nicholson微观经济理论（答案+ppt+习题库）-50-03-033593-0

INCOMEANDSUBSTITUTIONEFFECTSINTHISCHAPTERWEWILLUSETHEUTILITYMAXIMIZATIONMODELTOSTUDYHOWTHEQUANTITYOFAGOODTHATANINDIVIDUALCHOOSESISAFFECTEDBYACHANGEINTHATGOODSPRICETHISEXAMINATIONWILLALLOWUSTOCONSTRUCTTHEINDIVIDUALSDEMANDCURVEFORTHEGOODINTHEPROCESSWEWILLPROVIDEANUMBEROFINSIGHTSINTOTHENATUREOFTHISPRICERESPONSEANDINTOTHEKINDSOFCETERISPARIBUSASSUMPTIONSTHATLIEBEHINDMOSTANALYSESOFDEMAND5CHAPTERDEMANDFUNCTIONSASWEPOINTEDOUTINCHAPTER4,INPRINCIPLEITWILLOFTENBEPOSSIBLETOSOLVETHENECESSARYCONDITIONSOFAUTILITYMAXIMUMFORTHEOPTIMALLEVELSOFX1,X2,XNANDH9261,THELAGRANGIANMULTIPLIERASFUNCTIONSOFALLPRICESANDINCOMEMATHEMATICALLY,THISCANBEEXPRESSEDASNDEMANDFUNCTIONSOFTHEFORMX1H11005D1P1,P2,PN,I51X2H11005D2P1,P2,PN,IXNH11005DNP1,P2,PN,I,WHEREWENOWUSETHEFUNCTIONALNOTATIONDFORTHEINDIVIDUALS“DEMAND”ONCEWEKNOWTHEFUNCTIONSD1,D2,DNANDTHEVALUESOFP1,P2,PNANDI,ANDIFWEASSUMEPREFERENCESDONTCHANGEWECAN“PREDICT”HOWMUCHOFEACHGOODTHEINDIVIDUALWILLBUYINLATERSECTIONSWESHALLBEINTERESTEDINWHATHAPPENSTOTHEOPTIMALAMOUNTOF,SAY,X1WHENP1CHANGESWESHALLALSOINVESTIGATEWHATHAPPENSTOX1WHENINCOMECHANGESORINCHAPTER6WHENTHEPRICEOFANOTHERGOODCHANGESSUCHQUESTIONSINVOLVETHESTUDYOFTHEDERIVATIVESOFTHEDEMANDFUNCTIONSWEAREINTERESTEDINCOMPARINGUTILITYMAXIMIZATIONCHOICESUNDERALTERNATIVECIRCUMSTANCES,ANDTHEDEMANDFUNCTIONSPROVIDEASHORTHANDWAYTORECORDTHERESULTSOFTHISCOMPARATIVESTATICSANALYSISHOMOGENEITYONECOMPARATIVESTATICS“THEOREM”CANEASILYBEDEMONSTRATEDHEREIFWEWERETODOUBLEALLPRICESANDINCOMEINDEED,IFWEWERETOMULTIPLYTHEMALLBYANYPOSITIVECONSTANT,THEOPTIMALQUANTITIESDEMANDEDWOULDREMAINUNCHANGEDDOUBLINGALLPRICESANDINCOMECHANGESONLYTHEUNITSBYWHICHWECOUNT,NOTTHE“REAL”QUANTITYOFGOODSDEMANDEDTHISRESULTCANBESEENINANUMBEROFWAYS,ALTHOUGHPERHAPSTHEEASIESTISTHROUGHAGRAPHICAPPROACHREFERRINGBACKTOFIGURES41AND42,ITISCLEARTHATIFWEDOUBLEPX,PY,ANDI,WESHALLNOTAFFECTTHEGRAPHOFTHEBUDGETCONSTRAINTHENCE,X,YWILLSTILLBETHECOMBINATIONTHATISCHOSENPXXH11001PYYH11005IISTHESAMECONSTRAINTAS2PXXH110012PYYH110052ISOMEWHATMORETECHNICALLY,WECANWRITETHISRESULTASSAYINGTHATFORANYGOODXI,XIH11005DIP1,P2,PN,IH11005DITP1,TP2,TPN,TI52FORANYTH110220FUNCTIONSTHATOBEYTHEPROPERTYILLUSTRATEDINEQUATION52ARESAIDTOBEHOMOGENEOUSOFDEGREEZERO1HENCE,WEHAVESHOWNTHATINDIVIDUALDEMANDFUNCTIONSAREHOMOGENEOUSOFDEGREEZEROINALLPRICESANDINCOMECHANGINGALLPRICESANDINCOMEINTHESAMEPROPORTIONSWILLNOTAFFECTTHEPHYSICALQUANTITIESOFGOODSDEMANDEDTHISRESULTSHOWSTHATINDIVIDUALSDEMANDSWILLNOTBEAFFECTEDBYA116PARTIICHOICEANDDEMAND1MOREGENERALLY,AFUNCTIONFX1,X2,XNISSAIDTOBEHOMOGENEOUSOFDEGREEKIFFTX1,TX2,TXNH11005TKFX1,X2,XNFORANYTH110220THEMOSTCOMMONCASESOFHOMOGENEOUSFUNCTIONSAREKH110050ANDKH110051IFFISHOMOGENEOUSOFDEGREEZERO,DOUBLINGALLOFITSARGUMENTSLEAVESFUNCHANGEDINVALUEIFFISHOMOGENEOUSOFDEGREE1,DOUBLINGALLITSARGUMENTSWILLDOUBLETHEVALUEOFFWESHALLENCOUNTERFUNCTIONSHOMOGENEOUSOFDEGREE1INPARTIV“PURE”INATIONDURINGWHICHALLPRICESANDINCOMESRISEPROPORTIONALLYTHEYWILLCONTINUETODEMANDTHESAMEBUNDLEOFGOODSOFCOURSE,IFANINATIONWERENOTPURETHATIS,IFSOMEPRICESROSEMORERAPIDLYTHANOTHERS,THISWOULDNOTBETHECASEEXAMPLE51HOMOGENEITYHOMOGENEITYOFDEMANDISADIRECTRESULTOFTHEUTILITYMAXIMIZATIONASSUMPTIONDEMANDFUNCTIONSDERIVEDFROMUTILITYMAXIMIZATIONWILLBEHOMOGENEOUSAND,CONVERSELY,DEMANDFUNCTIONSTHATARENOTHOMOGENEOUSCANNOTREECTUTILITYMAXIMIZATIONUNLESSPRICESENTERINTOTHEUTILITYFUNCTIONITSELF,ASTHEYMIGHTFORGOODSWITHSNOBAPPEALIF,FOREXAMPLE,ANINDIVIDUALSUTILITYFORFOODXANDHOUSINGYISGIVENBYUTILITYH11005UX,YH11005X3Y7,53ITISASIMPLEMATTERFOLLOWINGTHEPROCEDUREUSEDINEXAMPLE41TODERIVETHEDEMANDFUNCTIONSXH1100554YH11005THESEFUNCTIONSOBVIOUSLYEXHIBITHOMOGENEITYADOUBLINGOFALLPRICESANDINCOMEWOULDLEAVEXANDYUNAFFECTEDIFTHEINDIVIDUALSPREFERENCESFORXANDYWEREREECTEDINSTEADBYTHECESFUNCTIONUX,YH11005X5H11001Y5,55WESHOWEDINEXAMPLE42THATTHEDEMANDFUNCTIONSAREGIVENBYXH11005H20898H20899H1108056YH11005H20898H20899H11080ASBEFORE,BOTHTHESEDEMANDFUNCTIONSAREHOMOGENEOUSOFDEGREEZEROADOUBLINGOFPX,PY,ANDIWOULDLEAVEXANDYUNAFFECTEDQUERYDOTHEDEMANDFUNCTIONSDERIVEDINTHISEXAMPLEENSURETHATTOTALSPENDINGONXANDYWILLEXHAUSTTHEINDIVIDUALSINCOMEFORANYCOMBINATIONOFPX,PY,ANDICANYOUPROVETHATTHISISTHECASECHANGESININCOMEASANINDIVIDUALSPURCHASINGPOWERRISES,ITISNATURALTOEXPECTTHATTHEQUANTITYOFEACHGOODPURCHASEDWILLALSOINCREASETHISSITUATIONISILLUSTRATEDINFIGURE51ASIH5007PY1H5007H50071H11001PY/PXIH5007PX1H5007H50071H11001PX/PY7IH5007PY3