nicholson微观经济理论（答案+ppt+习题库）-170-03-033593-0

THEEFFICIENCYOFPERFECTCOMPETITIONALTHOUGHMOSTPEOPLERECOGNIZETHEEQUILIBRIUMPROPERTIESOFTHECOMPETITIVEPRICESYSTEMAFTERALL,PRICESUSUALLYDONOTUCTUATEWIDELYFROMDAYTODAY,THEYSEELITTLEOVERALLPATTERNTOTHERESULTINGALLOCATIONOFRESOURCESTHERELATIONSHIPSDESCRIBEDBYTHECOMPETITIVEMODELPRESENTEDINTHEPREVIOUSCHAPTERARESOCOMPLEXITISHARDTOBELIEVETHATANYDESIRABLEOUTCOMEWILLEMERGEFROMTHECHAOSTHISVIEWPROVIDESANOPENENDEDRATIONALETOTINKERWITHTHESYSTEMBECAUSETHERESULTSOFMARKETFORCESARECHAOTIC,SURELYHUMANSOCIETIESCANDOBETTERTHROUGHCAREFULPLANNING17CHAPTERSMITHSINVISIBLEHANDHYPOTHESISITTOOKTHEGENIUSOFADAMSMITHTOCHALLENGETHISVIEW,WHICHWASPROBABLYTHEPREVALENTONEINTHEEIGHTEENTHCENTURYTOSMITH,THECOMPETITIVEMARKETSYSTEMREPRESENTEDTHEPOLAROPPOSITEFROMCHAOSRATHER,ITPROVIDEDAPOWERFUL“INVISIBLEHAND”THATENSUREDRESOURCESWOULDNDTHEIRWAYTOWHERETHEYWEREMOSTVALUED,THEREBYENHANCINGTHE“WEALTH”OFTHENATIONINSMITHSVIEW,RELIANCEONTHEECONOMICSELFINTERESTOFINDIVIDUALSANDRMSWOULDRESULTINAPERHAPSSURPRISINGLYDESIRABLESOCIALOUTCOMESMITHSINITIALINSIGHTSGAVERISETOMODERNWELFAREECONOMICSSPECICALLY,HISWIDELYQUOTED“INVISIBLEHAND”IMAGEPROVIDEDTHEIMPETUSFORWHATISNOWCALLEDTHE“FUNDAMENTALTHEOREM”OFWELFAREECONOMICSTHATTHEREISACLOSECORRESPONDENCEBETWEENTHEEFCIENTALLOCATIONOFRESOURCESANDTHECOMPETITIVEPRICINGOFTHESERESOURCESINTHISCHAPTERWEWILLINVESTIGATETHISCORRESPONDENCEINSOMEDETAILWEBEGINBYDENINGECONOMICEFCIENCYINAVARIETYOFCONTEXTSTHESEDENITIONS,ALLOFWHICHDRAWONTHEWORKOFTHENINETEENTHCENTURYECONOMISTVILFREDPARETO,HAVEALREADYBEENDESCRIBEDBRIEYINEARLIERCHAPTERSOURGOALHEREISTODRAWTHESEDISCUSSIONSTOGETHERANDILLUSTRATETHEIRUNDERLYINGRELATIONSHIPTOTHECOMPETITIVEALLOCATIONOFRESOURCESPARETOEFCIENCYWEBEGINWITHPARETOSDENITIONOFECONOMICEFCIENCYPARETOEFCIENTALLOCATIONANALLOCATIONOFRESOURCESISPARETOEFCIENTIFITISNOTPOSSIBLETHROUGHFURTHERREALLOCATIONSTOMAKEONEPERSONBETTEROFFWITHOUTMAKINGSOMEONEELSEWORSEOFFTHEPARETODENITIONTHENIDENTIESPARTICULARALLOCATIONSASBEING“INEFCIENT”IFUNAMBIGUOUSIMPROVEMENTSAREPOSSIBLENOTICETHATTHEDENITIONDOESNOTREQUIREINTERPERSONCOMPARISONSOFUTILITY“IMPROVEMENTS”AREDENEDBYINDIVIDUALSTHEMSELVESEFCIENCYINPRODUCTIONANECONOMYISEFCIENTINPRODUCTIONIFITISONITSPRODUCTIONPOSSIBILITYFRONTIERFORMALLY,WECANUSEPARETOSTERMINOLOGYTODENEPRODUCTIVEEFCIENCYASFOLLOWSPRODUCTIVEEFCIENCYANALLOCATIONOFRESOURCESISEFCIENTINPRODUCTIONOR“TECHNICALLYEFCIENT”IFNOFURTHERREALLOCATIONWOULDPERMITMOREOFONEGOODTOBEPRODUCEDWITHOUTNECESSARILYREDUCINGTHEOUTPUTOFSOMEOTHERGOODDEFINITIONDEFINITION456PARTVPERFECTCOMPETITIONASFORPARETOEFCIENCYITSELF,ITISPERHAPSEASIESTTOGRASPTHISDENITIONBYSTUDYINGITSCONVERSEANALLOCATIONWOULDBEINEFCIENTIFITWEREPOSSIBLETOMOVEEXISTINGRESOURCESAROUNDABITANDGETADDITIONALAMOUNTSOFONEGOODANDNOLESSOFANYTHINGELSEWITHTECHNICALLYEFCIENTALLOCATIONS,NOSUCHUNAMBIGUOUSIMPROVEMENTSAREPOSSIBLETHETRADEOFFSAMONGOUTPUTSNECESSITATEDBYMOVEMENTSALONGTHEPRODUCTIONPOSSIBILITYFRONTIERREECTTHETECHNICALLYEFCIENTNATUREOFALLOFTHEALLOCATIONSONTHEFRONTIERTECHNICALEFCIENCYISANOBVIOUSPRECONDITIONFOROVERALLPARETOEFCIENCYSUPPOSERESOURCESWEREALLOCATEDSOTHATPRODUCTIONWASINEFCIENTTHATIS,PRODUCTIONWASOCCURRINGATAPOINTINSIDETHEPRODUCTIONPOSSIBILITYFRONTIERITWOULDTHENBEPOSSIBLETOPRODUCEMOREOFATLEASTONEGOODANDNOLESSOFANYTHINGELSETHISINCREASEDOUTPUTCOULDBEGIVENTOSOMELUCKYPERSONMAKINGHIMORHERBETTEROFFANDNOONEELSEWORSEOFFHENCE,INEFCIENCYINPRODUCTIONISALSOPARETOINEFCIENCYASWESHALLSEEINTHENEXTSECTION,HOWEVER,TECHNICALEFCIENCYDOESNOTGUARANTEEPARETOEFCIENCYANECONOMYCANBEEFCIENTATPRODUCINGTHEWRONGGOODSDEVOTINGALLAVAILABLERESOURCESTOPRODUCINGLEFTSHOESWOULDBEATECHNICALLYEFCIENTUSEOFTHOSERESOURCES,BUTSURELYSOMEPARETOIMPROVEMENTCOULDBEFOUNDINWHICHEVERYONEWOULDBEBETTEROFFADISCUSSIONOFEFCIENCYINPRODUCTIONANDITSRELATIONSHIPTOTHEPRODUCTIONPOSSIBILITYFRONTIERISSOMEWHATMORECOMPLEXTHANOURSIMPLEPRESENTATIONINCHAPTER16MIGHTIMPLYBECAUSEPRODUCTIONISDIVIDEDAMONGMANYRMS,WEMUSTBECONCERNEDNOTONLYWITHTHEWAYSINWHICHASINGLERMUSESITSRESOURCESASWEESSENTIALLYWEREINTHEPREVIOUSCHAPTER,BUTALSOWITHHOWRESOURCESAREALLOCATEDAMONGRMSTOFACILITATETHISEXAMINATION,WEWILLBREAKTHEQUESTIONDOWNINTOTHREESEPARATEISSUES1RESOURCEALLOCATIONWITHINASINGLERM2ALLOCATIONOFPRODUCTIVERESOURCESAMONGRMSAND3COORDINATIONOFRMSOUTPUTCHOICESRESULTSFOREACHOFTHESEISSUESWILLBESUMMARIZEDBYAGENERAL“ALLOCATIONRULE”ALLOFTHESERULESMUSTHOLDTOENSUREPRODUCTIVEEFCIENCYEFCIENTCHOICEOFINPUTSFORASINGLEFIRMINCHAPTER16WEEXAMINEDTHESITUATIONOFARMHAVINGXEDINPUTSOFCAPITALANDLABORTHEREWESHOWEDTHATTHERMWILLHAVEALLOCATEDTHESEINPUTSEFCIENTLYIFTHEYAREFULLYEMPLOYEDANDIFTHERATEOFTECHNICALSUBSTITUTIONRTSBETWEENCAPITALANDLABORISTHESAMEFOREVERYOUTPUTTHERMPRODUCESPREVIOUSLY,WEDEVELOPEDADETAILEDGRAPHICALPROOFOFTHISASSERTIONHEREWEWILLUSEAMATHEMATICALAPPROACHASSUMETHERMPRODUCESTWOGOODS,XANDY,ANDTHATTHETOTALAVAILABLEINPUTSOFCAPITALANDLABORAREGIVENBYKH33526ANDLH33526THEPRODUCTIONFUNCTIONFORGOODXISGIVENBYXH11005FKX,LX,171WHEREKXANDLXARECAPITALANDLABORDEVOTEDTOXPRODUCTIONIFWEASSUMEFULLEMPLOYMENT,KYH11005KH33526H11002KX,LYH11005LH33526H11002LX,ANDTHEPRODUCTIONFUNCTIONFORGOODYISYH11005GKY,LYH11005GKH33526H11002KX,LH33526H11002LX172TECHNICALEFCIENCYREQUIRESTHATXOUTPUTBEASLARGEASPOSSIBLEFORANYPREDETERMINEDVALUEOFYOUTPUTSAY,YH33526SETTINGUPTHELAGRANGIANEXPRESSIONFORTHISCONSTRAINEDMAXIMUMPROBLEMYIELDSH5112H11005FKX,LXH11001H9261YH33526H11002GKH33526H11002KX,LH33526H11002LX173CHAPTER17THEEFCIENCYOFPERFECTCOMPETITION457DIFFERENTIATIONWITHRESPECTTOKX,LX,ANDH9261GIVESTHEFOLLOWINGRSTORDERCONDITIONSFORACONSTRAINEDMAXIMUMH11005FKH11001H9261GKH110050174H11005FLH11001H9261GLH110050H11005YH33526H11002GKH33526H11002KX,LH33526H11002LXH110050MOVINGTHETERMSINH9261TOTHERIGHTHANDSIDEOFTHERSTTWOOFTHESEEQUATIONS,WEHAVEH11005,175AND,USINGTHERESULTFROMCHAPTER11THATTHERTSISTHERATIOOFTHEINPUTSMARGINALPRODUCTIVITIES,THATIMPLIES1RTSXKFORLH11005RTSYKFORL176THISISPRECISELYTHERESULTWESHOWEDGRAPHICALLYINFIGURE163EFCIENTALLOCATIONOFRESOURCESAMONGFIRMSRESOURCESMUSTALSOBEALLOCATEDINSOMEEFCIENTWAYAMONGRMSTOENSUREOVERALLPRODUCTIVEEFCIENCYINTUITIVELY,RESOURCESSHOULDBEALLOCATEDTOTHOSERMSWHERETHEYCANBEMOSTEFCIENTLYUSEDMOREPRECISELY,THECONDITIONFOREFCIENTALLOCATIONISTHATTHEMARGINALPHYSICALPRODUCTOFANYRESOURCEINTHEPRODUCTIONOFAPARTICULARGOODISTHESAMENOMATTERWHICHRMPRODUCESTHATGOODAMATHEMATICALPROOFOFTHISRULEISSTRAIGHTFORWARDSUPPOSETHEREARETWORMSPRODUCINGTHESAMEGOODXANDTHEIRPRODUCTIONFUNCTIONSAREGIVENBYF1K1,L1ANDF2K2,L2ASSUMEALSOTHATTOTALSUPPLIESOFCAPITALANDLABORAREGIVENBYKH33526ANDLH33526THEALLOCATIONALPROBLEMISTHENTOMAXIMIZEXH11005F1K1,L1H11001F2K2,L2,177SUBJECTTOTHECONSTRAINTSK1H11001K2H11005KH33526178L1H11001L2H11005LH33526UPONSUBSTITUTINGTHECONSTRAINTSINTOEQUATION177,THEMAXIMIZATIONPROBLEMBECOMESXH11005F1K1,L1H11001F2KH33526H11002K1,LH33526H11002L1179GKH5007GLFKH5007FLH11128H5112H5007H11128