISHBETWEENTHESETWOVIEWSISTOCONSIDERHOWTHECOSTSOFVARIOUSINPUTSLABOR,CAPITAL,ANDENTREPRENEURIALSERVICESAREDENEDUNDEREACHSYSTEMLABORCOSTSECONOMISTSANDACCOUNTANTSREGARDLABORCOSTSINMUCHTHESAMEWAYTOACCOUNTANTS,EXPENDITURESONLABORARECURRENTEXPENSESANDHENCECOSTSOFPRODUCTIONFORECONOMISTS,LABORISANEXPLICITCOSTLABORSERVICESLABORHOURSARECONTRACTEDATSOMEHOURLYWAGERATEW,ANDITISUSUALLYASSUMEDTHATTHISISALSOWHATTHELABORSERVICESWOULDEARNINTHEIRBESTALTERNATIVEEMPLOYMENTCAPITALCOSTSINTHECASEOFCAPITALSERVICESMACHINEHOURS,THETWOCONCEPTSOFCOSTDIFFERGREATLYINCALCULATINGCAPITALCOSTS,ACCOUNTANTSUSETHEHISTORICALPRICEOFTHEPARTICULARMACHINEUNDERINVESTIGATIONANDAPPLYSOMEMOREORLESSARBITRARYDEPRECIATIONRULETODETERMINEHOWMUCHOFTHATMACHINESORIGINALPRICETOCHARGETOCURRENTCOSTSECONOMISTSREGARDTHEHISTORICALPRICEOFAMACHINEASA“SUNKCOST,”WHICHISIRRELEVANTTOOUTPUTDECISIONSTHEYINSTEADREGARDTHEIMPLICITCOSTOFTHEMACHINETOBEWHATSOMEONEELSEWOULDBEWILLINGTOPAYFORITSUSETHUSTHECOSTOFONEMACHINEHOURISTHERENTALRATEFORTHATMACHINEINITSBESTALTERNATIVEUSEBYCONTINUINGTOUSETHEMACHINEITSELF,THERMISIMPLICITLYFOREGOINGWHATSOMEONEELSEWOULDBEWILLINGTOPAYTOUSEITTHISRENTALRATEFORONEMACHINEHOURWILLBEDENOTEDBYV1COSTSOFENTREPRENEURIALSERVICESTHEOWNEROFARMISARESIDUALCLAIMANTWHOISENTITLEDTOWHATEVEREXTRAREVENUESORLOSSESARELEFTAFTERPAYINGALLINPUTCOSTSTOANACCOUNTANT,THESEWOULDBECALLEDPROTSWHICHMIGHTBEEITHERPOSITIVEORNEGATIVEECONOMISTS,HOWEVER,ASKWHETHEROWNERSORENTREPRENEURSALSOENCOUNTEROPPORTUNITYCOSTSBYWORKINGATAPARTICULARRMORDEVOTINGSOMEOFTHEIRFUNDSTOITSOPERATIONIFSO,THESESERV298PARTIVPRODUCTIONANDSUPPLY1SOMETIMESTHESYMBOLRISCHOSENTOREPRESENTTHERENTALRATEONCAPITALBECAUSETHISVARIABLEISOFTENCONFUSEDWITHTHERELATEDTHOUGHDISTINCTCONCEPTOFTHEMARKETINTERESTRATE,ANALTERNATIVESYMBOLWASCHOSENHERETHEEXACTRELATIONSHIPBETWEENVANDTHEINTERESTRATEISEXAMINEDINCHAPTER23ICESSHOULDBECONSIDEREDANINPUTANDSOMECOSTSHOULDBEIMPUTEDTOTHEMFOREXAMPLE,SUPPOSEAHIGHLYSKILLEDCOMPUTERPROGRAMMERSTARTSASOFTWARERMWITHTHEIDEAOFKEEPINGANYACCOUNTINGPROTSTHATMIGHTBEGENERATEDTHEPROGRAMMERSTIMEISCLEARLYANINPUTTOTHERM,ANDACOSTSHOULDBEINPUTEDFORITPERHAPSTHEWAGETHATTHEPROGRAMMERMIGHTCOMMANDIFHEORSHEWORKEDFORSOMEONEELSECOULDBEUSEDFORTHATPURPOSEHENCESOMEPARTOFTHEACCOUNTINGPROTSGENERATEDBYTHERMWOULDBECATEGORIZEDASENTREPRENEURIALCOSTSBYECONOMISTSECONOMICPROTSWOULDBESMALLERTHANACCOUNTINGPROTSANDMIGHTBENEGATIVEIFTHEPROGRAMMERSOPPORTUNITYCOSTSEXCEEDEDTHEACCOUNTINGPROTSBEINGEARNEDBYTHEBUSINESSECONOMICCOSTSINTHISBOOK,NOTSURPRISINGLY,WESHALLUSEECONOMISTSDENITIONOFCOSTECONOMICCOSTTHEECONOMICCOSTOFANYINPUTISTHEPAYMENTREQUIREDTOKEEPTHATINPUTINITSPRESENTEMPLOYMENTEQUIVALENTLY,THEECONOMICCOSTOFANINPUTISTHEREMUNERATIONTHEINPUTWOULDRECEIVEINITSBESTALTERNATIVEEMPLOYMENTUSEOFTHISDENITIONISNOTMEANTTOIMPLYTHATACCOUNTANTSCONCEPTSAREIRRELEVANTTOECONOMICBEHAVIORINDEED,ACCOUNTINGPROCEDURESAREINTEGRALLYIMPORTANTTOANYMANAGERSDECISIONMAKINGPROCESSBECAUSETHEYCANGREATLYAFFECTTHERATEOFTAXATIONTOBEAPPLIEDAGAINSTPROTSACCOUNTINGDATAAREALSOREADILYAVAILABLE,WHEREASDATAONECONOMICCOSTSMUSTOFTENBEDEVELOPEDSEPARATELYECONOMISTSDENITIONS,HOWEVER,DOHAVETHEDESIRABLEFEATURESOFBEINGBROADLYAPPLICABLETOALLRMSANDOFFORMINGACONCEPTUALLYCONSISTENTSYSTEMTHEYTHEREFOREAREBESTSUITEDFORAGENERALTHEORETICALANALYSISTWOSIMPLIFYINGASSUMPTIONSASASTART,WEWILLMAKETWOSIMPLICATIONSABOUTTHEINPUTSARMUSESFIRST,WEWILLASSUMETHATTHEREAREONLYTWOINPUTSHOMOGENEOUSLABORL,MEASUREDINLABORHOURSANDHOMOGENEOUSCAPITALK,MEASUREDINMACHINEHOURSENTREPRENEURIALCOSTSAREINCLUDEDINCAPITALCOSTSTHATIS,WEASSUMETHATTHEPRIMARYOPPORTUNITYCOSTSFACEDBYARMSOWNERARETHOSEASSOCIATEDWITHTHECAPITALTHATTHEOWNERPROVIDESSECOND,WEASSUMETHATINPUTSAREHIREDINPERFECTLYCOMPETITIVEMARKETSFIRMSCANBUYORSELLALLTHELABORORCAPITALSERVICESTHEYWANTATTHEPREVAILINGRENTALRATESWANDVINGRAPHICTERMSTHESUPPLYCURVEFORTHESERESOURCESISHORIZONTALATTHEPREVAILINGFACTORPRICESBOTHWANDVARETREATEDAS“PARAMETERS”INTHERMSDECISIONSTHEREISNOTHINGTHERMCANDOTOAFFECTTHEMTHESECONDITIONSWILLBERELAXEDINLATERCHAPTERSNOTABLYCHAPTER21,BUTFORTHEMOMENTTHEPERFECTLYCOMPETITIVEASSUMPTIONISACONVENIENTANDUSEFULONETOMAKEDEFINITIONCHAPTER12COSTS299ECONOMICPROTSANDCOSTMINIMIZATIONTOTALCOSTSFORTHERMDURINGAPERIODARETHEREFOREGIVENBYTOTALCOSTSH11005TCH11005WLH11001VK,121WHERE,ASBEFORE,LANDKREPRESENTINPUTUSAGEDURINGTHEPERIODASSUMINGTHERMPRODUCESONLYONEOUTPUT,