nicholson微观经济理论（答案+ppt+习题库）-210-03-033593-0

FIRMSDEMANDSFORINPUTSINTHISCHAPTERWEWILLEXAMINESEVERALGENERALMODELSOFTHEPRICINGOFINPUTSFORTHEMOSTPARTWEWILLSTUDYHOWDIFFERENCESINTHENATUREOFRMSDEMANDSFORINPUTSCANAFFECTTHEIRPRICESWEWILLDEVOTERELATIVELYLITTLEATTENTIONTOTHESUPPLYSIDEOFTHEMARKETCHAPTERS22AND23ARECONCERNEDWITHISSUESRELATEDTOTHESUPPLYOFLABORANDCAPITAL,RESPECTIVELY,SOWEWILLPOSTPONEANYVERYEXPLICITTREATMENTOFFACTORSUPPLYUNTILTHEN21CHAPTERPROTMAXIMIZATIONANDDERIVEDDEMANDINCHAPTER13WESHOWEDTHATARMSHIRINGOFINPUTSISDIRECTLYRELATEDTOITSDESIRETOMAXIMIZEPROTSNORMHIRESWORKERSORRENTSEQUIPMENTSIMPLYTOPROVIDEITSMANAGERSWITHCOMPANIONSHIPRATHER,HIRINGOFINPUTSISAPRIMARYCOMPONENTOFTHEPROTMAXIMIZATIONPROCESSSPECICALLY,ASWESHOWEDINCHAPTER13,ANYRMSPROTSH9266CANBEEXPRESSEDASTHEDIFFERENCEBETWEENTOTALREVENUESTRANDTOTALCOSTSTC,EACHOFWHICHCANBEREGARDEDASFUNCTIONSOFTHEINPUTSUSEDSAY,CAPITAL,K,ANDLABOR,LH9266H11005TRK,LH11002TCK,L211THERSTORDERCONDITIONSFORAPROTMAXIMUMAREH11005H11002H110050212H11005H11002H110050ORH11005ANDH11005213INWORDS,EQUATIONS213REPORTTHERATHEROBVIOUSRESULTTHATANYPROTMAXIMIZINGFIRMSHOULDHIREADDITIONALUNITSOFEACHFACTOROFPRODUCTIONUPTOTHEPOINTATWHICHTHEEXTRAREVENUEYIELDEDBYHIRINGONEMOREUNITISEQUALTOTHEEXTRACOSTOFHIRINGTHATUNITMARGINALREVENUEPRODUCTALLOFTHEDERIVATIVESINEQUATIONS213AREGIVENSPECIALNAMESINTHETHEORYOFINPUTDEMANDEXPRESSIONSFORTHECHANGEINREVENUEWITHRESPECTTOACHANGEINANINPUTTHATIS,THETERMSONTHELEFTINEQUATIONS213ARETERMEDTHEMARGINALREVENUEPRODUCTMRPFORTHATINPUTBYRECOGNIZINGTHATTHEHIRINGOFANEXTRAUNITOFANINPUTRESULTSINEXTRAREVENUEONLYTHROUGHTHEOUTPUTQITYIELDS,WECANGAINFURTHERINSIGHTINTOTHENATUREOFTHISCONCEPTFORTHECASEOFLABORINPUT,FOREXAMPLE,WEHAVEMRPLH11005H11005H11080H11005MRH11080MPL,214WHEREMRISTHEMARGINALREVENUEFORTHERMSOUTPUTANDMPLISTHEMARGINALPHYSICALPRODUCTOFLABORSUPPOSETHAT,ATCURRENTPRODUCTIONLEVELS,HIRINGANEXTRAAPPLEPICKERFORONEHOURWOULDYIELDTHREEEXTRABUSHELSOFAPPLESANDTHEMARGINALREVENUEYIELDEDFROMSELLINGABUSHELOFAPPLESIS4THEEXTRAREVENUEYIELDEDTOANORCHARDOWNERFROMHIRINGANEXTRAHOUROFANAPPLEPICKERSTIMEH11128QH5007H11128LH11128TRQH5007H11128QH11128TRQH5007H11128LH11128TCH5007H11128LH11128TRH5007H11128LH11128TCH5007H11128KH11128TRH5007H11128KH11128TCH5007H11128LH11128TRH5007H11128LH11128H9266H5007