H9261H11128H5112H5007H11128LXH11128H5112H5007H11128KX458PARTVPERFECTCOMPETITION1THESERESULTSHOLDONLYFORANINTERIORMAXIMUMINWHICHBOTHINPUTSAREACTUALLYUSEDTOPRODUCEBOTHGOODSIFTHATWERENOTTHECASE,THESERSTORDERCONDITIONSWOULDHAVETOBEAMENDEDFIRSTORDERCONDITIONSFORAMAXIMUMAREH11005H11001H11005H11002H1100501710H11005H11001H11005H11002H110050ORH11005ANDH11005,1711ASWASTOBESHOWNEXAMPLE171GAINSFROMEFCIENTLYALLOCATINGLABORTOEXAMINETHEQUANTITATIVEGAINSINOUTPUTFROMALLOCATINGRESOURCESEFCIENTLY,SUPPOSETWORICEFARMSHAVEPRODUCTIONFUNCTIONSOFTHESIMPLEFORMQH11005K1/4L3/4,1712BUTONERICEFARMISMOREMECHANIZEDTHANTHEOTHERIFCAPITALFORTHERSTFARMISGIVENBYK1H1100516ANDFORTHESECONDFARMBYK2H11005625,WEHAVEQ1H110052L31/4Q2H110055L32/41713IFTHETOTALLABORSUPPLYIS100,ANEQUALALLOCATIONOFLABORTOTHESETWOFARMSWILLPROVIDETOTALRICEOUTPUTOFQH11005Q1H11001Q2H110052503/4H110015503/4H1100513161714THEEFCIENTALLOCATIONISFOUNDBYSETTINGTHEMARGINALPRODUCTIVITIESEQUALH11005H20898H20899L1H110021/4H11005H11005L2H110021/41715HENCE,FOREFCIENCYLABORSHOULDBEALLOCATEDSOTHATL1H11005H20898H20899H110024L2H110050256L21716GIVENTHEGREATERCAPITALIZATIONOFFARM2,PRACTICALLYALLOFTHEAVAILABLELABORSHOULDBEDEVOTEDTOITWITH100UNITSOFLABOR,974UNITSSHOULDBEALLOCATEDTOFARM2WITHONLY26UNITSTOFARM1INTHISCASETOTALOUTPUTWILLBEQH11005Q1H11001Q2H110052263/4H1100159743/4H1100515911717THISREPRESENTSAGAINOFMORETHAN20PERCENTOVERTHERICEOUTPUTOBTAINEDUNDERTHEEQUALALLOCATIONQUERYSUPPOSECAPITALWERENOTXEDINTHISPROBLEMHOWSHOULDCAPITALANDLABORBEALLOCATEDBETWEENTHETWOFARMS5H5007215H50074H11128Q2H5007H11128L23H50072H11128Q1H5007H11128L1H11128F2H5007H11128L2H11128F1H5007H11128L1H11128F2H5007H11128K2H11128F1H5007H11128K1H11128F2H5007H11128L2H11128F1H5007H11128L1H11128F2H5007H11128L1H11128F1H5007H11128L1H11128XH5007H11128L1H11128F2H5007H11128K2H11128F1H5007H11128K1H11128F2H5007H11128K1H11128F1H5007H11128K1H11128XH5007H11128K1CHAPTER17THEEFCIENCYOFPERFECTCOMPETITION459EFCIENTCHOICEOFOUTPUTBYFIRMSALTHOUGHRESOURCESMAYBEEFCIENTLYALLOCATEDWITHINARMANDAMONGALLRMS,THEREISSTILLONEOTHERCONDITIONOFEFCIENTPRODUCTIONTHATMUSTBEOBEYEDFIRMSMUSTPRODUCEEFCIENTCOMBINATIONSOFOUTPUTSROUGHLYSPEAKING,RMSTHATAREGOODATPRODUCINGHAMBURGERSSHOULDPRODUCEHAMBURGERSANDTHOSEGOODATPRODUCINGCARSSHOULDPRODUCECARSAMATHEMATICALDERIVATIONOFTHECONDITIONREQUIREDFORTHISRESULTISSTRAIGHTFORWARDSUPPOSETHEREARETWOOUTPUTSXANDYEACHPRODUCEDBYTWORMS,ANDTHEPRODUCTIONPOSSIBILITYFRONTIERSFORTHESERMSAREGIVENINEXPLICITFORMBYYIH11005FIXIFORIH110051,21718THEOVERALLOPTIMIZATIONPROBLEM,THEN,ISTOPRODUCETHEMAXIMUMAMOUNTOFXFORANYGIVENVALUEOFYSAY,YSETTINGUPTHELAGRANGIANFORTHISPROBLEMASH5112H11005X1H11001X2H11001H9261YH11002F1X1H11002F2X21719YIELDSTHESIMPLERSTORDERCONDITIONH11128F1/H11128X1H11005H11128F2/H11128X21720INWORDS,THERATEOFPRODUCTTRANSFORMATIONSHOULDBETHESAMEFORALLRMSPRODUCINGTHESETWOGOODSTHISRESULTISSHOWNGRAPHICALLYINFIGURE171THERETWORMSHAVEOPTEDFOROUTPUTCOMBINATIONSONTHEIRRESPECTIVEPRODUCTIONPOSSIBILITYCURVESWITHUNEQUALRPTSBECAUSERMASRPTIS2,ITCOULDINCREASECARPRODUCTIONBY2TO102BYREDUCINGTRUCKOUTPUTBY1TO99FIRMBCOULDEXPANDTRUCKOUTPUTTO51BYREDUCINGCAROUTPUTTO99HENCETOTALOUTPUTOFCARSHASINCREASEDFROM200TO201WHEREASTRUCKOUTPUTHASREMAINEDAT100SUCHGAINSINPRODUCTIONAREALWAYSPOSSIBLEWHENRPTSDIFFERTHEORYOFCOMPARATIVEADVANTAGEONEOFTHEMOSTIMPORTANTAPPLICATIONSOFTHISCONCLUSIONISINTHESTUDYOFINTERNATIONALTRADE,WHEREITISUSEDASTHEBASISFORTHETHEORYOFCOMPARATIVEADVANTAGETHISTHEORYWASRSTPROPOSEDBYRICARDO,WHOARGUEDTHATCOUNTRIESSHOULDSPECIALIZEINPRODUCINGTHOSEGOODSOFWHICHTHEYARERELATIVELYMOREEFCIENTPRODUCERS2THECOUNTRIESSHOULDTHENTRADEWITHTHERESTOFTHEWORLDTOOBTAINNEEDEDCOMMODITIESIFCOUNTRIESDOSPECIALIZEINTHISWAY,TOTALWORLDPRODUCTIONWILLBEGREATERTHANIFEACHCOUNTRYTRIEDTOPRODUCEABALANCEDBUNDLEOFGOODSTODEMONSTRATETHISFACT,LETUSLOOKAGAINATFIGURE171NOWWECANTAKETHETWOPRODUCTIONPOSSIBILITYCURVESTOREPRESENTTHOSEOFTWODIFFERENTCOUNTRIESWITHXEDRESOURCESPOINTSPA1ANDPB1MAYREPRESENTTHECOUNTRIESPRETRADEPRODUCTIONCHOICESBECAUSETHERPTDIFFERSBETWEENTHETWOCOUNTRIES,WORLDOUTPUTCOULDBEINCREASEDBYHAVINGCOUNTRYAPRODUCEMORECARSANDCOUNTRYBPRODUCEMORETRUCKSTHECOUNTRIESSHOULDPROCEEDTOSPECIALIZEINTHISWAYUNTILTHEIRRPTSAREEQUILIBRATEDWITHCOUNTRYASPECIALIZINGINCARPRODUCTION,ITCANTRADEWITHCOUNTRYBTOGETTHETRUCKSITNEEDSSIMILARLY,BCANTRADEWITHAFORCARSBECAUSETOTAL460PARTVPERFECTCOMPETITION2SEEDRICARDO,THEPRINCIPLESOFPOLITICALECONOMYANDTAXATION1817REPRINTED,LONDONJMDENTANDSON,1965,PP8193WORLDOUTPUTHASBEENINCREASEDASARESULTOFSPECIALIZATION,BOTHCOUNTRIESMAYNOWBEBETTEROFFTHISISTHELOGICTHATPROVIDESINTELLECTUALSUPPORTFORTHEBELIEFTHAT“FREETRADEISTHEBESTPOLICY”ITISIMPORTANTTONOTETHATTHEANALYSISUSESONLYINFORMATIONABOUTTHEPRODUCTTRANSFORMATIONRATESBETWEENTHETWOGOODSINEACHCOUNTRY,NOTABOUTMARGINALPRODUCTIVITYDIFFERENCESBETWEENCOUNTRIESITISPOSSIBLETHATACOUNTRYCOULDHAVEAN“ABSOLUTE”ADVANTAGEINTHEPRODUCTIONOFEVERYGOODINTHESENSETHATITSMARGINALPRODUCTIVITYOFLABORINTHEPRODUCTIONOFEVERYGOODEXCEEDEDTHATOFITSTRADINGPARTNER,BUTSUCHACOUNTRYWOULDSTILLBENETFROMSPECIALIZATIONANDTRADEEXAMPLE172COMPARATIVEADVANTAGEINRICARDOSWORLDINHISORIGINALDISCUSSIONOFTHECOMPARATIVEADVANTAGECONCEPT,RICARDOASSUMEDTHATPRODUCTIONPOSSIBILITYFRONTIERSWERELINEARCONSIDERTHEFOLLOWINGHYPOTHETICALMARGINALCOSTDATAEXPRESSEDINACOMMONCURRENCYFORENGLANDANDPORTUGALFORTHETWOGOODSWINEANDCLOTHMARGINALCOSTSENGLANDPORTUGALWINE82CLOTH42CHAPTER17THEEFCIENCYOFPERFECTCOMPETITION461GRAPHICALDEMONSTRATIONOFEFCIENTOUTPUTCHOICEIFTWORMSRATESOFPRODUCTTRANSFORMATIONDIFFER,TOTALOUTPUTCANBEINCREASEDBYMOVINGTHESERMSTOWARDEQUALIZATIONOFTHOSERATESINTHEGURE,RMAISRELATIVELYEFCIENTATPRODUCINGCARS,ANDRMBISRELATIVELYEFCIENTATPRODUCINGTRUCKSIFEACHRMWERETOSPECIALIZEINITSEFCIENTPRODUCT,TOTALOUTPUTCOULDBEINCREASEDRPTH11005P1A12500OUTPUTOFTRUCKSAFIRMA100OUTPUTOFCARSRPTH11005P1B11500OUTPUTOFTRUCKSBFIRMB100OUTPUTOFCARSFIGURE171INRICARDOSANALYSIS,MARGINALCOSTSWEREASSUMEDTOBECONSTANTANDEQUALTOAVERAGECOSTSCONSEQUENTLY,IFWELETTOTALRESOURCECOSTSBEXEDFOREACHCOUNTRYAT100,THEPRODUCTIONPROBABILITYFRONTIERFORENGLANDIS8WH110014CH11005100,1721ANDFORPORTUGALITIS2WH110012CH11005100CLEARLY,THERPTSDIFFERBETWEENTHESECOUNTRIESRPTENGLANDH11005H11002H1100521722RPTPORTUGALH11005H11002H110051RICARDOARGUEDTHATALTHOUGHPORTUGALHASANABSOLUTECOSTADVANTAGEINPRODUCINGBOTHGOODS,BOTHCOUNTRIESCOULDBENETFROMTRADE,BECAUSEWINEISRELATIVELYLESSCOSTLYINPORTUGALANDCLOTHISRELATIVELYLESSCOSTLYINENGLANDTHATIS,ENGLANDHASA“COMPARATIVEADVANTAGE”INCLOTH,PORTUGALINWINETHEGAINSFROMRECOGNIZINGCOMPARATIVEADVANTAGESUPPOSEPRIORTOTRADE,EACHCOUNTRYDEVOTESHALFOFITSRESOURCESTOEACHGOODTHENFORENGLANDWH11005H110056251723CH11005H11005125,ANDFORPORTUGALWH11005H1100525CH11005H1100525WORLDOUTPUTCANBEUNAMBIGUOUSLYINCREASEDIFENGLANDWERETOPRODUCELESSWINEANDMORECLOTHWITHTHEOPPOSITECHANGEOCCURRINGINPORTUGALIF,FOREXAMPLE,ENGLANDWERETODEVOTEALLOFITSRESOURCESTOCLOTH,OUTPUTTHEREWOULDBECH1100525NOWIFPORTUGALWERETOSHIFTITSPRODUCTIONTOALLOCATING70PERCENTOFTOTALINPUTSTOWINE,ITWOULDPRODUCEWH11005H11005351724CH11005H1100515HENCE,WORLDWINEOUTPUTHASRISENFROM3125TO35,ANDCLOTHOUTPUTHASRISENFROM375TO40ALTHOUGHTHESUPPLYOFINPUTSINEACHCOUNTRYHASNOTCHANGED,WORLDOUTPUTHASBEENUNAMBIGUOUSLYINCREASEDTHROUGHRECOGNITIONOFCOMPARATIVEADVANTAGE30H5007270H5007250H5007250H5007250H5007450H50078DCH5007DWDCH5007DW462PARTVPERFECTCOMPETITIONQUERYINTHISEXAMPLEASINMOSTCASESINVOLVINGLINEARPRODUCTIONPOSSIBILITYFRONTIERS,ENGLANDSRESOURCEALLOCATIONHASBEEN“COMPLETELYSPECIALIZED”INCLOTHPRODUCTIONWOULDANYOUTPUTPATTERNSHORTOFCOMPLETESPECIALIZATIONPROMISEANUNAMBIGUOUSIMPROVEMENTOVERTHISALLOCATIONIFPRODUCTIONPOSSIBILITYCURVESWERECONCAVERATHERTHANLINEAR,ISCOMPLETESPECIALIZATIONLIKELYTOBEEFCIENTEFCIENCYINPRODUCTMIXTECHNICALEFCIENCYISNOTASUFCIENTCONDITIONFORPARETOEFCIENCYDEMANDMUSTALSOBEBROUGHTINTOTHESTORYITDOESLITTLEGOODFORANECONOMYTOBEANEFCIENTPRODUCEROFYOYOSANDXYLOPHONESIFNOONEWANTSTHESEGOODSINORDERTOENSUREPARETOEFCIENCY,WENEEDSOMEWAYTOTIEINDIVIDUALSPREFERENCESANDPRODUCTIONPOSSIBILITIESTOGETHERTHECONDITIONNECESSARYTOENSURETHATTHERIGHTGOODSAREPRODUCEDISTHATTHEMARGINALRATEOFSUBSTITUTIONFORANYTWOGOODSMUSTBEEQUALTOTHERATEOFPRODUCTTRANSFORMATIONOFTHETWOGOODSSIMPLYPHRASED,THEPSYCHOLOGICALRATEOFTRADEOFFBETWEENTHETWOGOODSINPEOPLESPREFERENCESMUSTBEEQUALTOTHERATEATWHICHTHEYCANBETRADEDOFFINPRODUCTIONAGRAPHICALPROOFFIGURE172ILLUSTRATESTHEREQUIREMENTFOREFCIENCYINPRODUCTMIXFORAVERYSIMPLECASE,ASINGLEPERSONECONOMYITASSUMESTHATTHEONEPERSONINTHISECONOMYROBINSONCRUSOEPRODUCESONLYTWOGOODSXANDYTHISANALYSISCOULDALSOAPPLYTOANECONOMYOFMANYINDIVIDUALSWITHIDENTICALPREFERENCESTHOSECOMBINATIONSOFXANDYTHATCANBEPRODUCEDAREGIVENBYTHEPRODUCTIONPOSSIBILITYFRONTIERPPANYPOINTONPPREPRESENTSAPOINTOFTECHNICALEFCIENCYBYSUPERIMPOSINGTHEINDIVIDUALSINDIFFERENCEMAPONFIGURE172,HOWEVER,WESEETHATONLYONEPOINTONPPPROVIDESMAXIMUMUTILITYTHISPOINTOFMAXIMUMUTILITYISATE,WHERETHECURVEPPISTANGENTTOTHEINDIVIDUALSHIGHESTINDIFFERENCECURVE,U2ATTHISPOINTOFTANGENCY,THEINDIVIDUALSMRSOFXFORYISEQUALTOTHETECHNICALRPTOFXFORYHENCE,THISISTHEREQUIREDCONDITIONFOROVERALLEFCIENCYNOTICETHATPOINTEISPREFERREDTOEVERYOTHERPOINTTHATISEFCIENTINAPRODUCTIVESENSEINFACT,FORANYPOINTOTHERTHANPOINTE,SUCHASF,ONTHECURVEPP,THEREEXISTPOINTSTHATAREINEFCIENTBUTAREPREFERREDTOFINFIGURE172,THE“INEFCIENT”POINTGISPREFERREDTOTHE“EFCIENT”POINTFITWOULDBEPREFERABLEFROMTHEINDIVIDUALSPOINTOFVIEWTOPRODUCEINEFCIENTLYRATHERTHANBEFORCEDTOPRODUCETHE“WRONG”COMBINATIONOFGOODSINANEFCIENTWAYPOINTEWHICHISEFCIENTLYPRODUCEDISSUPERIORTOANYSUCH“SECONDBEST”SOLUTIONSAMATHEMATICALPROOFTODEMONSTRATETHISRESULTMATHEMATICALLY,ASSUMETHEREAREONLYTWOGOODSXANDYANDONEINDIVIDUALINSOCIETYAGAINROBINSONCRUSOEWHOSEUTILITYFUNCTIONISGIVENBYUX,YASSUMEALSOTHATTHISSOCIETYSPRODUCTIONPOSSIBILITYFRONTIERCANBEWRITTENINIMPLICITFORMASTX,YH110050ROBINSONSPROBLEMISTOMAXIMIZEUTILITYSUBJECTTOTHISPRODUCTIONCONSTRAINTSETTINGUPTHELAGRANGIANEXPRESSIONFORTHISPROBLEMYIELDSH5112H11005UX,YH11001H9261TX,Y,1725CHAPTER17THEEFCIENCYOFPERFECTCOMPETITION463ANDTHERSTORDERCONDITIONSFORANINTERIORMAXIMUMAREH11005H11001H9261H1100501726H11005H11001H9261H110050H11005TX,YH110050COMBININGTHERSTTWOOFTHESEEQUATIONSYIELDSH110051727ORMRSXFORYH11005H11002ALONGTH11005RPTXFORY,1728ASFIGURE172ILLUSTRATEDWEHAVESHOWNTHATONLYIFINDIVIDUALSPREFERENCESARETAKENINTOACCOUNTWILLRESOURCESBEALLOCATEDINAPARETOEFCIENTWAYWITHOUTDYH5007DXH11128T/H11128XH5007H11128T/H11128YH11128U/H11128XH5007H11128U/H11128YH11128H5112H5007H11128H9261H11128TH5007H11128YH11128UH5007H11128YH11128H5112H5007H11128YH11128TH5007H11128XH11128UH5007H11128XH11128H5112H5007H11128X464PARTVPERFECTCOMPETITIONEFCIENCYINPRODUCTMIXINAROBINSONCRUSOEECONOMYINASINGLEPERSONECONOMY,THECURVEPPREPRESENTSTHOSECOMBINATIONSOFXANDYTHATCANBEPRODUCEDEVERYPOINTONPPISEFCIENTINAPRODUCTIONSENSEHOWEVER,ONLYTHEOUTPUTCOMBINATIONATPOINTEISATRUEUTILITYMAXIMUMFORTHEINDIVIDUALATETHEINDIVIDUALSMRSISEQUALTOTHERATEATWHICHXCANTECHNICALLYBETRADEDFORYRPTOUTPUTOFYU3FPGEOUTPUTOFXU2U1PFIGURE172SUCHANEXPLICITREFERENCETOPREFERENCES,ITWOULDBEPOSSIBLE,BYREALLOCATINGPRODUCTION,TORAISEATLEASTONEPERSONSUTILITYWITHOUTREDUCINGANYONEELSESEXAMPLE173UTILITYMAXIMIZINGPRODUCTMIXSEVERALEXAMPLESINCHAPTER16UTILIZEDAPRODUCTIONPOSSIBILITYFRONTIERFORGUNSXANDBUTTERYOFTHEFORMX2H110014Y2H110051001729ANDAUTILITYFUNCTIONOFTHEFORMUTILITYH11005UX,YH11005H20857XYH335261730TODESCRIBEAGENERALEQUILIBRIUMMODELOFPRICEDETERMINATIONFORTHETWOGOODSTHISSITUATIONCOULDALSOBE