nicholson微观经济理论（答案+ppt+习题库）-160-03-033593-0

GENERALCOMPETITIVEEQUILIBRIUMPARTIALEQUILIBRIUMMODELS,SUCHASTHOSEINCHAPTERS14AND15,ARECLEARLYINADEQUATETOANALYZEALLOFTHEEFFECTSTHATOCCURWHENPRICECHANGESINONEMARKETHAVEEFFECTSINOTHERMARKETSINSTEAD,WENEEDANECONOMICMODELTHATPERMITSUSTOVIEWMANYMARKETSSIMULTANEOUSLYALTHOUGHTHECONSTRUCTIONOFSUCHGENERALEQUILIBRIUMMULTIMARKETMODELSHASBEENOFINTERESTTOECONOMISTSFORSOMETIMEINDEED,MANYOFTHETOOLSWEWILLPRESENTINTHISCHAPTERWERERSTDEVELOPEDINTHENINETEENTHCENTURY,ITWASNOTUNTILTHEADVENTOFMODERNCOMPUTERTECHNOLOGYTHATITBECAMEPOSSIBLETOAPPLYSUCHMODELSTOACTUALMARKETSITUATIONSINTHISCHAPTERWEWILLONLYMAKEAFEWCOMMENTSABOUTTHESEIMPORTANTINNOVATIONSINECONOMICMODELBUILDINGWEWILLBEMOREINTERESTEDINDEVELOPINGTHETHEORYOFGENERALEQUILIBRIUMPRICEDETERMINATIONTHEEXTENSIONSTOTHISCHAPTERDESCRIBEAFEWRECENTATTEMPTSATCOMPUTERORIENTEDMODELBUILDING16CHAPTERPERFECTLYCOMPETITIVEPRICESYSTEMTHEMODELWEWILLDEVELOPINTHISCHAPTERISPRIMARILYANELABORATIONOFTHESUPPLYDEMANDMODELWEPRESENTEDINCHAPTER14HEREWEWILLASSUMETHATALLMARKETSAREOFTHETYPEDESCRIBEDINTHATCHAPTERANDREFERTOSUCHASETOFMARKETSASAPERFECTLYCOMPETITIVEPRICESYSTEMTHEASSUMPTIONISTHATTHEREISSOMELARGENUMBEROFHOMOGENEOUSGOODSINTHISSIMPLEECONOMYINCLUDEDINTHISLISTOFGOODSARENOTONLYCONSUMPTIONITEMSBUTALSOFACTORSOFPRODUCTIONWHOSEPRICINGISDESCRIBEDINPARTVIIEACHOFTHESEGOODSHASANEQUILIBRIUMPRICE,ESTABLISHEDBYTHEACTIONOFSUPPLYANDDEMAND1ATTHISSETOFPRICES,EVERYMARKETISCLEAREDINTHESENSETHATSUPPLIERSAREWILLINGTOSUPPLYTHATQUANTITYWHICHISDEMANDEDANDCONSUMERSWILLDEMANDTHATQUANTITYWHICHISSUPPLIEDWEALSOASSUMETHATTHEREARENOTRANSACTIONORTRANSPORTATIONCHARGESANDTHATBOTHINDIVIDUALSANDRMSHAVEPERFECTKNOWLEDGEOFPREVAILINGMARKETPRICESTHELAWOFONEPRICEBECAUSEOFTHEZEROTRANSACTIONSCOSTANDPERFECTINFORMATIONASSUMPTIONS,EACHGOODOBEYSTHELAWOFONEPRICEAHOMOGENEOUSGOODTRADESATTHESAMEPRICENOMATTERWHOBUYSITORWHICHRMSELLSITIFONEGOODTRADEDATTWODIFFERENTPRICES,DEMANDERSWOULDRUSHTOBUYTHEGOODWHEREITWASCHEAPER,ANDRMSWOULDTRYTOSELLALLTHEIROUTPUTWHERETHEGOODWASMOREEXPENSIVETHESEACTIONSINTHEMSELVESWOULDTENDTOEQUALIZETHEPRICEOFTHEGOODINTHEPERFECTLYCOMPETITIVEMARKET,THEN,EACHGOODMUSTHAVEONLYONEPRICETHISISWHYWEMAYSPEAKUNAMBIGUOUSLYOFTHEPRICEOFAGOODASSUMPTIONSABOUTPERFECTCOMPETITIONTHEPERFECTLYCOMPETITIVEMODELASSUMESTHATPEOPLEANDRMSREACTTOPRICESINSPECICWAYS1THEREAREASSUMEDTOBEALARGENUMBEROFPEOPLEBUYINGANYONEGOODEACHPERSONTAKESALLPRICESASGIVENANDADJUSTSHISORHERBEHAVIORTOMAXIMIZEUTILITY,GIVENTHEPRICESANDHISORHERBUDGETCONSTRAINTPEOPLEMAYALSOBESUPPLIERSOFPRODUCTIVESERVICESFOREXAMPLE,LABOR,ANDINSUCHDECISIONSTHEYALSOREGARDPRICESASGIVEN22THEREAREASSUMEDTOBELARGENUMBEROFRMSPRODUCINGEACHGOOD,ANDEACHRMPRODUCESONLYASMALLSHAREOFTHEOUTPUTOFANYONEGOODINMAKINGINPUTANDOUTPUTCHOICES,RMSAREASSUMEDTOOPERATETOMAXIMIZEPROTSTHERMSTREATALLPRICESASGIVENWHENMAKINGTHESEPROTMAXIMIZINGDECISIONS422PARTVPERFECTCOMPETITION1ONEASPECTOFTHISMARKETINTERACTIONSHOULDBEMADECLEARFROMTHEOUTSETTHEPERFECTLYCOMPETITIVEMARKETDETERMINESONLYRELATIVENOTABSOLUTEPRICESINTHISCHAPTER,WESPEAKPRIMARILYOFRELATIVEPRICESITMAKESNODIFFERENCEWHETHERTHEPRICESOFAPPLESANDORANGESARE10AND20,RESPECTIVELY,OR10AND20THEIMPORTANTPOINTINEITHERCASEISTHATTWOAPPLESCANBEEXCHANGEDFORONEORANGEINTHEMARKETINTHENALSECTIONSOFTHECHAPTER,WEWILLBRIEYEXAMINETHEROLEOFMONEYANDTHEDETERMINATIONOFABSOLUTEPRICES2BECAUSEONEPRICEREPRESENTSTHEWAGERATE,THERELEVANTBUDGETCONSTRAINTISINREALITYATIMECONSTRAINTTHISISTHEWAYWETREATINDIVIDUALSLABORLEISURECHOICESINCHAPTER22THESEVARIOUSASSUMPTIONSSHOULDBEFAMILIARBECAUSEWEHAVEBEENMAKINGTHEMTHROUGHOUTTHISBOOKOURPURPOSEHEREISTOSHOWHOWANENTIREECONOMICSYSTEMOPERATESWHENALLMARKETSWORKINTHISWAYASIMPLEGRAPHICALMODELOFGENERALEQUILIBRIUMWEBEGINOURANALYSISWITHAVERYSIMPLEGRAPHICALMODELOFGENERALEQUILIBRIUMINVOLVINGONLYTWOGOODS,WHICHWEWILLCALLXANDYTHISMODELWILLPROVEVERYUSEFULBECAUSEITINCORPORATESMANYOFTHEFEATURESOFFARMORECOMPLEXGENERALEQUILIBRIUMREPRESENTATIONSOFTHEECONOMYWEWILLMAKEEXTENSIVEUSEOFTHEMODELINLATERCHAPTERSINCASESWHEREAMULTIMARKETANALYSISISNEEDEDGENERALEQUILIBRIUMDEMANDULTIMATELY,DEMANDPATTERNSINANECONOMYAREDETERMINEDBYINDIVIDUALSPREFERENCESFOROURSIMPLEMODELWEWILLASSUMETHATALLINDIVIDUALSHAVEIDENTICALPREFERENCES,WHICHCANBEREPRESENTEDBYANINDIFFERENCECURVEMAP3DENEDOVERQUANTITIESOFTHETWOGOODS,XANDYTHEBENETOFTHISAPPROACHFOROURPURPOSESISTHATTHISINDIFFERENCECURVEMAPWHICHISIDENTICALTOTHEONESUSEDINCHAPTERS36SHOWSHOWINDIVIDUALSRANKCONSUMPTIONBUNDLESCONTAININGBOTHGOODSTHESERANKINGSAREPRECISELYWHATWEMEANTBY“DEMAND”INAGENERALEQUILIBRIUMCONTEXTOFCOURSE,WECANNOTACTUALLYILLUSTRATEWHICHBUNDLESOFCOMMODITIESWILLBECHOSENUNTILWEKNOWTHEBUDGETCONSTRAINTSTHATDEMANDERSFACEBECAUSEINCOMESAREGENERATEDASINDIVIDUALSSUPPLYLABOR,CAPITAL,ANDOTHERRESOURCESTOTHEPRODUCTIONPROCESS,WEMUSTDELAYTHISILLUSTRATIONUNTILWEHAVEEXAMINEDTHEFORCESOFPRODUCTIONANDSUPPLYINOURMODELGENERALEQUILIBRIUMSUPPLYDEVELOPINGANOTIONOFGENERALEQUILIBRIUMSUPPLYINTHISTWOGOODMODELISASOMEWHATMORECOMPLEXPROCESSTHANDESCRIBINGTHEDEMANDSIDEOFTHEMARKETBECAUSEWEHAVENOTTHUSFARILLUSTRATEDPRODUCTIONANDSUPPLYOFTWOGOODSSIMULTANEOUSLYOURAPPROACHISTOUSETHEFAMILIARPRODUCTIONPOSSIBILITYCURVESEECHAPTER1FORTHISPURPOSEBYDETAILINGTHEWAYINWHICHTHISCURVEISCONSTRUCTED,WECANALSOUSETHISCONSTRUCTIONTOEXAMINETHEWAYSINWHICHMARKETSFOROUTPUTSANDINPUTSARERELATEDEDGEWORTHBOXDIAGRAMCONSTRUCTIONOFTHEPRODUCTIONPOSSIBILITYCURVEFORTWOOUTPUTSXANDYBEGINSWITHTHEASSUMPTIONTHATTHEREAREXEDAMOUNTSOFCAPITALANDLABORINPUTSTHATMUSTBEALLOCATEDTOTHEPRODUCTIONOFTHETWOGOODSTHEPOSSIBLEALLOCATIONSOFCHAPTER16GENERALCOMPETITIVEEQUILIBRIUM4233THEREARESOMETECHNICALPROBLEMSINUSINGASINGLEINDIFFERENCECURVEMAPTOREPRESENTTHEPREFERENCESOFANENTIRECOMMUNITYOFINDIVIDUALSINTHISCASETHEMARGINALRATEOFSUBSTITUTIONTHATIS,THESLOPEOFTHECOMMUNITYINDIFFERENCECURVEWILLDEPENDONHOWTHEAVAILABLEGOODSAREDISTRIBUTEDAMONGINDIVIDUALSTHEINCREASEINTOTALYREQUIREDTOCOMPENSATEFORAONEUNITREDUCTIONINXWILLDEPENDONWHICHSPECICINDIVIDUALSTHEXISTAKENFROMALTHOUGHWEWILLNOTDISCUSSTHISISSUEINDETAILHERE,ITHASBEENWIDELYEXAMINEDINTHEINTERNATIONALTRADELITERATUREFORANEARLYEXAMPLE,SEETIBORDESCITOVSZKY,“ARECONSIDERATIONOFTHETHEORYOFTARIFFS,”REVIEWOFECONOMICSTUDIESSUMMER194289110THESEINPUTSCANBEILLUSTRATEDWITHANEDGEWORTHBOXDIAGRAMWITHDIMENSIONSGIVENBYTHETOTALAMOUNTSOFCAPITALANDLABORAVAILABLEINFIGURE161THELENGTHOFTHEBOXREPRESENTSTOTALLABORHOURSANDTHEHEIGHTOFTHEBOXREPRESENTSTOTALCAPITALHOURSTHELOWERLEFTHANDCORNEROFTHEBOXREPRESENTSTHE“ORIGIN”FORMEASURINGCAPITALANDLABORDEVOTEDTOPRODUCTIONOFGOODXTHEUPPERRIGHTHANDCORNEROFTHEBOXREPRESENTSTHEORIGINFORRESOURCESDEVOTEDTOYUSINGTHESECONVENTIONS,ANYPOINTINTHEBOXCANBEREGARDEDASAFULLYEMPLOYEDALLOCATIONOFTHEAVAILABLERESOURCESBETWEENGOODSXANDYPOINTA,FOREXAMPLE,REPRESENTSANALLOCATIONINWHICHTHEINDICATEDNUMBEROFLABORHOURSAREDEVOTEDTOXPRODUCTIONTOGETHERWITHASPECIEDNUMBEROFHOURSOFCAPITALPRODUCTIONOFGOODYUSESWHATEVERLABORANDCAPITALARE“LEFTOVER”POINTAINFIGURE162,FOREXAMPLE,ALSOSHOWSTHEEXACTAMOUNTOFLABORANDCAPITALUSEDINTHEPRODUCTIONOFGOODYANYOTHERPOINTINTHEBOXHASASIMILARINTERPRETATIONTHUS,THEEDGEWORTHBOXSHOWSEVERYPOSSIBLEWAYTHEEXISTINGCAPITALANDLABORMIGHTBEUSEDTOPRODUCEXANDYEFCIENTALLOCATIONSMANYOFTHEALLOCATIONSSHOWNINFIGURE161ARETECHNICALLYINEFCIENTINTHATITISPOSSIBLETOPRODUCEBOTHMOREXANDMOREYBYSHIFTINGCAPITALANDLABORAROUND424PARTVPERFECTCOMPETITIONCONSTRUCTIONOFANEDGEWORTHBOXDIAGRAMFORPRODUCTIONTHEDIMENSIONSOFTHISDIAGRAMAREGIVENBYTHETOTALQUANTITIESOFLABORANDCAPITALAVAILABLEQUANTITIESOFTHESERESOURCESDEVOTEDTOXPRODUCTIONAREMEASUREDFROMORIGINOXQUANTITIESDEVOTEDTOYAREMEASUREDFROMOYANYPOINTINTHEBOXREPRESENTSAFULLYEMPLOYEDALLOCATIONOFTHEAVAILABLERESOURCESTOTHETWOGOODSAOXTOTALLABORLABORFORXLABORINYPRODUCTIONLABORFORYTOTALCAPITALCAPITALFORYCAPITALINYPRODUCTIONLABORINXPRODUCTIONCAPITALINXPRODUCTIONOYCAPITALFORXFIGURE161ABITINOURMODELWEASSUMETHATCOMPETITIVEMARKETSWILLNOTEXHIBITSUCHINEFCIENTINPUTCHOICESFORREASONSWEWILLEXPLOREINMOREDETAILINTHENEXTCHAPTERHENCEWEWISHTODISCOVERTHEEFCIENTALLOCATIONSINFIGURE161,BECAUSETHESEILLUSTRATETHEACTUALPRODUCTIONOUTCOMESINTHISMODELTODOSO,WEINTRODUCEISOQUANTMAPSFORGOODXUSINGOXASTHEORIGINANDGOODYUSINGOYASTHEORIGIN,ASSHOWNINFIGURE162INTHISGUREITISCLEARTHATTHEARBITRARILYCHOSENALLOCATIONAISINEFCIENTWITHCAPITALKANDLABORLALLOCATEDINTHISWAY,Y2ISPRODUCEDTOGETHERWITHX2BYMOVINGALONGTHEY2ISOQUANTTOP3,WECANHOLDYOUTPUTCONSTANTANDINCREASEXOUTPUTTOX3THUS,POINTAWASNOTANEFCIENTALLOCATION,BECAUSEWEWEREABLETOINCREASEOUTPUTOFONEGOODXWITHOUTDECREASINGOUTPUTOFTHEOTHERGOODYALTHOUGHBOTHPOINTAANDPOINTP3REPRESENTFULLYEMPLOYEDALLOCATIONSOFTHEAVAILABLERESOURCES,THEALLOCATIONATPOINTP3RESULTSINGOODXUSINGMORECAPITALANDLESSLABORWHEREASYUSESMORELABORANDLESSCAPITALTHANATPOINTATHEEFCIENTALLOCATIONSINFIGURE162ARETHOSESUCHASP1,P2,P3,ANDP4,WHERETHEISOQUANTSARETANGENTTOONEANOTHERATANYOTHERPOINTSINTHEBOXDIAGRAM,THETWOGOODSISOQUANTSWILLINTERSECT,ANDWECANSHOWINEFCIENCYASWEDIDFORPOINTAATTHEPOINTSOFTANGENCY,HOWEVER,THISKINDOFUNAMBIGUOUSIMPROVEMENTCANNOTBEMADEINGOINGFROMP2TOP3,FOREXAMPLE,MOREXISBEINGPRODUCED,BUTATTHECOSTOFLESSYBEINGPRODUCED,SOP3ISNOT“MOREEFCIENT”THANP2BOTHOFTHEPOINTSAREEFCIENTTANGENCYOFTHEISOQUANTSFORGOODXANDGOODYIMPLIESTHATTHEIRSLOPESAREEQUALTHATIS,THERTSOFCAPITALFORLABORISEQUALINCHAPTER16GENERALCOMPETITIVEEQUILIBRIUM425EDGEWORTHBOXDIAGRAMOFEFCIENCYINPRODUCTIONTHISDIAGRAMADDSPRODUCTIONISOQUANTSFORXANDYTOFIGURE161ITTHENSHOWSTECHNICALLYEFCIENTWAYSTOALLOCATETHEXEDAMOUNTSOFKANDLBETWEENTHEPRODUCTIONOFTHETWOOUTPUTSTHELINEJOININGOXANDOYISTHELOCUSOFTHESEEFCIENTPOINTSALONGTHISLINETHERTSOFLFORKINTHEPRODUCTIONOFGOODXISEQUALTOTHERTSINTHEPRODUCTIONOFYTOTALLP1TOTALKOXOYP2P3P4X1X2X3X4Y1Y2Y3Y4AFIGURE162XANDYPRODUCTIONINTHENEXTCHAPTER,WEWILLSHOWHOWCOMPETITIVEINPUTMARKETSWILLLEADRMSTOMAKESUCHEFCIENTINPUTCHOICESTHECURVEJOININGOXANDOYTHATINCLUDESALLOFTHESEPOINTSOFTANGENCYTHEREFORESHOWSALLOFTHEEFCIENTALLOCATIONSOFCAPITALANDLABORPOINTSOFFTHISCURVEAREINEFCIENTINTHATUNAMBIGUOUSINCREASESINOUTPUTCANBEOBTAINEDBYRESHUFINGINPUTSBETWEENTHETWOGOODSPOINTSINOXOYAREALLEFCIENTALLOCATIONS,HOWEVER,BECAUSEMOREXCANBEPRODUCEDONLYBYCUTTINGBACKONYPRODUCTIONANDVICEVERSAPRODUCTIONPOSSIBILITYFRONTIERTHEEFCIENCYLOCUSINFIGURE162SHOWSTHEMAXIMUMOUTPUTOFYTHATCANBEPRODUCEDFORANYPREASSIGNEDOUTPUTOFXWECANUSETHISINFORMATIONTOCONSTRUCTAPRODUCTIONPOSSIBILITYFRONTIER,WHICHSHOWSTHEALTERNATIVEOUTPUTSOFXANDYTHATCANBEPRODUCEDWITHTHEXEDCAPITALANDLABORINPUTSINFIGURE163THEOXOYLOCUSHASBEENTAKENFROMFIGURE162ANDTRANSFERREDONTOAGRAPHWITHXANDYOUTPUTSONTHEAXESATOX,FOREXAMPLE,NORESOURCES426PARTVPERFECTCOMPETITIONPRODUCTIONPOSSIBILITYFRONTIERTHEPRODUCTIONPOSSIBILITYFRONTIERSHOWSTHEALTERNATIVECOMBINATIONSOFXANDYTHATCANBEEFCIENTLYPRODUCEDBYARMWITHXEDRESOURCESTHECURVECANBEDERIVEDFROMFIGURE162BYVARYINGINPUTSBETWEENTHEPRODUCTIONOFXANDYWHILEMAINTAININGTHECONDITIONSFOREFCIENCYTHENEGATIVEOFTHESLOPEOFTHEPRODUCTIONPOSSIBILITYCURVEISCALLEDTHERATEOFPRODUCTTRANSFORMATIONRPTOYX4AP1P2P3P4X3X2X1Y1Y2Y3Y4OXQUANTITYOFXQUANTITYOFYFIGURE163AREDEVOTEDTOXPRODUCTIONCONSEQUENTLY,YOUTPUTISASLARGEASISPOSSIBLEWITHTHEEXISTINGRESOURCESSIMILARLY,ATOY,THEOUTPUTOFXISASLARGEASPOSSIBLETHEOTHERPOINTSONTHEPRODUCTIONPOSSIBILITYFRONTIERSAY,P1,P2,P3,ANDP4AREDERIVEDFROMTHEEFCIENCYLOCUSINANIDENTICALWAYHENCEWEHAVEDERIVEDTHEFOLLOWINGDENITIONPRODUCTIONPOSSIBILITYFRONTIERTHEPRODUCTIONPOSSIBILITYFRONTIERSHOWSTHOSEALTERNATIVECOMBINATIONSOFTWOOUTPUTSTHATCANBEPRODUCEDWITHXEDQUANTITIESOFINPUTSIFTHOSEINPUTSAREEMPLOYEDEFCIENTLYRATEOFPRODUCTTRANSFORMATIONTHESLOPEOFTHEPRODUCTIONPOSSIBILITYFRONTIERSHOWSHOWXOUTPUTCANBESUBSTITUTEDFORYOUTPUTWHENTOTALRESOURCESAREHELDCONSTANTFOREXAMPLE,FORPOINTSNEAROXONTHEPRODUCTIONPOSSIBILITYFRONTIER,THESLOPEISASMALLNEGATIVENUMBER,SAY,H11002H500714H5007,IMPLYINGTHATBYREDUCINGYOUTPUTBY1UNIT,XOUTPUTCOULDBEINCREASEDBY4NEAROY,ONTHEOTHERHAND,THESLOPEISALARGENEGATIVENUMBER,SAY,H110025,IMPLYINGTHATYOUTPUTMUSTBEREDUCEDBY5UNITSTOPERMITTHEPRODUCTIONOFONEMOREXTHESLOPEOFTHEPRODUCTIONPOSSIBILITYFRONTIER,THEN,CLEARLYSHOWSTHEPOSSIBILITIESTHATEXISTFORTRADINGYFORXINPRODUCTIONTHENEGATIVEOFTHISSLOPEISCALLEDTHERATEOFPRODUCTTRANSFORMATIONRPTRATEOFPRODUCTTRANSFORMATIONTHERATEOFPRODUCTTRANSFORMATIONRPTBETWEENTWOOUTPUTSISTHENEGATIVEOFTHESLOPEOFTHEPRODUCTIONPOSSIBILITYFRONTIERFORTHOSEOUTPUTSMATHEMATICALLY,RPTOFXFORYH11005H11002SLOPEOFPRODUCTIONPOSSIBILITYFRONTIER161H11005H11002ALONGOXOYTHERPTRECORDSHOWXCANBETECHNICALLYTRADEDFORYWHILECONTINUINGTOKEEPTHEAVAILABLEPRODUCTIVEINPUTSEFCIENTLYEMPLOYEDSHAPEOFTHEPRODUCTIONPOSSIBILITYFRONTIERTHEPRODUCTIONPOSSIBILITYFRONTIERILLUSTRATEDINFIGURE163EXHIBITSANINCREASINGRPTFOROUTPUTLEVELSNEAROX,RELATIVELYLITTLEYMUSTBESACRICEDTOOBTAINONEMOREXH11002DY/DXISSMALLNEAROY,ONTHEOTHERHAND,ADDITIONALXMAYBEOBTAINEDONLYBYSUBSTANTIALREDUCTIONSINYOUTPUTH11002DY/DXISLARGEINTHISSECTIONWESHALLSHOWWHYTHISCONCAVESHAPEMIGHTBEEXPECTEDTOCHARACTERIZEMOSTPRODUCTIONSITUATIONSDYH5007DXDEFINITIONDEFINITIONCHAPTER16GENERALCOMPETITIVEEQUILIBRIUM427ARSTSTEPINTHATANALYSISISTORECOGNIZETHATRPTISEQUALTOTHERATIOOFTHEMARGINALCOSTOFXMCXTOTHEMARGINALCOSTOFYMCYINTUITIVELY,THISRESULTISOBVIOUSSUPPOSE,FOREXAMPLE,THATXANDYAREPRODUCEDONLYWITHLABORIFITTAKES2LABORHOURSTOPRODUCEONEMOREX,WEMIGHTSAYTHATMCXISEQUALTO2SIMILARLY,IFITTAKESONLY1LABORHOURTOPRODUCEANEXTRAY,MCYISEQUALTO1BUTINTHISSITUATIONITISCLEARTHATTHERPTIS2TWOYMUSTBEFOREGONETOPROVIDEENOUGHLABORSOTHATXMAYBEINCREASEDBY1UNITHENCE,THERPTISINDEEDEQUALTOTHERATIOOFTHEMARGINALCOSTSOFTHETWOGOODSMOREFORMALLY,SUPPOSETHATTHECOSTSSAY,INTERMSOFTHE“DISUTILITY”EXPERIENCEDBYFACTORSUPPLIERSOFANYOUTPUTCOMBINATIONAREDENOTEDBYCX,YALONGTHEPRODUCTIONPOSSIBILITYFRONTIER,CX,YWILLBECONSTANTBECAUSETHEINPUTSAREINXEDSUPPLYHENCEWECANWRITETHETOTALDIFFERENTIALOFTHECOSTFUNCTIONASDCH11005H11080DXH11001H11080DYH110050162FORCHANGESINXANDYALONGTHEPRODUCTIONPOSSIBILITYFRONTIERMANIPULATINGEQUATION162YIELDSRPTH11005H11002ALONGOXOYH11005H11005,163WHICHWASPRECISELYWHATWEWISHEDTOSHOWTHERPTISAMEASUREOFTHERELATIVEMARGINALCOSTSOFTHETWOGOODSTODEMONSTRATEREASONSWHYTHERPTMIGHTBEEXPECTEDTORISEFORCLOCKWISEMOVEMENTSALONGTHEPRODUCTIONPOSSIBILITYFRONTIER,WECANPROCEEDBYSHOWINGWHYTHERATIOOFMCXTOMCYSHOULDRISEASXOUTPUTEXPANDSANDYOUTPUTCONTRACTSWERSTPRESENTTWORELATIVELYSIMPLEARGUMENTSTHATAPPLYONLYTOSPECIALCASESTHENWETURNTOAMORESOPHISTICATEDGENERALARGUMENTDIMINISHINGRETURNSTHEMOSTCOMMONRATIONALEOFFEREDFORTHECONCAVESHAPEOFTHEPRODUCTIONPOSSIBILITYFRONTIERISTHEASSUMPTIONTHATBOTHGOODSAREPRODUCEDUNDERCONDITIONSOFDIMINISHINGRETURNSHENCEINCREASINGTHEOUTPUTOFGOODXWILLRAISEITSMARGINALCOST,WHEREASDECREASINGTHEOUTPUTOFYWILLREDUCEITSMARGINALCOSTEQUATION163THENSHOWSTHATTHERPTWILLINCREASEFORMOVEMENTSALONGTHEPRODUCTIONPOSSIBILITYFRONTIERFROMOXTOOYAPROBLEMWITHTHISEXPLANATION,OFCOURSE,ISTHATITAPPLIESONLYTOCASESINWHICHBOTHGOODSEXHIBITDIMINISHINGRETURNSTOSCALE,ANDTHATASSUMPTIONISATVARIANCEWITHTHETHEORETICALREASONSFORPREFERRINGTHEASSUMPTIONOFCONSTANTOREVENINCREASINGRETURNSTOSCALEWEHAVEMENTIONEDELSEWHEREINTHISBOOKSPECIALIZEDINPUTSIFSOMEINPUTSWERE“MORESUITED”FORXPRODUCTIONTHANFORYPRODUCTIONANDVICEVERSA,THECONCAVESHAPEOFTHEPRODUCTIONFRONTIERALSOCOULDBEEXPLAINEDINTHATCASE,INCREASESINXOUTPUTWOULDREQUIREDRAWINGPROGRESSIVELYLESSSUITABLEINPUTSINTOTHEPRODUCTIONOFTHATGOODMARGINALCOSTSOFXTHEREFOREWOULDRISEMARGINALCOSTSFORY,ONTHEOTHERHAND,WOULDFALL,ASSMALLEROUTPUTLEVELSFORYWOULDPERMITTHEUSEOFONLYTHOSEINPUTSMOSTSUITEDFORYPRODUCTIONSUCHANARGUMENTMIGHTAPPLY,FOREXAMPLE,TOAFARMERWITHAVARIETYOFTYPESOFLANDUNDERMCXH5007MCYH11128C/H11128XH5007H11128C/H11128YDYH5007DXH11128CH5007H11128YH11128CH5007H11128X428PARTVPERFECTCOMPETITIONCULTIVATIONINDIFFERENTCROPSINTRYINGTOINCREASETHEPRODUCTIONOFANYONECROP,THEFARMERWOULDBEFORCEDTOGROWITONINCREASINGLYUNSUITABLEPARCELSOFLANDALTHOUGHTHISTYPEOFSPECIALIZEDINPUTASSUMPTIONHASCONSIDERABLEIMPORTANCEINEXPLAININGAVARIETYOFREALWORLDPHENOMENA,ITISNONETHELESSATVARIANCEWITHOURGENERALASSUMPTIONOFHOMOGENEOUSFACTORSOFPRODUCTIONITCANNOTSERVEASAFUNDAMENTALEXPLANATIONFORCONCAVITYDIFFERINGFACTORINTENSITIESEVENIFINPUTSAREHOMOGENEOUSANDPRODUCTIONFUNCTIONSEXHIBITCONSTANTRETURNSTOSCALE,THEPRODUCTIONPOSSIBILITYFRONTIERWILLBECONCAVEIFGOODSXANDYUSEINPUTSINDIFFERENTPROPORTIONS4INTHEPRODUCTIONBOXDIAGRAMOFFIGURE162,FOREXAMPLE,GOODXISCAPITALINTENSIVERELATIVETOGOODYTHATIS,ATEVERYPOINTALONGTHEOXOYCONTRACTCURVE,THERATIOOFKTOLINXPRODUCTIONEXCEEDSTHERATIOOFKTOLINYPRODUCTIONTHEBOWEDCURVEOXOYISALWAYSABOVETHEMAINDIAGONALOFTHEEDGEWORTHBOXIF,ONTHEOTHERHAND,GOODYHADBEENRELATIVELYCAPITALINTENSIVE,THEOXOYCONTRACTCURVEWOULDHAVEBEENBOWEDDOWNWARDBELOWTHEDIAGONALALTHOUGHAFORMALPROOFTHATUNEQUALFACTORINTENSITIESRESULTINACONCAVEPRODUCTIONPOSSIBILITYFRONTIERWILLNOTBEPRESENTEDHERE,ITISPOSSIBLETOSUGGESTINTUITIVELYWHYTHATOCCURSCONSIDERANYTWOPOINTSONTHEFRONTIEROXOYINFIGURE163SAY,P1WITHCOORDINATESX1,Y4ANDP3WITHCOORDINATESX3,Y2ONEWAYOFPRODUCINGANOUTPUTCOMBINATION“BETWEEN”P1ANDP3WOULDBETOPRODUCETHECOMBINATION,BECAUSEOFTHECONSTANTRETURNSTOSCALEASSUMPTION,THATCOMBINATIONWOULDBEFEASIBLEANDWOULDFULLYUTILIZEBOTHFACTORSOFPRODUCTIONTHECOMBINATIONWOULDLIEATTHEMIDPOINTOFASTRAIGHTLINECHORDJOININGPOINTSP1ANDP3ALTHOUGHSUCHAPOINTISFEASIBLE,ITISNOTEFCIENT,ASCANBESEENBYEXAMININGPOINTSP1ANDP3INTHEBOXDIAGRAMOFFIGURE162BECAUSEOFTHEBOWEDNATUREOFTHECONTRACTCURVE,PRODUCTIONATAPOINTMIDWAYBETWEENP1ANDP3WOULDBEOFFTHECONTRACTCURVEPRODUCINGATAPOINTSUCHASP2WOULDPROVIDEMOREOFBOTHGOODSTHEPRODUCTIONPOSSIBILITYFRONTIERINFIGURE163MUSTTHEREFORE“BULGEOUT”BEYONDTHESTRAIGHTLINEP1P3BECAUSESUCHAPROOFCOULDBECONSTRUCTEDFORANYTWOPOINTSONOXOY,WEHAVESHOWNTHATTHEFRONTIERISCONCAVETHATIS,THERPTINCREASESASTHEOUTPUTOFGOODXINCREASESWHENPRODUCTIONISREALLOCATEDINANORTHEASTDIRECTIONALONGTHEOXOYCONTRACTCURVEINFIGURE162,THECAPITALLABORRATIODECREASESINTHEPRODUCTIONOFBOTHXANDYBECAUSEGOODXISCAPITALINTENSIVE,THISCHANGERAISESMCXONTHEOTHERHAND,BECAUSEGOODYISLABORINTENSIVE,MCYFALLSHENCETHERELATIVEMARGINALCOSTOFXASREPRESENTEDBYTHERPTRISESOPPORTUNITYCOSTTHEPRODUCTIONPOSSIBILITYCURVETHEREFOREDEMONSTRATESTHATTHEREAREMANYPOSSIBLEEFCIENTCOMBINATIONSOFTHETWOGOODSANDTHATPRODUCINGMOREOFONEGOODY4H11001Y2H50072X1H11001X3H50072CHAPTER16GENERALCOMPETITIVEEQUILIBRIUM4294IF,INADDITIONTOHOMOGENEOUSFACTORSANDCONSTANTRETURNSTOSCALE,EACHGOODALSOUSEDKANDLINTHESAMEPROPORTIONSUNDEROPTIMALALLOCATIONS,THEPRODUCTIONPOSSIBILITYFRONTIERWOULDBEASTRAIGHTLINENECESSITATESCUT