H11128LH11128TCH5007H11128KH11128TRH5007H11128KH11128H9266H5007H11128K578PARTVIIPRICINGININPUTMARKETSWOULDBE12THATIS,THEMARGINALREVENUEPRODUCTOFLABORIS12ANIDENTICALARGUMENTWOULDFOLLOWFORTHEHIRINGOFANYOTHERINPUTWEHAVE,THEREFORE,DEVELOPEDTHEFOLLOWINGDENITIONMARGINALREVENUEPRODUCTTHEMARGINALREVENUEPRODUCTMRPFROMHIRINGANEXTRAUNITOFANYINPUTISTHEEXTRAREVENUEYIELDEDBYSELLINGWHATTHATEXTRAINPUTPRODUCESITCANBEFOUNDBYMULTIPLYINGTHEINPUTSMARGINALPHYSICALPRODUCTIVITYTIMESTHEMARGINALREVENUEOBTAINABLEFROMTHERMSOUTPUTINTHEMARKETFORGOODSMRPH11005MRH11080MP215MARGINALEXPENSEEQUATIONS213SHOWTHATANADDITIONALUNITOFINPUTSHOULDBEHIREDUPTOTHEPOINTATWHICHTHEINPUTSMRPISEQUALTOTHEADDITIONALCOSTOFHIRINGTHATUNITIFTHESUPPLYCURVESFACINGTHERMFORTHEINPUTSITHIRESAREINNITELYELASTICATPREVAILINGPRICESTHATIS,IFTHERMCANHIREALLITWANTSWITHOUTAFFECTINGINPUTPRICES,THISEXTRACOSTISSIMPLYTHEINPUTSPRICEIFOURORCHARDOWNERCANHIREANYNUMBEROFPICKERSATAMARKETWAGEOF10PERHOUR,THENTHEMARGINALEXPENSEOFHIRINGLABORISGIVENBYTHISMARKETWAGEINTHISCASEITWOULDINDEEDMAKESENSETOHIRETHEWORKERBECAUSEHISORHERMRPL12EXCEEDSTHISMARKETWAGEIFINPUTSUPPLYISNOTINNITELYELASTIC,HOWEVER,ARMSHIRINGDECISIONSMAYHAVESOMEEFFECTONINPUTPRICESINTHISCASE,ASWEWILLSHOWLATERINTHISCHAPTER,THEMARGINALEXPENSEOFHIRINGANOTHERUNITOFINPUTWILLEXCEEDITSMARKETPRICEBECAUSETHERMSHIRINGWILLDRIVEUPINPUTPRICESFORTHEMOMENT,HOWEVER,WEWILLNOTEXAMINETHISPOSSIBILITY,BUTWILLINSTEADASSUMETHERMISAPRICETAKERFORTHEINPUTSITBUYSTHATIS,H11005V216H11005W,WHEREVANDWARETHEPREVAILINGPERUNITHIRINGCOSTSOFCAPITALANDLABORTHERSTORDERCONDITIONSFORPROTMAXIMIZATIONTHEREFOREBECOMEMRPKH11005V217MRPLH11005WANALTERNATIVEDERIVATIONBEFORETURNINGTOEXAMINETHEIMPLICATIONSOFEQUATIONS217FORTHERMSDEMANDFORINPUTS,WEPRESENTANALTERNATIVEDERIVATIONOFTHESEPROTMAXIMIZINGCONDITIONSTHATOFFERSADDITIONALINSIGHTSINTOTHERELATIONSHIPBETWEENTHERMSINPUTANDOUTPUTCHOICESINCHAPTER12WEEXAMINEDAMODELINWHICHTHERMH11128TCH5007H11128LH11128TCH5007H11128KDEFINITIONCHAPTER21FIRMSDEMANDSFORINPUTS579WASASSUMEDTOMINIMIZETHECOSTSOFPRODUCINGANYLEVELOFITSOUTPUTSAY,Q0THELAGRANGIANEXPRESSIONASSOCIATEDWITHTHISMINIMIZATIONPROBLEMISH5112H11005VKH11001WLH11001H9261Q0H11002FK,L,218WHEREFK,LISTHERMSPRODUCTIONFUNCTIONASSUMINGAGAINTHATTHERMSINPUTCHOICESDONOTAFFECTTHEINPUTPRICES,VANDW,THERSTORDERCONDITIONSFORAMINIMUMAREH11005VH11002H9261H110050219H11005WH11002H9261H110050H11005Q0H11002FK,LH110050THERSTTWOOFTHESEEQUATIONSCANBEWRITTENASH9261H11005H9261MPKH11005V2110H9261H11005H9261MPLH11005WBUT,ASWEPOINTEDOUTINCHAPTER12,THELAGRANGIANMULTIPLIER,H9261,CANBEINTERPRETEDASMARGINALCOSTMCINTHISPROBLEMBECAUSEITREECTSTHECHANGEINTHEOBJECTIVETOTALCOSTSFORAONEUNITCHANGEINTHECONSTRAINTOUTPUTH11002Q0USINGTHISINTERPRETATION,WEHAVEMCH11080MPKH11005V2111MCH11080MPLH11005WOUTPUTCHOICESCANNOWBEINCORPORATEDINTOTHISTHEORYOFINPUTCHOICEBYINTRODUCINGTHEOLDRELIABLEMRH11005MCRULEFORPROTMAXIMIZATIONMRH11080MPKH11005V2112MRH11080MPLH11005W,WHICHISPRECISELYTHERESULTWEDEVELOPEDEARLIERTHISAPPROACHMAKESESPECIALLYCLEARTHATTHERMSDEMANDFORANYINPUTSTEMSNOTONLYFROMITSDESIRETOMINIMIZECOSTSBUTALSOFROMITSDESIRETOMAKEPROTMAXIMIZINGOUTPUTCHOICESASWESHALLSEE,EXAMININGHOWRMSREACTTOCHANGESININPUTPRICESREQUIRESTHATWETAKEACCOUNTOFBOTHOFTHESEMOTIVATIONSPRICETAKINGINTHEOUTPUTMARKETMARGINALVALUEPRODUCTANALOBSERVATIONTHATMIGHTBEMADEABOUTPROTMAXIMIZINGINPUTCHOICESCONCERNSTHEPOSSIBILITYTHATTHERMMAYEXHIBITPRICETAKINGBEHAVIORINTHEMARKETFORITSOUTPUTINTHISCASEMARGINALREVENUEISIDENTICALTOMARKETPRICE,ANDEQUATIONS2112BECOMEPH11080MPKH11005V2113PH11080MPLH11005WH11128FH5007H11128LH11128FH5007H11128KH11128H5112H5007H11128H9261H11128FH5007H11128LH11128H5112H5007H11128LH11128FH5007H11128KH11128H5112H5007H11128K580PARTVIIPRICINGININPUTMARKETSTHETERMSONTHELEFTOFTHESEEQUATIONSREPRESENTASPECIALCASEOFTHEMARGINALREVENUEPRODUCTNOTIONINWHICHTHEPHYSICALQUANTITYOFOUTPUTPRODUCEDBYONEEXTRAUNITOFANINPUTISVALUEDATITSMARKETPRICEALTHOUGHFORPRICETAKERSTHEREISNODISTINCTIONBETWEENTHISCONCEPTANDTHEMRP,FORRMSTHATARENOTPRICETAKERS,MRH11021PSOITDOESMAKEADIFFERENCEWHETHERONEVALUESANINPUTSPHYSICALPRODUCTIVITYATTHERMSMARGINALREVENUEORATMARKETPRICEFORTHEOUTPUTBEINGPRODUCEDSOMETIMESTHETERMMARGINALVALUEPRODUCTISUSEDTOREFERTOTHISVALUATIONBYMARKETPRICE,BUTWEWILLNOTUSETHATTERMHEREINSTEAD,WEWILLUSEONLYTHEMARGINALREVENUEPRODUCTCONCEPTINREFERRINGTOTHEELEMENTSTHATINUENCEARMSDEMANDFORINPUTSFORTHEMOSTPART,HOWEVER,WEWILLALSOASSUMEPRICETAKINGBEHAVIORINTHEGOODSMARKETSOTHEREISNONECESSITYTOMAKETHEDISTINCTIONCOMPARATIVESTATICSOFINPUTDEMANDINTHISSECTIONWEUSETHEPROTMAXIMIZATIONASSUMPTIONTOSTUDYTHECOMPARATIVESTATICSOFINPUTDEMANDSPECICALLY,WESHALLLOOKATTHEDEMANDFORLABORTHEANALYSISFORCAPITALWOULDBESYMMETRICANDASKABOUTTHEDIRECTIONANDSIZEOFH11128L/H11128WASWEHAVEINDICATEDPREVIOUSLY,ITISLIKELYTHISDERIVATIVEWILLBENEGATIVEADECREASEINWWILLCAUSEMORELABORTOBEHIRED,BUTNOWWEAREINAPOSITIONTOGIVEADETAILEDTREATMENTOFTHEISSUESINGLEINPUTCASEONEREASONFOREXPECTINGH11128L/H11128WTOBENEGATIVEISBASEDONTHEPRESUMPTIONTHATTHEMARGINALPHYSICALPRODUCTOFLABORDECLINESASTHEQUANTITYOFLABOREMPLOYEDINCREASESADECREASEINWMEANSTHATMORELABORMUSTBEHIREDTOBRINGABOUTTHEEQUALITYWH11005PH11080MPLAFALLINWMUSTBEMETBYAFALLINMPLBECAUSEPISXED,ANDTHISCANBEBROUGHTABOUTBYINCREASINGLTHATTHISARGUMENTISSTRICTLYCORRECTFORTHECASEOFONEINPUTCANBESHOWNASFOLLOWSWRITETHETOTALDIFFERENTIALOFTHEPROTMAXIMIZINGEQUATION2113ASDWH11005PH11080H11080H11080DWOR1H11005PH11080H110802114ORH11005IFWEASSUMETHATH11128MPL/H11128LH110210THATIS,THATMPLDECREASESASLINCREASES,WEHAVEH1102102115ACETERISPARIBUSFALLINWWILLCAUSEMORELABORTOBEHIREDAND,PARENTHETICALLY,THISALSOWILLCAUSEMOREOUTPUTTOBEPRODUCEDH11128LH5007H11128W1H5007H5007PH11080H11128MPL/H11128LH11128LH5007H11128WH11128LH5007H11128WH11128MPLH5007H11128LH11128LH5007H11128WH11128MPLH5007H11128LCHAPTER21FIRMSDEMANDSFORINPUTS581EXAMPLE211SINGLEINPUTDEMANDSUPPOSETHENUMBEROFPOUNDSOFTRUFESHARVESTEDINAPARTICULARFORESTDURINGONESEASONISGIVENBYQH11005100H20857LH33526,2116WHERELISTHENUMBEROFSEARCHERSHIREDTOLOOKFORTHEFRAGRANTFUNGIASSUMINGTRUFESSELLFOR50PERPOUND,TOTALREVENUEFORTHEFORESTOWNERISTRH11005PH11080QH110055,000H20857LH33526,2117ANDTHEMARGINALREVENUEPRODUCTISGIVENBYH110052,500LH110021/22118IFTRUFESEARCHERSSEASONALWAGESARE500,THEOWNERWILLDETERMINELBY500H110052,500LH110021/22119ORLH11005252120WITH25SEARCHERS,THEMARGINALREVENUEPRODUCTIS500,WHICHISPRECISELYWHATTHEOWNERMUSTPAYINWAGESTHE25WORKERSNDATOTALOF500POUNDSOFTRUFESDURINGTHESEASONATALOWERWAGERATEOF250,THEOWNERWOULDHIRE100SEARCHERSBECAUSETHELOWERMARGINALREVENUEPRODUCTOBTAINEDFROMSUCHALARGEWORKFORCEWOULDBEJUSTIEDBYTHELOWERWAGENOTICETHATATTHELOWERWAGE,TRUFEOUTPUTEXPANDSTO1,000DURINGTHESEASONQUERYHOWWOULDTHEFORESTOWNERSHIRINGCHANGEIFTRUFEPRICESROSETO60PERPOUNDEXPLAINTHEREASONSFORTHISRESULTTWOINPUTCASEFORTHECASEOFTWOORMOREINPUTS,THESTORYISMORECOMPLEXTHEASSUMPTIONOFADIMINISHINGMARGINALPHYSICALPRODUCTOFLABORCANBEMISLEADINGHEREIFWFALLS,THEREWILLNOTONLYBEACHANGEINLBUTALSOACHANGEINKASANEWCOSTMINIMIZINGCOMBINATIONOFINPUTSISCHOSENWHENKCHANGES,THEENTIREMPLFUNCTIONCHANGESLABORNOWHASADIFFERENTAMOUNTOFCAPITALTOWORKWITH,ANDTHESIMPLEARGUMENTWEUSEDABOVECANNOTBEMADEINTHEREMAINDEROFTHISSECTIONWEWILLUSEAGRAPHICAPPROACHTOSUGGESTWHY,EVENINTHETWOINPUTCASE,H11128L/H11128WMUSTBENEGATIVEAMOREPRECISE,MATHEMATICALANALYSISISPRESENTEDINTHENEXTSECTIONSUBSTITUTIONEFFECTINSOMEWAYS,ANALYZINGTHETWOINPUTCASEISSIMILARTOTHEANALYSISOFTHEINDIVIDUALSRESPONSETOACHANGEINTHEPRICEOFAGOODTHATWASPRESENTEDINCHAPTER5WHENWFALLS,WECANDECOMPOSETHETOTALEFFECTONTHEQUANTITYOFLHIREDINTOTWOCOMPONENTSTHERSTOFTHESEMIGHTBECALLEDTHESUBSTITUTIONEFFECTIFQISHELDH11128TRH5007H11128L582PARTVIIPRICINGININPUTMARKETSCONSTANTATQ1,THEREWILLBEATENDENCYTOSUBSTITUTELFORKINTHEPRODUCTIVEPROCESSTHISEFFECTISILLUSTRATEDINFIGURE211ABECAUSETHECONDITIONFORMINIMIZINGTHECOSTOFPRODUCINGQ1REQUIRESTHATRTSH11005W/V,AFALLINWWILLNECESSITATEAMOVEMENTFROMINPUTCOMBINATIONATOCOMBINATIONBBECAUSETHEISOQUANTSHAVEBEENASSUMEDTOEXHIBITADIMINISHINGRTS,ITISCLEARFROMTHEDIAGRAMTHATTHISSUBSTITUTIONEFFECTMUSTBENEGATIVEADECREASEINWWILLCAUSEANINCREASEINLABORHIREDIFOUTPUTISHELDCONSTANTOUTPUTEFFECTITISNOTCORRECT,HOWEVER,TOHOLDOUTPUTCONSTANTITISINCONSIDERINGACHANGEINQTHEOUTPUTEFFECTTHATTHEANALOGYTOTHEINDIVIDUALSUTILITYMAXIMIZATIONPROBLEMBREAKSDOWNCONSUMERSHAVEBUDGETCONSTRAINTS,BUTRMSDONOTFIRMSPRODUCEASMUCHASTHEAVAILABLEDEMANDALLOWSTOINVESTIGATEWHATHAPPENSTOTHEQUANTITYOFOUTPUTPRODUCED,WEMUSTINVESTIGATETHERMSPROTMAXIMIZINGOUTPUTDECISIONACHANGEINW,BECAUSEITCHANGESRELATIVEFACTORCOSTS,WILLSHIFTTHERMSEXPANSIONPATHCONSEQUENTLY,ALLTHERMSCOSTCURVESWILLBESHIFTED,ANDPROBABLYSOMEOUTPUTLEVELOTHERTHANQ1WILLBECHOSENINFIGURE211BWHATMIGHTBECONSIDEREDTHE“NORMAL”CASEHASBEENDRAWNTHERETHEFALLINTHEMARGINALCOSTCURVEFORTHERMTOWCAUSESASHIFTDOWNWARDTOMCH11032CONSEQUENTLY,THEPROTMAXIMIZINGLEVELOFOUTPUTRISESFROMQ1TOQ2THEPROTMAXIMIZINGCONDITIONPH11005MCISNOWSATISEDATAHIGHERLEVELOFOUTPUTRETURNINGTOFIGURE211A,CHAPTER21FIRMSDEMANDSFORINPUTS583THESUBSTITUTIONANDOUTPUTEFFECTSOFADECREASEINTHEPRICEOFAFACTORWHENTHEPRICEOFLABORFALLS,TWOANALYTICALLYDIFFERENTEFFECTSCOMEINTOPLAYONEOFTHESE,THESUBSTITUTIONEFFECT,WOULDCAUSEMORELABORTOBEPURCHASEDIFOUTPUTWEREHELDCONSTANTTHISISSHOWNASAMOVEMENTFROMPOINTATOPOINTBINAATPOINTBTHECOSTMINIMIZINGCONDITIONRTSH11005W/VISSATISEDFORTHENEW,LOWERWTHISCHANGEINW/VWILLALSOSHIFTTHERMSEXPANSIONPATHANDITSMARGINALCOSTCURVEANORMALSITUATIONMIGHTBEFORTHEMCCURVETOSHIFTDOWNWARDINRESPONSETOADECREASEINWASSHOWNINBWITHTHISNEWCURVEMCH11032AHIGHERLEVELOFOUTPUTQ2WILLBECHOSENCONSEQUENTLY,THEHIRINGOFLABORWILLINCREASETOL2,ALSOFROMTHISOUTPUTEFFECTPRICEK1K2PQ1Q2ABCL1L2LPERPERIODKPERPERIODQ1Q2OUTPUTPERPERIODATHEISOQUANTMAPBTHEOUTPUTDECISIONMCMCH11032FIGURE211THISINCREASEINOUTPUTWILLCAUSEEVENMORELTOBEDEMANDED,PROVIDINGLISNOTANINFERIORINPUTSEEBELOWTHERESULTOFBOTHTHESUBSTITUTIONANDOUTPUTEFFECTSWILLBETOMOVETHEINPUTCHOICETOPOINTCONTHERMSISOQUANTMAPBOTHEFFECTSWORKTOINCREASETHEQUANTITYOFLABORHIREDINRESPONSETOADECREASEINTHEREALWAGETHEANALYSISPROVIDEDINFIGURE211ASSUMEDTHATTHEMARKETPRICEONMARGINALREVENUE,IFTHISDOESNOTEQUALPRICEOFTHEGOODBEINGPRODUCEDREMAINEDCONSTANTTHISWOULDBEANAPPROPRIATEASSUMPTIONIFONLYONERMINANINDUSTRYEXPERIENCEDAFALLINUNITLABORCOSTSHOWEVER,IFASSEEMSMORELIKELYTHEDECLINEWEREINDUSTRYWIDE,ASLIGHTLYDIFFERENTANALYSISWOULDBEREQUIREDINTHATCASEALLRMSMARGINALCOSTCURVESWOULDSHIFTOUTWARD,ANDHENCETHEINDUSTRYSUPPLYCURVEWOULDSHIFTALSOASSUMINGTHATDEMANDISDOWNWARDSLOPING,THISWILLLEADTOADECLINEINPRODUCTPRICEOUTPUTFORTHEINDUSTRYANDFORTHETYPICALRMWILLSTILLINCREASEAND,ASBEFORE,MORELABORWILLBEHIREDBECAUSETHISLATTER,INDUSTRYWIDEOUTPUTEFFECTARISINGFROMSHIFTSINTHEMARKETSUPPLYCURVEISMORECOMMONLYUSED,ITISTHEONEWEWILLUSEINOURSUBSEQUENTMATHEMATICALDEVELOPMENTCROSSPRICEEFFECTSWEHAVESHOWNTHATATLEASTINSIMPLECASES,H11128L/H11128WISUNAMBIGUOUSLYNEGATIVESUBSTITUTIONANDOUTPUTEFFECTSCAUSEMORELABORTOBEHIREDWHENTHEWAGERATEFALLSFROMFIGURE211ITSHOULDBECLEARTHATNODENITESTATEMENTCANBEMADEABOUTHOWCAPITALUSAGERESPONDSTOTHEWAGECHANGETHATIS,THESIGNOFH11128K/H11128WISINDETERMINATEINTHESIMPLETWOINPUTCASE,AFALLINTHEWAGEWILLCAUSEASUBSTITUTIONAWAYFROMCAPITALTHATIS,LESSCAPITALWILLBEUSEDTOPRODUCEAGIVENOUTPUTLEVELBUTTHEOUTPUTEFFECTWILLCAUSEMORECAPITALTOBEDEMANDEDASPARTOFTHERMSINCREASEDPRODUCTIONPLANSO,SUBSTITUTIONANDOUTPUTEFFECTSINTHISCASEWORKINOPPOSITEDIRECTIONS,ANDNODENITECONCLUSIONABOUTTHESIGNOFH11128K/H11128WISPOSSIBLEASUMMARYOFSUBSTITUTIONANDOUTPUTEFFECTSTHERESULTSOFTHISDISCUSSIONCANBESUMMARIZEDBYTHEFOLLOWINGPRINCIPLESUBSTITUTIONANDOUTPUTEFFECTSININPUTDEMANDWHENTHEPRICEOFANINPUTFALLS,TWOEFFECTSCAUSETHEQUANTITYDEMANDEDOFTHATINPUTTORISE1THESUBSTITUTIONEFFECTCAUSESANYGIVENOUTPUTLEVELTOBEPRODUCEDUSINGMOREOFTHEINPUTAND2THEFALLINCOSTSCAUSESMOREOFTHEGOODTOBESOLD,THEREBYCREATINGANADDITIONALOUTPUTEFFECTTHATINCREASESDEMANDFORTHEINPUTFORARISEININPUTPRICE,BOTHSUBSTITUTIONANDOUTPUTEFFECTSCAUSETHEQUANTITYOFANINPUTDEMANDEDTODECLINEWEWILLNOWPROVIDEAMOREPRECISEDEVELOPMENTOFTHESECONCEPTSUSINGAMATHEMATICALAPPROACHTOTHEANALYSISOPTIMIZATIONPRINCIPLE584PARTVIIPRICINGININPUTMARKETSMATHEMATICALDERIVATIONASWESHOWEDINCHAPTER13,GENERALINPUTDEMANDFUNCTIONSGENERATEDBYCONSIDERINGTHERMSPROTMAXIMIZINGDECISIONCANBESTATEDFORTHETWOINPUTCASEASLH11005LP,W,V2121KH11005KP,W,V,WHEREPISTHEPRODUCTPRICETHEPRESENCEOFTHISTERMINTHEDEMANDFUNCTIONAGAINILLUSTRATESTHECLOSECONNECTIONBETWEENPRODUCTDEMANDANDTHEDERIVEDDEMANDFORINPUTSHEREWEWILLEXAMINEHOWCHANGESININPUTPRICESAFFECTTHESEDEMANDS1FORSIMPLICITY,WEWILLFOCUSONLYONLABORDEMANDTHEARGUMENTFORCAPITALORFORANYOTHERVARIABLEINPUTWOULDBEIDENTICALASINOURGRAPHICANALYSIS,WESTARTBYDIVIDINGH11128L/H11128WINTOTWOCOMPONENTS1THECHANGEINLINDUCEDBYTHECHANGEINW,HOLDINGOUTPUTCONSTANTAND2THECHANGEINLINDUCEDBYCHANGESINOUTPUTHENCEH11005QCONSTANTH11001FROMCHANGESINQ2122WENOWEXAMINEEACHOFTHESETERMSSEPARATELYCONSTANTOUTPUTDEMANDFUNCTIONSANDSHEPHARDSLEMMAWEHAVEALREADYDISCUSSEDTHERSTTERMONTHERIGHTOFEQUATION2122INCONNECTIONWITHANANALYSISOFCOSTMINIMIZATIONINCHAPTER12WEDEMONSTRATEDSHEPHARDSLEMMA,WHICHUSESTHEENVELOPETHEOREMTOSHOWTHATTHECONSTANTOUTPUTDEMANDFUNCTIONFORLCANBEFOUNDSIMPLYBYPARTIALLYDIFFERENTIATINGTOTALCOSTSWITHRESPECTTOWSEEFOOTNOTE8INTHATCHAPTERTHATIS,H11005LH11032Q,W,V,2123WHERETHEFUNCTIONLH11032PERMITSOUTPUTTOBEHELDCONSTANTINSTUDYINGLABORDEMANDTWOARGUMENTSSUGGESTWHYH11128LH11032/H11128WWILLBENEGATIVEINTHETWOINPUTCASETHEASSUMPTIONTHATTHERATEOFTECHNICALSUBSTITUTIONDIMINISHESFORSOUTHEASTERLYMOVEMENTSALONGANISOQUANT,COMBINEDWITHTHEASSUMPTIONOFCOSTMINIMIZATION,REQUIRESTHATWANDLMOVEINOPPOSITEDIRECTIONSWHENOUTPUTISHELDCONSTANTTHATRESULTHASALREADYBEENDEMONSTRATEDGRAPHICALLYINFIGURE211ASECOND,EVENINTHEMANYINPUTCASEITCANBESHOWNTHATH11128LH11032/H11128WH11005H111282TC