ITSTOTALREVENUESAREGIVENBYTHEPRICEOFITSPRODUCTPTIMESITSTOTALOUTPUTQH11005FK,LWHEREFK,LISTHERMSPRODUCTIONFUNCTIONECONOMICPROTSH9266ARETHENTHEDIFFERENCEBETWEENTOTALREVENUESANDTOTALECONOMICCOSTSECONOMICPROTSECONOMICPROTSH9266ARETHEDIFFERENCEBETWEENARMSTOTALREVENUESANDITSTOTALCOSTSH9266H11005TOTALREVENUEH11002TOTALCOSTH11005PQH11002WLH11002VK122H11005PFK,LH11002WLH11002VKEQUATION122SHOWSTHATTHEECONOMICPROTSOBTAINEDBYARMAREAFUNCTIONOFTHEAMOUNTOFCAPITALANDLABOREMPLOYEDIF,ASWEWILLASSUMEINMANYPLACESINTHISBOOK,THERMSEEKSMAXIMUMPROTS,WEMIGHTSTUDYITSBEHAVIORBYEXAMININGHOWKANDLARECHOSENSOASTOMAXIMIZEEQUATION122THISWOULD,INTURN,LEADTOATHEORYOFTHE“DERIVEDDEMAND”FORCAPITALANDLABORINPUTSATOPICWETAKEUPEXPLICITLYINCHAPTER21HERE,HOWEVER,WEWISHTODEVELOPATHEORYOFCOSTSTHATISSOMEWHATMOREGENERALANDMIGHTAPPLYTORMSTHATARENOTNECESSARILYPROTMAXIMIZERSHENCE,WEBEGINTHESTUDYOFCOSTSBYNESSING,FORTHEMOMENT,ADISCUSSIONOFOUTPUTCHOICETHATIS,WEASSUMETHATFORSOMEREASONTHERMHASDECIDEDTOPRODUCEAPARTICULAROUTPUTLEVELSAY,Q0THERMSREVENUESARETHEREFOREXEDATPQ0NOWWEWISHTOEXAMINEHOWTHERMMIGHTCHOOSETOPRODUCEQ0ATMINIMALCOSTSCOSTMINIMIZINGINPUTCHOICESMATHEMATICALLY,THISISACONSTRAINEDMINIMIZATIONPROBLEMBUTBEFOREPROCEEDINGWITHARIGOROUSSOLUTION,ITMIGHTBEUSEFULTOSTATETHERESULTTOBEDERIVEDWITHANINTUITIVEARGUMENTTOMINIMIZETHECOSTOFPRODUCINGAGIVENLEVELOFOUTPUT,ARMSHOULDCHOOSETHATPOINTONTHEQ0ISOQUANTATWHICHTHERATEOFTECHNICALSUBSTITUTIONOFLFORKISEQUALTOTHERATIOW/VITSHOULDEQUATETHERATEATWHICHKCANBETRADEDFORLINTHEPRODUCTIVEPROCESSTOTHERATEATWHICHTHEYCANBETRADEDINTHEMARKETPLACESUPPOSETHATTHISWERENOTTRUEINPARTICULAR,SUPPOSETHATTHERMWEREPRODUCINGOUTPUTLEVELQ0USINGKH1100510,LH1100510,ANDASSUMETHATTHERTSWAS2ATTHISPOINTASSUMEALSOTHATWH110051,VH110051,ANDHENCETHATW/VH110051WHICHISUNEQUALTO2ATTHISINPUTCOMBINATION,THECOSTOFPRODUCINGQ0IS20ITISEASYTOSHOWTHISISNOTTHEMINIMALINPUTCOSTQ0CANALSOBEPRODUCEDUSINGKH110058ANDDEFINITION300PARTIVPRODUCTIONANDSUPPLYLH1100511WECANGIVEUPTWOUNITSOFKANDKEEPOUTPUTCONSTANTATQ0BYADDINGONEUNITOFLBUTATTHISINPUTCOMBINATIONTHECOSTOFPRODUCINGQ0IS19,ANDHENCETHEINITIALINPUTCOMBINATIONWASNOTOPTIMALAPROOFSIMILARTOTHISONECANBEDEMONSTRATEDWHENEVERTHERTSANDTHERATIOOFTHEINPUTCOSTSDIFFERMATHEMATICALANALYSISMATHEMATICALLY,WESEEKTOMINIMIZETOTALCOSTS,GIVENQH11005FK,LH11005Q0SETTINGUPTHELAGRANGIANEXPRESSIONH5112H11005WLH11001VKH11001H9261Q0H11002FK,L,123THERSTORDERCONDITIONSFORACONSTRAINEDMINIMUMAREH11005WH11002H9261H110050124H11005VH11002H9261H110050H11005Q0H11002FK,LH110050OR,DIVIDINGTHERSTTWOEQUATIONS,H11005H11005RTSLFORK125THISSAYSTHATTHECOSTMINIMIZINGRMSHOULDEQUATETHERTSFORTHETWOINPUTSTOTHERATIOOFTHEIRPRICES2GRAPHICALANALYSISTHERESULTISSHOWNGRAPHICALLYINFIGURE121GIVENTHEOUTPUTISOQUANTQ0,WEWISHTONDTHELEASTCOSTLYPOINTONTHEISOQUANTFROMEQUATION121,ALLLINESOFEQUALCOSTAREPARALLELSTRAIGHTLINESWITHSLOPESH11002W/VTHREELINESOFEQUALTOTALCOSTARESHOWNINFIGURE121TC1H11021TC2H11021TC3ITISCLEARFROMTHEGURETHATTHEMINIMUMTOTALCOSTFORPRODUCINGQ0ISGIVENBYTC1,WHERETHETOTALCOSTCURVEISJUSTTANGENTTOTHEISOQUANTTHECOSTMINIMIZINGINPUTCOMBINATIONISL,KTHISCOMBINATIONWILLBEATRUEMINIMUMIFTHEISOQUANTISCONVEXIFTHERTSH11128F/H11128LH5007H11128F/H11128KWH5007VH11128H5112H5007H11128H9261H11128FH5007H11128KH11128H5112H5007H11128KH11128FH5007H11128LH11128H5112H5007H11128LCHAPTER12COSTS3012EQUATION124ALSOSHOWSTHATH11005H11005THISMEANSTHATTHEMARGINALPRODUCTIVITYPERDOLLARSPENTSHOULDBETHESAMEFORALLINPUTSUSEDINOTHERWORDS,THERATIOOFMARGINALBENETTHATIS,INCREASEDOUTPUTTOMARGINALCOSTSHOULDBETHESAMEFORALLINPUTSACTUALLYEMPLOYEDIFANINPUTDIDNOTMEETTHISBENETCOSTTEST,ITWOULDNOTBEUSEDTHELAGRANGIANMULTIPLIER,H9261,HEREREPRESENTSMARGINALCOSTTHATIS,THEEXTRACOSTINVOLVEDINPRODUCINGONEMOREUNITOFOUTPUTH11128F/H11128KH5007VH11128F/H11128LH5007W1H5007H9261DIMINISHESFORDECREASESINK/LTHEMATHEMATICALANDGRAPHICANALYSESARRIVEATTHESAMECONCLUSIONCOSTMINIMIZATIONINORDERTOMINIMIZETHECOSTOFANYGIVENLEVELOFINPUTQ0,THERMSHOULDPRODUCEATTHATPOINTONTHEQ0ISOQUANTFORWHICHTHERTSOFLFORKISEQUALTOTHERATIOOFTHEINPUTSRENTALPRICESW/VDUALPROBLEMOUTPUTMAXIMIZATIONARESULTIDENTICALTOTHATJUSTDERIVEDCANBEOBTAINEDBYCONSIDERINGTHEDUALFORMULATIONOFTHERMSPRIMALCOSTMINIMIZATIONPROBLEMFORAGIVENTOTALCOSTOFINPUTSSAY,TC1,MAXIMIZETHELEVELOFOUTPUTMATHEMATICALLY,THELAGRANGIANEXPRESSIONFORTHISPROBLEMISH5112DH11005FK,LH11001H9261DTC1H11002