nicholson微观经济理论（答案+ppt+习题库）-130-03-033593-0

PROFITMAXIMIZATIONANDSUPPLYINCHAPTER12WEEXAMINEDTHEWAYINWHICHRMSMINIMIZECOSTSFORANYLEVELOFOUTPUTTHEYMAYCHOOSEINTHISCHAPTERWEWILLFOCUSONHOWTHELEVELOFOUTPUTISCHOSENBYPROTMAXIMIZINGRMSBEFOREINVESTIGATINGTHATDECISION,HOWEVER,ITISAPPROPRIATETODISCUSSBRIEYTHENATUREOFRMSANDTHEWAYSINWHICHTHEIRCHOICESMAYBEANALYZED13CHAPTERTHENATUREANDBEHAVIOROFFIRMSASWEPOINTEDOUTATTHEBEGINNINGOFOURANALYSISOFPRODUCTION,ARMISANASSOCIATIONOFINDIVIDUALSWHOHAVEORGANIZEDTHEMSELVESFORTHEPURPOSEOFTURNINGINPUTSINTOOUTPUTSDIFFERENTINDIVIDUALSWILLPROVIDEDIFFERENTTYPESOFINPUTS,SUCHASWORKERSSKILLSANDVARIETIESOFCAPITALEQUIPMENT,WITHTHEEXPECTATIONOFRECEIVINGSOMESORTOFREWARDFORDOINGSOCONTRACTUALRELATIONSHIPSWITHINFIRMSTHENATUREOFTHECONTRACTUALRELATIONSHIPBETWEENTHEPROVIDERSOFINPUTSTOARMMAYBEQUITECOMPLICATEDEACHPROVIDERAGREESTODEVOTEHISORHERINPUTTOPRODUCTIONACTIVITIESUNDERASETOFUNDERSTANDINGSABOUTHOWITISTOBEUSEDANDWHATBENETISTOBEEXPECTEDFROMTHATUSEINSOMECASESTHESECONTRACTSAREEXPLICITWORKERSOFTENNEGOTIATECONTRACTSTHATSPECIFYINCONSIDERABLEDETAILWHATHOURSARETOBEWORKED,WHATRULESOFWORKARETOBEFOLLOWED,ANDWHATRATEOFPAYISTOBEEXPECTEDSIMILARLY,CAPITALOWNERSINVESTINARMUNDERASETOFEXPLICITLEGALPRINCIPLESABOUTTHEWAYSINWHICHTHATCAPITALMAYBEUSED,THECOMPENSATIONTHEOWNERCANEXPECTTORECEIVE,ANDWHETHERTHEOWNERRETAINSANYPROTSORLOSSESAFTERALLECONOMICCOSTSHAVEBEENPAIDDESPITETHESEFORMALARRANGEMENTS,ITISCLEARTHATMANYOFTHEUNDERSTANDINGSBETWEENTHEPROVIDERSOFINPUTSTOARMAREIMPLICITRELATIONSHIPSBETWEENMANAGERSANDWORKERSFOLLOWCERTAINPROCEDURESABOUTWHOHASTHEAUTHORITYTODOWHATINMAKINGPRODUCTIONDECISIONSAMONGWORKERS,NUMEROUSIMPLICITUNDERSTANDINGSEXISTABOUTHOWWORKTASKSARETOBESHAREDANDCAPITALOWNERSMAYDELEGATEMUCHOFTHEIRAUTHORITYTOMANAGERSANDWORKERSTOMAKEDECISIONSONTHEIRBEHALFGENERALMOTORSSHAREHOLDERS,FOREXAMPLE,ARENEVERINVOLVEDINHOWASSEMBLYLINEEQUIPMENTWILLBEUSED,THOUGHTECHNICALLYTHEYOWNITALLOFTHESEEXPLICITANDIMPLICITRELATIONSHIPSCHANGEINRESPONSETOEXPERIENCESANDEVENTSEXTERNALTOTHERMMUCHASABASKETBALLTEAMWILLTRYOUTNEWPLAYSANDDEFENSIVESTRATEGIES,SOTOORMSWILLALTERTHENATUREOFTHEIRINTERNALORGANIZATIONSTOACHIEVEBETTERLONGTERMRESULTS1MODELINGFIRMSBEHAVIORALTHOUGHSOMEECONOMISTSHAVEADOPTEDA“BEHAVIORAL”APPROACHTOSTUDYINGRMSDECISIONS,MOSTHAVEFOUNDTHATAPPROACHTOOCUMBERSOMEFORGENERALPURPOSESRATHER,THEYHAVEADOPTEDA“HOLISTIC”APPROACHTHATTREATSTHERMASASINGLEDECISIONMAKINGUNITANDSWEEPSAWAYALLTHECOMPLICATEDBEHAVIORALISSUESABOUTRELATIONSHIPSAMONGINPUTPROVIDERSUNDERTHISAPPROACH,ITISOFTENCONVENIENTTOASSUMETHATARMSDECISIONSAREMADEBYASINGLEDICTATORIALMANAGERWHORATIONALLYPURSUESSOMEGOAL,USUALLYPROTMAXIMIZATIONTHATISTHEAPPROACHWETAKEHERE334PARTIVPRODUCTIONANDSUPPLY1THEINITIALDEVELOPMENTOFTHETHEORYOFTHERMFROMTHENOTIONOFTHECONTRACTUALRELATIONSHIPSINVOLVEDCANBEFOUNDINRHCOASE,“THENATUREOFTHEFIRM,”ECONOMICANOVEMBER1937386405PROTMAXIMIZATIONMOSTMODELSOFSUPPLYASSUMETHATTHERMANDITSMANAGERPURSUETHEGOALOFACHIEVINGTHELARGESTECONOMICPROTSPOSSIBLEHENCEWEWILLUSETHEFOLLOWINGDENITIONPROTMAXIMIZINGRMAPROTMAXIMIZINGRMCHOOSESBOTHITSINPUTSANDITSOUTPUTSWITHTHESOLEGOALOFACHIEVINGMAXIMUMECONOMICPROTSTHATIS,THERMSEEKSTOMAKETHEDIFFERENCEBETWEENITSTOTALREVENUESANDITSTOTALECONOMICCOSTSASLARGEASPOSSIBLETHISASSUMPTIONTHATRMSSEEKMAXIMUMECONOMICPROTSHASALONGHISTORYINECONOMICLITERATUREITHASMUCHTORECOMMENDITITISPLAUSIBLEBECAUSERMOWNERSMAYINDEEDSEEKTOMAKETHEIRASSETASVALUABLEASPOSSIBLE,ANDCOMPETITIVEMARKETSMAYPUNISHRMSTHATDONOTMAXIMIZEPROTSTHEASSUMPTIONALSOYIELDSINTERESTINGTHEORETICALRESULTSTHATCANEXPLAINACTUALRMSDECISIONSPROTMAXIMIZATIONANDMARGINALISMIFRMSARESTRICTPROTMAXIMIZERS,THEYWILLMAKEDECISIONSINA“MARGINAL”WAYTHEENTREPRENEURWILLPERFORMTHECONCEPTUALEXPERIMENTOFADJUSTINGTHOSEVARIABLESTHATCANBECONTROLLEDUNTILITISIMPOSSIBLETOINCREASEPROTSFURTHERTHISINVOLVES,SAY,LOOKINGATTHEINCREMENTAL,OR“MARGINAL,”PROTOBTAINABLEFROMPRODUCINGONEMOREUNITOFOUTPUT,ORATTHEADDITIONALPROTAVAILABLEFROMHIRINGONEMORELABORERASLONGASTHISINCREMENTALPROTISPOSITIVE,THEEXTRAOUTPUTWILLBEPRODUCEDORTHEEXTRALABORERWILLBEHIREDWHENTHEINCREMENTALPROTOFANACTIVITYBECOMESZERO,THEENTREPRENEURHASPUSHEDTHATACTIVITYFARENOUGH,ANDITWOULDNOTBEPROTABLETOGOFURTHEROUTPUTCHOICEFIRSTWEEXAMINETHEOUTPUTLEVELARMWILLCHOOSETOPRODUCEINATTEMPTINGTOOBTAINMAXIMUMPROTSARMSELLSSOMELEVELOFOUTPUT,Q,ATAMARKETPRICEOFPPERUNITTOTALREVENUESTRAREGIVENBYTRQH11005PQH11080Q,131WHEREWEHAVEALLOWEDFORTHEPOSSIBILITYTHATTHESELLINGPRICETHERMRECEIVESMIGHTBEAFFECTEDBYHOWMUCHITSELLSINTHEPRODUCTIONOFQ,CERTAINECONOMICCOSTSAREINCURREDAND,ASINCHAPTER12,WEWILLDENOTETHESEBYTCQTHEDIFFERENCEBETWEENREVENUESANDCOSTSISCALLEDECONOMICPROTSH9266BECAUSEBOTHREVENUESANDCOSTSDEPENDONTHEQUANTITYPRODUCED,ECONOMICPROTSWILLALSOTHATIS,H9266QH11005PQH11080QH11002TCQH11005TRQH11002TCQ132DEFINITIONCHAPTER13PROTMAXIMIZATIONANDSUPPLY335THENECESSARYCONDITIONFORCHOOSINGTHEVALUEOFQTHATMAXIMIZESPROTSISFOUNDBYSETTINGTHEDERIVATIVEOFEQUATION132WITHRESPECTTOQEQUALTO02H11005H9266H11032QH11005H11002H110050,133SOTHERSTORDERCONDITIONFORAMAXIMUMISTHATH11005134THISISJUSTAMATHEMATICALSTATEMENTOFTHEMARGINALREVENUEEQUALSMARGINALCOSTRULEUSUALLYSTUDIEDININTRODUCTORYECONOMICSCOURSESHENCEWEHAVETHEFOLLOWINGPROTMAXIMIZATIONTOMAXIMIZEECONOMICPROTS,THERMSHOULDCHOOSETHATOUTPUTFORWHICHMARGINALREVENUEISEQUALTOMARGINALCOSTTHATIS,MRH11005H11005H11005MC135SECONDORDERCONDITIONSEQUATION134OR135ISONLYANECESSARYCONDITIONFORAPROTMAXIMUMFORSUFCIENCY,ITISALSOREQUIREDTHATH20841QH11005QH11005H20841QH11005QH110210,136ORTHAT“MARGINAL”PROTMUSTBEDECREASINGATTHEOPTIMALLEVELOFQFORQLESSTHANQTHEOPTIMALLEVELOFOUTPUT,PROTMUSTBEINCREASINGH9266H11032QH110220ANDFORQGREATERTHANQ,PROTMUSTBEDECREASINGH9266H11032QH110210ONLYIFTHISCONDITIONHOLDSHASATRUEMAXIMUMOFPROTSBEENACHIEVEDGRAPHICALANALYSISTHESERELATIONSHIPSAREILLUSTRATEDINFIGURE131,WHERETHETOPPANELDEPICTSTYPICALCOSTANDREVENUEFUNCTIONSFORLOWLEVELSOFOUTPUT,COSTSEXCEEDREVENUESANDTHEREFOREECONOMICPROTSARENEGATIVEINTHEMIDDLERANGESOFOUTPUT,REVENUESEXCEEDCOSTSTHISMEANSTHATPROTSAREPOSITIVEFINALLY,ATHIGHLEVELSOFOUTPUT,COSTSRISESHARPLYANDAGAINEXCEEDREVENUESTHEVERTICALDISTANCEBETWEENTHEREVENUEANDCOSTCURVESTHATIS,PROTSISSHOWNINFIGURE131BHEREPROTSREACHAMAXIMUMATQATTHISLEVELOFOUTPUTITISALSOTRUETHATTHESLOPEOFTHEREVENUECURVEMARGINALREVENUEISEQUALTOTHESLOPEOFTHECOSTCURVEMARGINALCOSTITDH9266H11032QH5007DQD2H9266H5007DQ2DTCH5007DQDTRH5007DQOPTIMIZATIONPRINCIPLEDTCH5007DQDTRH5007DQDTCH5007DQDTRH5007DQDH9266H5007DQ336PARTIVPRODUCTIONANDSUPPLY2NOTICETHATTHISISANUNCONSTRAINEDMAXIMIZATIONPROBLEMTHECONSTRAINTSINTHEPROBLEMAREIMPLICITINTHEREVENUEANDCOSTFUNCTIONSSPECICALLY,THEDEMANDCURVEFACINGTHERMDETERMINESTHEREVENUEFUNCTION,ANDTHERMSPRODUCTIONFUNCTIONTOGETHERWITHINPUTPRICESDETERMINESITSCOSTSWEWILLEXPLORETHESE“BUILTIN”CONSTRAINTSFURTHERLATERINTHISCHAPTERANDINTHEEXTENSIONSCHAPTER13PROTMAXIMIZATIONANDSUPPLY337MARGINALREVENUEMUSTEQUALMARGINALCOSTFORPROTMAXIMIZATIONBECAUSEPROTSAREDENEDTOBEREVENUESTRMINUSCOSTSTC,ITISCLEARTHATPROTSREACHAMAXIMUMWHENTHESLOPEOFTHEREVENUEFUNCTIONMARGINALREVENUEISEQUALTOTHESLOPEOFTHECOSTFUNCTIONMARGINALCOSTTHISEQUALITYISONLYANECESSARYCONDITIONFORAMAXIMUM,ASMAYBESEENBYCOMPARINGPOINTSQATRUEMAXIMUMANDQATRUEMINIMUM,FORBOTHOFWHICHMARGINALREVENUEEQUALSMARGINALCOSTREVENUES,COSTSPROFITSLOSSESOUTPUTPERPERIODOUTPUTPERPERIODABQQQTCTR0FIGURE131ISCLEARFROMTHEGURETHATTHESUFCIENTCONDITIONSFORAMAXIMUMAREALSOSATISEDATTHISPOINT,BECAUSEPROTSAREINCREASINGTOTHELEFTOFQANDDECREASINGTOTHERIGHTOFQOUTPUTLEVELQISTHEREFOREATRUEPROTMAXIMUMTHISISNOTSOFOROUTPUTLEVELQALTHOUGHMARGINALREVENUEISEQUALTOMARGINALCOSTATTHISOUTPUT,PROTSAREINFACTATAMINIMUMTHEREMARGINALREVENUEITISTHEREVENUEOBTAINEDFROMSELLINGONEMOREUNITOFOUTPUTTHATISRELEVANTTOTHEPROTMAXIMIZINGRMSOUTPUTDECISIONIFTHERMCANSELLALLITWISHESWITHOUTHAVINGANYEFFECTONMARKETPRICE,THEMARKETPRICEWILLINDEEDBETHEEXTRAREVENUEOBTAINEDFROMSELLINGONEMOREUNITPHRASEDINANOTHERWAY,IFARMSOUTPUTDECISIONSWILLNOTAFFECTMARKETPRICE,MARGINALREVENUEISEQUALTOTHEPRICEATWHICHAUNITSELLSARMMAYNOTALWAYSBEABLETOSELLALLITWANTSATTHEPREVAILINGMARKETPRICE,HOWEVERIFITFACESADOWNWARDSLOPINGDEMANDCURVE,MOREOUTPUTCANBESOLDONLYBYREDUCINGTHEGOODSPRICEINTHISCASETHEREVENUEOBTAINEDFROMSELLINGONEMOREUNITWILLBELESSTHANTHEPRICEOFTHATUNITBECAUSE,INORDERTOGETCONSUMERSTOTAKETHEEXTRAUNIT,THEPRICEOFALLOTHERUNITSMUSTBELOWEREDTHISRESULTCANBEEASILYDEMONSTRATEDASBEFORE,TOTALREVENUETRISSIMPLYTHEPRODUCTOFTHEQUANTITYSOLDQTIMESTHEPRICEATWHICHITISSOLDP,WHICHMAYALSODEPENDONQMARGINALREVENUEMRISTHENDENEDTOBETHECHANGEINTRRESULTINGFROMACHANGEINQMARGINALREVENUEMARGINALREVENUEH11005MRQH11005H11005H11005PH11001QH11080137NOTICETHATTHEMARGINALREVENUESISAFUNCTIONOFOUTPUTINGENERAL,MRWILLBEDIFFERENTFORDIFFERENTLEVELSOFQFROMEQUATION137ITISEASYTOSEETHATIFPRICEDOESNOTCHANGEASQUANTITYINCREASESDP/DQH110050,MARGINALREVENUEWILLBEEQUALTOPRICEINTHISCASEWESAYTHATTHERMISAPRICETAKERBECAUSEITSDECISIONSDONOTINUENCETHEPRICEITRECEIVESONTHEOTHERHAND,IFPRICEFALLSASQUANTITYINCREASESDP/DQH110210,MARGINALREVENUEWILLBELESSTHANPRICEAPROTMAXIMIZINGENTREPRENEURMUSTKNOWHOWINCREASESINOUTPUTWILLAFFECTTHEPRICERECEIVEDBEFOREMAKINGANOPTIMALOUTPUTDECISIONIFINCREASESINQCAUSEMARKETPRICETOFALL,THISMUSTBETAKENINTOACCOUNTEXAMPLE131MARGINALREVENUEFROMALINEARDEMANDFUNCTIONSUPPOSEASUBSANDWICHALSOCALLEDGRINDERS,TORPEDOES,OR,INPHILADELPHIA,HOAGIESSHOPFACESALINEARDEMANDCURVEFORITSDAILYOUTPUTOVERPERIODQOFTHEFORMQH11005100H1100210P138DPH5007DQDPQH11080QH5007H5007DQDTRH5007DQDEFINITION338PARTIVPRODUCTIONANDSUPPLYSOLVINGFORPRICE,WEHAVEPH11005H11002Q/10H1100110,139ANDTOTALREVENUESASAFUNCTIONOFQAREGIVENBYTRH11005PQH11005H11002Q2/10H1100110Q1310THESUBRMSMARGINALREVENUEFUNCTIONISMRH11005H11005H1100110,1311AND,INTHISCASE,MRH11021PFORALLVALUESOFQIF,FOREXAMPLE,THERMPRODUCES40SUBSPERDAY,EQUATION139SHOWSTHATITWILLRECEIVEAPRICEOF6PERSANDWICHBUTATTHISLEVELOFOUTPUTEQUATION1311SHOWSTHATMRISONLY2IFTHERMPRODUCES40SUBSPERDAY,TOTALREVENUEWILLBE240H110056H1100340,WHEREAS,IFITPRODUCED39SUBS,TOTALREVENUEWOULDBE238H1100561H1100339SINCEPRICEWILLRISESLIGHTLYWHENLESSISPRODUCEDHENCETHEMARGINALREVENUEFROMTHEFORTIETHUNITSOLDISCONSIDERABLYLESSTHANITSPRICEINDEED,FORQH1100550,MARGINALREVENUEISZEROTOTALREVENUESAREAMAXIMUMAT250H110055H1100350,ANDANYFURTHEREXPANSIONINDAILYSUBOUTPUTWILLACTUALLYRESULTINAREDUCTIONINTOTALREVENUETOTHERMTODETERMINETHEPROTMAXIMIZINGLEVELOFSUBOUTPUT,WEMUSTKNOWTHERMSCOSTSIFSUBSCANBEPRODUCEDATACONSTANTAVERAGEANDMARGINALCOSTOF4,EQUATION1311SHOWSTHATMRH11005MCATADAILYOUTPUTOF30SUBSWITHTHISLEVELOFOUTPUT,EACHSUBWILLSELLFOR7ANDPROTSARE90H110057H110024H1108030ALTHOUGHPRICEEXCEEDSAVERAGEANDMARGINALCOSTHEREBYASUBSTANTIALMARGIN,ITWOULDNOTBEINTHERMSINTERESTTOEXPANDOUTPUTWITHQH1100535,FOREXAMPLE,PRICEWILLFALLTO650ANDPROTSWILLFALLTO8750H11005650H11002400H1108035MARGINALREVENUE,NOTPRICE,ISTHEPRIMARYDETERMINANTOFPROTMAXIMIZINGBEHAVIORQUERYHOWWOULDANINCREASEINTHEMARGINALCOSTOFSUBPRODUCTIONTO5AFFECTTHEOUTPUTDECISIONOFTHISRMHOWWOULDITAFFECTTHERMSPROTSMARGINALREVENUEANDELASTICITYTHECONCEPTOFMARGINALREVENUEISDIRECTLYRELATEDTOTHEELASTICITYOFTHEDEMANDCURVEFACINGTHERMREMEMBERTHATTHEELASTICITYOFMARKETDEMANDEQ,PISDENEDASTHEPERCENTAGECHANGEINQUANTITYTHATRESULTSFROMA1PERCENTCHANGEINPRICEEQ,PH11005H11005H11080IFWEUSEEQ,PTODENOTETHEPRICEELASTICITYOFTHEDEMANDCURVEFACINGASINGLERM,THISDENITIONCANBECOMBINEDWITHEQUATION137TOGIVEMRH11005PH11001H11005PH208981H11001H11080H20899H11005PH208981H11001H208991312IFTHEDEMANDCURVEFACINGTHERMISNEGATIVELYSLOPED,EQ,PH110210ANDMARGINALREVENUEWILLBELESSTHANPRICE,ASWEHAVEALREADYSHOWNIFDEMANDISELASTIC1H5007EQ,PDPH5007DQQH5007PQDPH5007DQPH5007QDQH5007DPDQ/QH5007DP/PH11002QH50075DTRH5007DQCHAPTER13PROTMAXIMIZATIONANDSUPPLY339EQ,PH11021H110021,MARGINALREVENUEWILLBEPOSITIVEIFDEMANDISELASTIC,THESALEOFONEMOREUNITWILLNOTAFFECTPRICE“VERYMUCH,”ANDHENCEMOREREVENUEWILLBEYIELDEDBYTHESALEINFACT,IFDEMANDFACINGTHERMISINNITELYELASTICEQ,PH11005H11002H11009,MARGINALREVENUEWILLEQUALPRICETHERMIS,INTHISCASE,APRICETAKERHOWEVER,IFDEMANDISINELASTICEQ,PH11022H110021,MARGINALREVENUEWILLBENEGATIVEINCREASESINQCANBEOBTAINEDONLYTHROUGH“LARGE”DECLINESINMARKETPRICE,ANDTHESEDECLINESWILLACTUALLYCAUSETOTALREVENUETODECREASETHERELATIONSHIPBETWEENMARGINALREVENUEANDELASTICITYISSUMMARIZEDBYTABLE131THEINVERSEELASTICITYRULEIFWEASSUMETHERMWISHESTOMAXIMIZEPROTS,EQUATION1312CANBEEXTENDEDTOILLUSTRATETHECONNECTIONBETWEENPRICEANDMARGINALCOSTSETTINGMRH11005MCYIELDSMCH11005PH208981H11001H20899ORH11005H110021313THATIS,THEGAPBETWEENPRICEANDMARGINALCOSTWILLDECREASEASTHEDEMANDCURVEFACINGTHERMBECOMESMOREELASTICINDEED,INTHECASEOFAPRICETAKINGRM,EQ,PH11005H11002H11009SOPH11005MRH11005MCANDTHEREISNOGAPBECAUSE,ASWESHALLSEEINLATERCHAPTERS,THEGAPBETWEENPRICEANDMARGINALCOSTISANIMPORTANTMEASUREOFINEFCIENTRESOURCEALLOCATION,EQUATION1313ISWIDELYUSEDINEMPIRICALSTUDIESOFMARKETORGANIZATIONNOTICEALSOTHATEQUATION1313MAKESSENSEONLYIFTHEDEMANDCURVEFACINGTHERMISELASTICEQ,PH11021H110021IFEQ,PWEREGREATERTHANH110021,EQUATION1313WOULDIMPLYANEGATIVEMARGINALCOSTANOBVIOUSIMPOSSIBILITYHENCEPROTMAXIMIZINGRMSWILLCHOOSETOOPERATEONLYATPOINTSONTHEDEMANDCURVESWHEREDEMANDISELASTICOFCOURSE,WHENTHEREAREMANYRMSPRODUCINGASINGLEGOOD,THEDEMANDCURVEFACINGONERMMAYBEQUITEELASTICEVENTHOUGHTHEOVERALLMARKETDEMANDCURVEMAYBERELATIVELYINELASTICMARGINALREVENUECURVEANYDEMANDCURVEHASAMARGINALREVENUECURVEASSOCIATEDWITHITIF,ASWEOFTENASSUME,THERMMUSTSELLALLITSOUTPUTATONEPRICE,ITISCONVENIENTTOTHINKOFTHE1H5007EQ,PPH11002MCH5007P1H5007EQ,P340PARTIVPRODUCTIONANDSUPPLYRELATIONSHIPBETWEENELASTICITYANDMARGINALREVENUEEQ,PH11021H110021MRH110220EQ,PH11005H110021MRH110050EQ,PH11022H110021MRH110210TABLE131DEMANDCURVEFACINGTHERMASANAVERAGEREVENUECURVETHATIS,THEDEMANDCURVESHOWSTHEREVENUEPERUNITINOTHERWORDS,THEPRICEYIELDEDBYALTERNATIVEOUTPUTCHOICESTHEMARGINALREVENUECURVE,ONTHEOTHERHAND,SHOWSTHEEXTRAREVENUEPROVIDEDBYTHELASTUNITSOLDINTHEUSUALCASEOFADOWNWARDSLOPINGDEMANDCURVE,THEMARGINALREVENUECURVEWILLLIEBELOWTHEDEMANDCURVEBECAUSE,ACCORDINGTOEQUATION137,MRH11021PINFIGURE132WEHAVEDRAWNSUCHACURVE,TOGETHERWITHTHEDEMANDCURVEFROMWHICHITWASDERIVEDNOTICETHATFOROUTPUTLEVELSGREATERTHANQ1,MARGINALREVENUEISNEGATIVEASOUTPUTINCREASESFROM0TOQ1,TOTALREVENUESPH11080QINCREASEHOWEVER,ATQ1TOTALREVENUESP1H11080Q1AREASLARGEASPOSSIBLEBEYONDTHISOUTPUTLEVEL,PRICEFALLSPROPORTIONATELYFASTERTHANOUTPUTRISESINCHAPTER7WETALKEDINDETAILABOUTTHEPOSSIBILITYOFADEMANDCURVESSHIFTINGBECAUSEOFCHANGESININCOME,PRICESOFOTHERGOODS,ORPREFERENCESWHENEVERADEMANDCURVEDOESSHIFT,ITSASSOCIATEDMARGINALREVENUECURVEALSOSHIFTSTHISSHOULDBEOBVIOUS,BECAUSEAMARGINALREVENUECURVECANNOTBECALCULATEDWITHOUTREFERRINGTOASPECICDEMANDCURVECHAPTER13PROTMAXIMIZATIONANDSUPPLY341MARKETDEMANDCURVEANDASSOCIATEDMARGINALREVENUECURVEBECAUSETHEDEMANDCURVEISNEGATIVELYSLOPED,THEMARGINALREVENUECURVEWILLFALLBELOWTHEDEMAND“AVERAGEREVENUE”CURVEFOROUTPUTLEVELSBEYONDQ1,MRISNEGATIVEATQ1,TOTALREVENUESP1H11003Q1AREAMAXIMUMBEYONDTHISPOINTADDITIONALINCREASESINQACTUALLYCAUSETOTALREVENUESTOFALLBECAUSEOFTHECONCOMITANTDECLINESINPRICEPRICEQUANTITYPERPERIODDAVERAGEREVENUEP1Q1MR0FIGURE132EXAMPLE132THECONSTANTELASTICITYCASEINCHAPTER7WESHOWEDTHATADEMANDFUNCTIONOFTHEFORMQH11005APB1314HASACONSTANTPRICEELASTICITYOFDEMAND,ANDTHATTHISELASTICITYISGIVENBYTHEPARAMETERBTOCOMPUTETHEMARGINALREVENUEFUNCTIONFORTHISFUNCTIONRSTSOLVEFORPPH110051/A1/BQ1/BH11005KQ1/B,1315WHEREKH110051/A1/BHENCETRH11005PQH11005KQ1H11001B/BANDMRH11005DTR/DQH110051H11001B/BKQ1/BH110051H11001B/BP1316FORTHISPARTICULARFUNCTION,THEN,THEMRCURVEISPROPORTIONALTOTHEDEMANDCURVEITSELFIF,FOREXAMPLE,EQ,PH11005BH11005H110022,MRH1100505PFORAMOREELASTICCASE,SUPPOSEBH11005H1100210THENMRH1100509PTHEMRCURVEAPPROACHESTHEDEMANDCURVEASDEMANDBECOMESMOREELASTICAGAIN,IFBH11005H11002H11009,MRH11005PTHATIS,INTHECASEOFINNITELYELASTICDEMAND,THERMISAPRICETAKERFORINELASTICDEMAND,ONTHEOTHERHAND,MRISNEGATIVEANDPROTMAXIMIZATIONWOULDBEIMPOSSIBLEQUERYSUPPOSEDEMANDDEPENDEDONOTHERFACTORSINADDITIONTOPHOWWOULDTHISCHANGETHEANALYSISOFTHISEXAMPLEHOWWOULDACHANGEINONEOFTHESEOTHERFACTORSSHIFTTHEDEMANDCURVEANDITSMARGINALREVENUECURVESHORTRUNSUPPLYBYAPRICETAKINGFIRMWEARENOWREADYTOSTUDYTHESUPPLYDECISIONOFAPROTMAXIMIZINGRMINTHISCHAPTERWEWILLEXAMINEONLYTHECASEINWHICHTHERMISAPRICETAKERWEWILLBELOOKINGATOTHERCASESINCONSIDERABLYMOREDETAILLATERONALSO,WEWILLFOCUSONLYONSUPPLYDECISIONSINTHESHORTRUNHERELONGRUNQUESTIONSARETHEPRIMARYFOCUSOFCHAPTER14THERMSSETOFSHORTRUNCOSTCURVESARETHEREFORETHEAPPROPRIATEMODELFOROURANALYSISPROTMAXIMIZINGDECISIONFIGURE133SHOWSTHERMSSHORTRUNDECISIONTHEMARKETPRICEISGIVENBYPTHEDEMANDCURVEFACINGTHERMISTHEREFOREAHORIZONTALLINETHROUGHPTHISLINEISLABELEDPH11005MRASAREMINDERTHATANEXTRAUNITCANALWAYSBESOLDBYTHISPRICETAKINGRMWITHOUTAFFECTINGTHEPRICEITRECEIVESOUTPUTLEVELQPROVIDESMAXIMUMPROTS,BECAUSEATQPRICEISEQUALTOSHORTRUNMARGINALCOSTTHEFACTTHATPROTSAREPOSITIVECANBESEENBYNOTINGTHATATQPRICEEXCEEDSAVERAGECOSTSTHERMEARNSAPROTONEACHUNITSOLDIFPRICEWEREBELOWAVERAGECOSTASISTHE342PARTIVPRODUCTIONANDSUPPLYCASEFORP,THERMWOULDHAVEALOSSONEACHUNITSOLDIFPRICEANDAVERAGECOSTWEREEQUAL,PROTSWOULDBEZERONOTICETHATATQTHEMARGINALCOSTCURVEHASAPOSITIVESLOPETHISISREQUIREDIFPROTSARETOBEATRUEMAXIMUMIFPH11005MCONANEGATIVELYSLOPEDSECTIONOFTHEMARGINALCOSTCURVE,THISWOULDNOTBEAPOINTOFMAXIMUMPROTS,BECAUSEINCREASINGOUTPUTWOULDYIELDMOREINREVENUESPRICETIMESTHEAMOUNTPRODUCEDTHANTHISPRODUCTIONWOULDCOSTMARGINALCOSTWOULDDECLINEIFTHEMCCURVEHASANEGATIVESLOPECONSEQUENTLY,PROTMAXIMIZATIONREQUIRESBOTHTHATPH11005MCANDTHATMARGINALCOSTBEINCREASINGATTHISPOINT3THEFIRMSSHORTRUNSUPPLYCURVETHEPOSITIVELYSLOPEDPORTIONOFTHESHORTRUNMARGINALCOSTCURVEISTHESHORTRUNSUPPLYCURVEFORTHISPRICETAKINGRMTHATCURVESHOWSHOWMUCHTHERMWILLCHAPTER13PROTMAXIMIZATIONANDSUPPLY343SHORTRUNSUPPLYCURVEFORAPRICETAKINGFIRMINTHESHORTRUN,APRICETAKINGRMWILLPRODUCETHELEVELOFOUTPUTFORWHICHSMCH11005PATP,FOREXAMPLE,THERMWILLPRODUCEQTHESMCCURVEALSOSHOWSWHATWILLBEPRODUCEDATOTHERPRICESFORPRICESBELOWSAVC,HOWEVER,THERMWILLCHOOSETOPRODUCENOOUTPUTTHEHEAVYLINESINTHEGUREREPRESENTTHERMSSHORTRUNSUPPLYCURVEPRICEQUANTITYPERPERIODSMCSAVCSACPPQQQPH11005MRP10FIGURE1333MATHEMATICALLY,BECAUSEH9266QH11005PQH11002TCQ,PROTMAXIMIZATIONREQUIRESTHERSTORDERCONDITIONH9266H11032QH11005PH11002MCQH110050ANDTHESECONDORDERCONDITIONH9266H11033QH11005H11002MC