/H11128W2MUSTBENEGATIVEIFCOSTSARETRULYMINIMIZED2HENCE,THESUBSTITUTIONEFFECTININPUTDEMANDTHEORYISUNAMBIGUOUSLYNEGATIVEH11128TCH5007H11128WH11128LH5007H11128WH11128LH5007H11128WH11128LH5007H11128WCHAPTER21FIRMSDEMANDSFORINPUTS5851INGENERAL,H11128L/H11128PANDH11128K/H11128PWILLBEPOSITIVEBECAUSEMARGINALCOSTISINCREASING,ANINCREASEINPRODUCTPRICEWILLINCREASEOUTPUTANDTHEDERIVEDDEMANDFORBOTHINPUTSINTHEINFERIORINPUTCASE,HOWEVER,THISANALYSISWILLNOTHOLDINTHISCASEANINCREASEINOUTPUTWILLACTUALLYCAUSELESSOFTHEINFERIORINPUTTOBEPURCHASED2FORAPROOF,SEEESILBERBERG,THESTRUCTUREOFECONOMICSAMATHEMATICALANALYSISNEWYORKMCGRAWHILL,1978,CHAPTER8SILBERBERGALSOUSESSHEPHARDSLEMMATOSHOWTHATCROSSPRICEEFFECTSININPUTDEMANDFUNCTIONSAREEQUALTHATIS,FORTHETWOINPUTCASE,H11128LH11032/H11128VH11005H111282TC/H11128WH11128VH11005H111282TC/H11128VH11128WH11005H11128KH11032/H11128WWHEREKH11032ISTHECONSTANTOUTPUTDEMANDFUNCTIONFORCAPITALANANALOGOUSPROOFHOLDSFORTHEMANYINPUTCASEOUTPUTEFFECTSDERIVATIONOFTHEOUTPUTEFFECTINEQUATION2122ISCONSIDERABLYMORETEDIOUS,ANDWEWILLPROVIDEONLYAHEURISTICPROOFHERE3TODOSOWEMAKEUSEOFA“CHAINRULE”TYPEOFARGUMENTTOEXAMINETHECAUSALLINKSTHATDETERMINEHOWCHANGESINWAFFECTTHEDEMANDFORLTHROUGHINDUCEDOUTPUTCHANGESSPECICALLY,WECANWRITEFROMCHANGESINQH11005H11080H11080H110802124TORECORDTHEWAYINWHICHWAFFECTSLTHROUGHITSEFFECTONMARGINALCOSTS,PRODUCTPRICES,ANDMARKETDEMANDEVALUATIONOFTHEMIDDLETWOTERMSONTHERIGHTSIDEOFEQUATION2124ISSTRAIGHTFORWARDBECAUSEPH11005MCFORPROTMAXIMIZATIONUNDERPERFECTCOMPETITION,H11128P/H11128MCH110051THEDERIVATIVEH11128Q/H11128PSHOWSHOWMARKETDEMANDOR,MOREPRECISELY,THERMSSHAREOFTHATDEMANDRESPONDSTOPRICECHANGESINTHEUSUALCASE,H11128Q/H11128PH110210THISTERMINDICATESHOWBEHAVIORINTHEGOODSMARKETAFFECTSINPUTDEMANDASWEWILLSEEINTHENEXTSECTION,THEPRICEELASTICITYOFDEMANDFORWHATISBEINGPRODUCEDPLAYSANIMPORTANTROLEINDETERMININGTHEPRICEELASTICITYOFDEMANDFORINPUTSEVALUATIONOFTHETERMSH11128L/H11128QANDH11128MCH11005H11128WINEQUATION2124ISTEDIOUSBUTWEHAVEALREADYSHOWNINFOOTNOTE9OFCHAPTER12THATBOTHTHESETERMSMUSTHAVETHESAMESIGNHENCE,THEIRPRODUCTMUSTBEPOSITIVEOVERALLTHEN,THERIGHTHANDSIDEOFEQUATION2124MUSTBENEGATIVEBECAUSEOFTHENEGATIVELYSLOPEDMARKETDEMANDCURVEFORTHEGOODBEINGPRODUCEDASINOURGRAPHICANALYSIS,THEMATHEMATICALCONCLUSIONISTHATH111