WLH11002VK,126ANDITISASIMPLEMATTERTOSHOWTHATTHERSTORDERCONDITIONSFORTHISPROBLEMAREIDENTICALTOTHOSEALREADYDERIVEDINEQUATION124AGRAPHICDEMONSTRATIONISPROOPTIMIZATIONPRINCIPLE302PARTIVPRODUCTIONANDSUPPLYMINIMIZATIONOFCOSTSGIVENQH11005Q0ARMISASSUMEDTOCHOOSEKANDLTOMINIMIZETOTALCOSTSTHECONDITIONFORTHISMINIMIZATIONISTHATTHERATEATWHICHKANDLCANBETRADEDTECHNICALLYWHILEKEEPINGQH11005Q0SHOULDBEEQUALTOTHERATEATWHICHTHESEINPUTSCANBETRADEDINTHEMARKETINOTHERWORDS,THERTSOFLFORKSHOULDBESETEQUALTOTHEPRICERATIOW/VTHISTANGENCYISSHOWNINTHEGURECOSTSAREMINIMIZEDATTC1BYCHOOSINGINPUTSKANDLTC1TC2TC3KPERPERIODLPERPERIODQ0KLFIGURE121VIDEDINFIGURE122THERETHEMAXIMUMOUTPUTATTAINABLEWITHTOTALCOSTTC1ISQ0,WHICHRESULTSWHENTHEINPUTCOMBINATIONL,KISUSEDALLOTHERCOMBINATIONSOFINPUTSTHATLIEALONGTC1AREBELOWTHEQ0ISOQUANTANDHENCEYIELDLESSOUTPUTTHANDOESTHISOPTIMALCOMBINATIONTHEREFORETHESOLUTIONDERIVEDINFIGURE122ISIDENTICALTOTHATINFIGURE121FORMOSTOFOURSUBSEQUENTANALYSISWEWILLMAKEUSEOFTHEPRIMALCOSTMINIMIZATIONAPPROACH,BUTATTIMESWEWILLRELYONTHEDUALFORMULATIONOFTHEPROBLEMTOPROVIDEINSIGHTSINTOTHEECONOMICCONSEQUENCESOFCOSTMINIMIZATIONDERIVEDDEMANDFORINPUTSFIGURE122EXHIBITSTHEFORMALSIMILARITYBETWEENTHERMSCOSTMINIMIZATIONPROBLEMANDTHEINDIVIDUALSUTILITYMAXIMIZATIONPROBLEMINBOTHCASES,WETOOKPRICESASXEDPARAMETERSANDDERIVEDTHETANGENCYCONDITIONSINCHAPTER5,WETHENASKEDTHECOMPARATIVESTATICSQUESTIONOFHOWTHEUTILITYMAXIMIZINGCHOICEOFGOODSWOULDCHANGEIFAPRICEWERETOCHANGETHEANALYSISOFTHISCHANGEPERMITTEDTHECONSTRUCTIONOFTHEFAMILIARDOWNWARDSLOPINGDEMANDCURVEANINTERESTINGQUESTIONISWHETHERTHERMSDEMANDFORANINPUTCOULDBEDEVELOPEDANALOGOUSLYHERECOULDWECHANGESOMEINPUTPRICECHANGETHESLOPEOFTHETCCURVESANDTHENTRACETHEEFFECTSOFTHISPRICECHANGEONTHEQUANTITYOFTHEFACTORCHAPTER12COSTS303DUALOUTPUTMAXIMIZATIONPROBLEMTHEDUALAPPROACHTOCOSTMINIMIZATIONISFORTHERMTOMAXIMIZEOUTPUTFORAGIVENEXPENDITUREOFTOTALCOSTTC1UNDERTHISAPPROACHTOO,THERMCHOOSESTHEINPUTCOMBINATIONL,KFORWHICHTHERTSISEQUALTOTHERATIOOFTHEINPUTSRENTALRATES,W/VTC1H11005WLH11001VKQ1Q0Q00LPERPERIODKPERPERIODKLFIGURE122DEMANDEDTHEANALOGYTOTHEINDIVIDUALSUTILITYMAXIMIZATIONPROCESSCANBEMISLEADINGATTHISPOINTTOANALYZEWHATHAPPENSTOK,SAY,ASVCHANGES,WEALSOHAVETOKNOWWHATHAPPENSTOTHEOUTPUTLEVELCHOSENBYTHERMTHEDEMANDFORKISADERIVEDDEMAND,BASEDONTHEDEMANDFORTHERMSOUTPUTWECANNOTANSWERQUESTIONSABOUTKWITHOUTLOOKINGATTHEINTERACTIONOFSUPPLYANDDEMANDINTHEGOODSMARKETALTHOUGHTHEANALOGYTOTHETHEORYOFINDIVIDUALBEHAVIORISUSEFULINPOINTINGOUTBASICSIMILARITIES,ITISNOTANEXACTANALOGYTHEDERIVATIONOFARMSDEMANDFORANINPUTINVOLVESADDITIONALISSUESABOUTTHERMSDESIREDOUTPUTLEVELTHATDONOTARISEINTHECONSUMERSPROBLEMTHESEARETAKENUPINCHAPTER21THEFIRMSEXPANSIONPATHARMCANPERFORMANANALYSISSUCHASTHATPRESENTEDABOVEFOREACHLEVELOFOUTPUTFOREACHQITNDSTHEINPUTCHOICETHATMINIMIZESTHECOSTOFPRODUCINGQIFINPUTCOSTSWANDVREMAINCONSTANTFORALLAMOUNTSTHERMMAYDEMAND,WECANEASILYTRACETHISLOCUSOFCOSTMINIMIZINGCHOICESTHISPROCEDUREISSHOWNINFIGURE123THELINE0ERECORDSTHECOSTMINIMIZINGTANGENCIESFORSUCCESSIVELYHIGHERLEVELSOFOUTPUTFOREXAMPLE,THEMINIMUMCOSTFORPRODUCINGOUTPUTLEVELQ1ISGIVENBYTC1,ANDINPUTSK1ANDL1AREUSEDOTHERTANGENCIESINTHEGURECANBEINTERPRETEDINASIMILARWAYTHELOCUSOFTHESETANGENCIESISCALLEDTHERMSEXPANSIONPATH,BECAUSEITRECORDSHOWINPUTEXPANDSASOUTPUTEXPANDSWHILEHOLDINGTHEPRICESOFTHEINPUTSCONSTANT304PARTIVPRODUCTIONANDSUPPLYTHEFIRMSEXPANSIONPATHTHERMSEXPANSIONPATHISTHELOCUSOFCOSTMINIMIZINGTANGENCIESASSUMINGXEDINPUTPRICES,THECURVESHOWSHOWINPUTSINCREASEASOUTPUTINCREASESL1K1TC2TC1TC3Q1Q2Q3LPERPERIODKPERPERIOD0EFIGURE123ASFIGURE123SHOWS,THEEXPANSIONPATHNEEDNOTBEASTRAIGHTLINETHEUSEOFSOMEINPUTSMAYINCREASEFASTERTHANOTHERSASOUTPUTEXPANDSWHICHINPUTSEXPANDMORERAPIDLYWILLDEPENDONTHESHAPEOFTHEPRODUCTIONISOQUANTSBECAUSECOSTMINIMIZATIONREQUIRESTHATTHERTSALWAYSBESETEQUALTOTHERATIOW/V,ANDBECAUSETHEW/VRATIOISASSUMEDTOBECONSTANT,THESHAPEOFTHEEXPANSIONPATHWILLBEDETERMINEDBYWHEREAPARTICULARRTSOCCURSONSUCCESSIVELYHIGHERISOQUANTSIFTHEPRODUCTIONFUNCTIONEXHIBITSCONSTANTRETURNSTOSCALEOR,MOREGENERALLY,IFITISHOMOTHETIC,THEEXPANSIONPATHWILLBEASTRAIGHTLINE,BECAUSETHERTSDEPENDSONLYONTHERATIOOFKTOLITWOULDSEEMREASONABLETOASSUMETHATTHEEXPANSIONPATHWILLBEPOSITIVELYSLOPEDTHATIS,SUCCESSIVELYHIGHEROUTPUTLEVELSWILLREQUIREMOREOFBOTHINPUTSTHISNEEDNOTBETHECASE,HOWEVER,ASFIGURE124ILLUSTRATESINCREASESOFOUTPUTBEYONDQ2ACTUALLYCAUSETHEQUANTITYOFLABORUSEDTODECREASEINTHISRANGE,LABORWOULDBESAIDTOBEANINFERIORINPUTTHEOCCURRENCEOFINFERIORINPUTSISTHENATHEORETICALPOSSIBILITYTHATMAYHAPPEN,EVENWHENISOQUANTSHAVETHEIRUSUALCONVEXSHAPEMUCHTHEORETICALDISCUSSIONHASCENTEREDONTHEANALYSISOFFACTORINFERIORITYWHETHERINFERIORITYISLIKELYTOOCCURINREALWORLDPRODUCTIONFUNCTIONSISADIFCULTEMPIRICALQUESTIONTOANSWERITSEEMSUNLIKELYTHATSUCHCOMPREHENSIVEMAGNITUDESAS“CAPITAL”AND“LABOR”COULDBEINFERIOR,BUTANERCLASSICATIONOFINPUTSMAYBRINGINFERIORITYTOLIGHTFOREXAMPLE,THEUSEOFSHOVELSMAYDECLINEASPROCHAPTER12COSTS305FACTORINFERIORITYWITHTHISPARTICULARSETOFISOQUANTS,LABORISANINFERIORINPUT,BECAUSELESSLISCHOSENASOUTPUTEXPANDSBEYONDQ2KPERPERIODLPERPERIOD0Q4Q3Q2Q1EFIGURE124DUCTIONOFBUILDINGFOUNDATIONSANDTHEUSEOFBACKHOESINCREASESINTHISBOOKWESHALLNOTBEPARTICULARLYCONCERNEDWITHTHEANALYTICALISSUESRAISEDBYTHISPOSSIBILITY,ALTHOUGHCOMPLICATIONSRAISEDBYINFERIORINPUTSWILLBEMENTIONEDINAFEWPLACESEXAMPLE121MINIMIZINGCOSTSFORACOBBDOUGLASPRODUCTIONFUNCTIONSUPPOSETHATTHEHOURLYPRODUCTIONOFHAMBURGERSATHAMBURGERHEAVENQDEPENDSONTHENUMBEROFGRILLSKANDWORKERSLHIREDEACHHOUR,ACCORDINGTOTHECOBBDOUGLASPRODUCTIONFUNCTIONQH1100510K1/2L1/2127IFGRILLSCANBERENTEDFORVPERHOURANDWORKERSCANBEHIREDATWPERHOUR,TOTALCOSTSOFHAMBURGERPRODUCTIONAREGIVENBYTCH11005VKH11001WL128SUPPOSETHISBURGEREMPORIUMWISHEDTOPRODUCE,SAY,40HAMBURGERSPERHOURTHENTHERELEVANTLAGRANGIANEXPRESSIONFORTHERMSCOSTMINIMIZATIONPROBLEMWOULDBEH5112H11005VKH11001WLH11001H926140H1100210K1/2L1/2129FIRSTORDERCONDITIONSFORAMINIMUMAREH11005VH11002H92615L/K1/2H110050H11005WH11002H92615K/L1/2H1100501210H1100540H1100210K1/2L1/2H110050THETHIRDOFTHESESIMPLYSAYSTHATPRODUCTIONMUSTTAKEPLACEONTHEQH1100540ISOQUANTDIVIDINGTHESECONDEQUATIONBYTHERSTYIELDSH11005H11005RTS1211IF,FOREXAMPLE,WANDVWEREEACH4PERHOUR,EQUATION1211INDICATESTHATTHERMSHOULDUSEEQUALAMOUNTSOFKANDLINTHISCASEKH110054,LH110054WOULDBESUFCIENTTOPRODUCE40HAMBURGERSTOTALCOSTSOFTHE40HAMBURGERSWOULDBE32ANYOTHERINPUTCOMBINATIONTHATCANALSOPRODUCE40HAMBURGERSHASAGREATERTOTALCOSTFOREXAMPLE,KH110058,LH110052WILLALSOYIELDANOUTPUTOF40,BUTINTHISCASETOTALCOSTIS40COSTMINIMIZATIONISALSOINDICATEDBYCONSIDERINGMARGINALPRODUCTIVITIESWITHKH11005LH110054,MPLH11005MPKH110055HAMBURGERSPERHOURANEXTRA1SPENTONEITHERLABORORGRILLSWOULDYIELD125EXTRAHAMBURGERS025UNITSOFTHEINPUTTIMESAMARGINALPRODUCTIVITYOF5ALTERNATIVELY,ANEXTRAHAMBURGERCOSTS80H110051/125BECAUSEITCANBEPRODUCEDBYHIRINGEITHER1/5OFALABORHOUROR1/5OFAGRILLHOURKH5007LWH5007VH11128H5112H5007H11128H9261H11128H5112H5007H11128LH11128H5112H5007H11128K306PARTIVPRODUCTIONANDSUPPLYTHEEXPANSIONPATHNOTICETHATINTHISPROBLEMTHEPRODUCTIONFUNCTIONEXHIBITSCONSTANTRETURNSTOSCALESOTHATTHEEXPANSIONPATHISASTRAIGHTLINEEQUATION1211SHOWSTHEEQUATIONFORTHISSTRAIGHTLINEIFWH11005V,THERMWILLALSOCHOOSEKH11005LFORCOSTMINIMIZATIONOFCOURSE,IFWH11014V,INPUTCOMBINATIONSWHEREKH11005LWOULDNOTBECOSTMINIMIZINGALTHOUGHTHEEXPANSIONPATHWOULDSTILLBELINEARIF,FOREXAMPLE,GRILLSRENTEDFOR12PERHOURANDWAGESWERE4,EQUATION1211INDICATESTHATTHEEXPANSIONPATHWOULDBETHOSECOMBINATIONSOFGRILLSANDWORKERSFORWHICHK/LH110051/3THERMWOULDPRODUCEHAMBURGERSUSINGRELATIVELYMOREOFTHECHEAPERINPUTLABORANDLESSOFTHEEXPENSIVEINPUTCAPITALQUERYIFVH1100512,WH110054,WHATSHOULDBETRUEABOUTMPKANDMPLATTHECOSTMINIMIZINGINPUTCOMBINATIONISTHISINFACTTHECASEWHENQH1100540COSTFUNCTIONSWEARENOWINAPOSITIONTOEXAMINETHERMSOVERALLCOSTSTRUCTURETODOSOITWILLBECONVENIENTTOUSETHEEXPANSIONPATHSOLUTIONSTODERIVETHETOTALCOSTFUNCTIONTOTALCOSTFUNCTIONTHETOTALCOSTFUNCTIONSHOWSTHATFORANYSETOFINPUTCOSTSANDFORANYOUTPUTLEVEL,THEMINIMUMTOTALCOSTINCURREDBYTHERMISTCH11005TCV,W,Q1212FIGURE123MAKESCLEARTHATTOTALCOSTSINCREASEASOUTPUT,Q,INCREASESWEWILLBEGINBYANALYZINGTHISRELATIONSHIPBETWEENTOTALCOSTANDOUTPUTWHILEHOLDINGINPUTPRICESXEDTHENWEWILLCONSIDERHOWACHANGEINANINPUTPRICESHIFTSTHEEXPANSIONPATHANDITSRELATEDCOSTFUNCTIONSAVERAGEANDMARGINALCOSTFUNCTIONSALTHOUGHTHETOTALCOSTFUNCTIONPROVIDESCOMPLETEINFORMATIONABOUTTHEOUTPUTCOSTRELATIONSHIP,ITISOFTENCONVENIENTTOANALYZECOSTSONAPERUNITOFOUTPUTBASIS,BECAUSETHATAPPROACHCORRESPONDSMORECLOSELYTOTHEANALYSISOFDEMAND,WHICHFOCUSEDONTHEPRICEPERUNITOFACOMMODITYTWODIFFERENTUNITCOSTMEASURESAREWIDELYUSEDINECONOMICS1AVERAGECOST,WHICHISTHECOSTPERUNITOFOUTPUTAND2MARGINALCOST,WHICHISTHECOSTOFONEMOREUNITOFOUTPUTTHERELATIONSHIP