IH5007PXCHAPTER5INCOMEANDSUBSTITUTIONEFFECTS117EXPENDITURESINCREASEFROMI1TOI2TOI3,THEQUANTITYOFXDEMANDEDINCREASESFROMX1TOX2TOX3ALSO,THEQUANTITYOFYINCREASESFROMY1TOY2TOY3NOTICETHATTHEBUDGETLINESI1,I2,ANDI3AREALLPARALLEL,REECTINGTHEFACTTHATONLYINCOMEISCHANGING,NOTTHERELATIVEPRICESOFXANDYBECAUSETHERATIOPX/PYSTAYSCONSTANT,THEUTILITYMAXIMIZINGCONDITIONSALSOREQUIRETHATTHEMRSSTAYCONSTANTASTHEINDIVIDUALMOVESTOHIGHERLEVELSOFSATISFACTIONTHEMRSISTHEREFORETHESAMEATPOINTX3,Y3ASATX1,Y1NORMALANDINFERIORGOODSINFIGURE51,BOTHXANDYINCREASEASINCOMEINCREASESH11128X/H11128IANDH11128Y/H11128IAREBOTHPOSITIVETHISMIGHTBECONSIDEREDTHEUSUALSITUATION,ANDGOODSTHATEXHIBITTHISPROPERTYARECALLEDNORMALGOODSOVERTHERANGEOFINCOMECHANGEBEINGOBSERVEDFORSOMEGOODS,HOWEVER,THEQUANTITYCHOSENMAYDECREASEASINCOMEINCREASESINSOMERANGESSOMEEXAMPLESOFTHESEGOODSMIGHTBEROTGUTWHISKEY,POTATOES,ANDSECONDHANDCLOTHINGAGOODZFORWHICHH11128Z/H11128IISNEGATIVEISCALLEDANINFERIORGOODTHISPHENOMENONISILLUSTRATEDINFIGURE52INTHISDIAGRAMTHEGOODZISIN118PARTIICHOICEANDDEMANDEFFECTOFANINCREASEININCOMEONTHEQUANTITIESOFXANDYCHOSENASINCOMEINCREASESFROMI1TOI2TOI3,THEOPTIMALUTILITYMAXIMIZINGCHOICESOFXANDYARESHOWNBYTHESUCCESSIVELYHIGHERPOINTSOFTANGENCYNOTICETHATTHEBUDGETCONSTRAINTSHIFTSINAPARALLELWAYBECAUSEITSSLOPEGIVENBYH11002PX/PYDOESNOTCHANGEQUANTITYOFXQUANTITYOFYY3U1U2U3U3I3U2I2U1I1Y2Y1X1X2X3FIGURE51FERIORBECAUSEFORINCREASESININCOMEINTHERANGESHOWN,LESSOFZISACTUALLYCHOSENNOTICETHATINDIFFERENCECURVESDONOTHAVETOBE“ODDLY”SHAPEDTOEXHIBITINFERIORITYTHECURVESCORRESPONDINGTOGOODSYANDZINFIGURE52CONTINUETOOBEYTHEASSUMPTIONOFADIMINISHINGMRSGOODZISINFERIORBECAUSEOFTHEWAYITRELATESTOTHEOTHERGOODSAVAILABLEGOODYHERE,NOTBECAUSEOFAPECULIARITYUNIQUETOITHENCE,WEHAVEDEVELOPEDTHEFOLLOWINGDENITIONSINFERIORANDNORMALGOODSAGOODXIFORWHICHH11128XI/H11128IH110210OVERSOMERANGEOFINCOMECHANGESISANINFERIORGOODINTHATRANGEIFH11128XI/H11128IH113500OVERSOMERANGEOFINCOMEVARIATION,THEGOODISANORMAL,OR“NONINFERIOR,”GOODINTHATRANGEENGELSLAWSINCETHEEIGHTEENTHCENTURY,THERELATIONSHIPBETWEENINCOMEANDTHECONSUMPTIONOFSPECICITEMSHASBEENSTUDIEDEXTENSIVELYBYECONOMISTSMOSTCOMMONLY,EXPENDITUREDATAARECOLLECTEDFROMASAMPLEOFFAMILIESANDARETHENCLASSIEDBYINCOMELEVELSORBY“SOCIALCLASS”TOSEEIFANYIMPORTANTREGULARITIESAREVISIBLEDEFINITIONCHAPTER5INCOMEANDSUBSTITUTIONEFFECTS119ANINDIFFERENCECURVEMAPEXHIBITINGINFERIORITYINTHISDIAGRAM,GOODZISINFERIORBECAUSETHEQUANTITYPURCHASEDACTUALLYDECLINESASINCOMEINCREASESYISANORMALGOODASITMUSTBEIFTHEREAREONLYTWOGOODSAVAILABLE,ANDPURCHASESOFYINCREASEASTOTALEXPENDITURESINCREASEQUANTITYOFZQUANTITYOFYY3U3I3U2U1I2I1Y2Y1Z3Z2Z1FIGURE52PROBABLYTHEMOSTWIDELYREFERENCEDSAMPLEDATAARETHOSEUSEDBYTHEPRUSSIANECONOMISTERNSTENGELINHISORIGINALSTUDIESANABBREVIATEDSETOFTHESEDATA,SHOWINGTHEAVERAGEBUDGETARYALLOCATIONSMADEBYASAMPLEOF153BELGIANFAMILIESIN1857,APPEARSINTABLE51FROMTHESEDATAENGELDREWWHATWASPERHAPSTHERSTEMPIRICALGENERALIZATIONABOUTCONSUMERBEHAVIORTHEPROPORTIONOFTOTALEXPENDITUREDEVOTEDTOFOODDECLINESASINCOMERISESINOTHERWORDS,FOODISANECESSITYWHOSECONSUMPTIONRISESLESSRAPIDLYTHANDOESINCOMETHATHYPOTHESISHASCOMETOBEKNOWNAS“ENGELSLAW,”ANDITHASBEENVERIEDINHUNDREDSOFSTUDIESITHOLDSTRUENOTONLYWITHINAPARTICULARGEOGRAPHICAREA,BUTALSOACROSSCOUNTRIESANDCONTINENTSCROSSCOUNTRYCOMPARISONSSHOWTHAT,ONTHEAVERAGE,INDIVIDUALSINLESSDEVELOPEDCOUNTRIESSPENDALARGERPERCENTAGEOFTHEIRINCOMESONFOODTHANDOINDIVIDUALSINTHEINDUSTRIALECONOMIESTHEPERCENTAGEOFINCOMESPENTONFOODALSOTENDSTODECLINEOVERTIMEASINCOMESRISEFOREXAMPLE,INNINETEENTHCENTURYAMERICA,INDIVIDUALSSPENTNEARLY50PERCENTOFTHEIRINCOMESONFOODTODAYTHATGUREHASFALLENTOBELOW20PERCENTINDEED,ENGELSLAWAPPEARSTOBESUCHACONSISTENTEMPIRICALNDINGTHATSOMEECONOMISTSHAVESUGGESTEDTHATTHEPROPORTIONOFINCOMESPENTONFOODMIGHTBEAUSEFULINDICATOROFPOVERTYFAMILIESTHATSPENDMORETHAN,SAY,35PERCENTOFTHEIRINCOMEONFOODMIGHTBEREGARDEDAS“POOR,”WHEREASTHOSEWHOSPENDLESSTHANTHATPERCENTAGEWOULDNOTBESOREGARDEDTABLE51CHANGESINAGOODSPRICETHEEFFECTOFAPRICECHANGEONTHEQUANTITYOFAGOODDEMANDEDISMORECOMPLEXTOANALYZETHANISTHEEFFECTOFACHANGEININCOMEGEOMETRICALLY,THISISBECAUSECHANGINGAPRICEINVOLVESCHANGINGNOTONLYTHEINTERCEPTSOFTHEBUDGETCONSTRAINT,BUTALSOITSSLOPECONSEQUENTLY,MOVINGTOTHENEWUTILITYMAXIMIZINGCHOICEENTAILSNOTONLYMOVINGTOANOTHERINDIFFERENCECURVE,BUTALSOCHANGINGTHEMRSWHENAPRICECHANGES,THEREFORE,TWOANALYTICALLYDIFFERENTEFFECTSCOMEINTOPLAYONEOFTHESEISASUBSTITUTIONEFFECTEVENIFTHEINDIVIDUALWERETOSTAYONTHESAMEINDIFFERENCECURVE,CONSUMPTIONPATTERNSWOULDBEALLOCATEDSOASTOEQUATETHEMRSTOTHENEWPRICERATIOASECONDEFFECT,THEINCOMEEFFECT,ARISESBECAUSEAPRICECHANGE120PARTIICHOICEANDDEMANDPERCENTAGEOFTOTALEXPENDITURESONVARIOUSITEMSBYBELGIANFAMILIESIN1857ANNUALINCOMEEXPENDITUREITEM2253004506007501,000FOOD620550500CLOTHING160180180LODGING,LIGHT,ANDFUEL170170170SERVICESEDUCATION,LEGAL,HEALTH4075115COMFORTANDRECREATION102535TOTAL100010001000SOURCEADAPTEDFROMAMARSHALL,PRINCIPLESOFECONOMICS,8THEDLONDONMACMILLAN,1920,P97TABLE51NECESSARILYCHANGESANINDIVIDUALS“REAL”INCOMETHEINDIVIDUALCANNOTSTAYONTHEINITIALINDIFFERENCECURVE,BUTMUSTMOVETOANEWONEWEBEGINBYANALYZINGTHESEEFFECTSGRAPHICALLYTHENWEWILLPROVIDEAMATHEMATICALDEVELOPMENTGRAPHICALANALYSISOFAFALLINPRICEINCOMEANDSUBSTITUTIONEFFECTSAREILLUSTRATEDINFIGURE53THISINDIVIDUALISINITIALLYMAXIMIZINGUTILITYSUBJECTTOTOTALEXPENDITURES,IBYCONSUMINGTHECOMBINATIONX,YTHEINITIALBUDGETCONSTRAINTISIH11005P1XXH11001PYYNOWSUPPOSETHATTHEPRICEOFXFALLSTOP2XTHENEWBUDGETCONSTRAINTISGIVENBYTHEEQUATIONCHAPTER5INCOMEANDSUBSTITUTIONEFFECTS121DEMONSTRATIONOFTHEINCOMEANDSUBSTITUTIONEFFECTSOFAFALLINTHEPRICEOFXWHENTHEPRICEOFXFALLSFROMP1XTOP2X,THEUTILITYMAXIMIZINGCHOICESHIFTSFROMX,YTOX,YTHISMOVEMENTCANBEBROKENDOWNINTOTWOANALYTICALLYDIFFERENTEFFECTSRST,THESUBSTITUTIONEFFECT,INVOLVINGAMOVEMENTALONGTHEINITIALINDIFFERENCECURVETOPOINTB,WHERETHEMRSISEQUALTOTHENEWPRICERATIOANDSECONDLY,THEINCOMEEFFECT,ENTAILINGAMOVEMENTTOAHIGHERLEVELOFUTILITY,BECAUSEREALINCOMEHASINCREASEDINTHEDIAGRAM,BOTHTHESUBSTITUTIONANDINCOMEEFFECTSCAUSEMOREXTOBEBOUGHTWHENITSPRICEDECLINESNOTICETHATPOINTI/PYISTHESAMEASBEFORETHEPRICECHANGETHISISBECAUSEPYHASNOTCHANGEDPOINTI/PYTHEREFOREAPPEARSONBOTHTHEOLDANDNEWBUDGETCONQUANTITYOFXQUANTITYOFYU2U2U1U1XYXBXYSUBSTITUTIONEFFECTINCOMEEFFECTTOTALINCREASEINXBIH11005PXXH11001PYYIH11005PXXH11001PYY12IPYFIGURE53IH11005P2XXH11001PYYINFIGURE53ITISCLEARTHATTHENEWPOSITIONOFMAXIMUMUTILITYISATX,Y,WHERETHENEWBUDGETLINEISTANGENTTOTHEINDIFFERENCECURVEU2THEMOVEMENTTOTHISNEWPOINTCANBEVIEWEDASBEINGCOMPOSEDOFTWOEFFECTSFIRST,THECHANGEINTHESLOPEOFTHEBUDGETCONSTRAINTWOULDHAVEMOTIVATEDAMOVETOPOINTB,EVENIFCHOICESHADBEENCONNEDTOTHOSEONTHEORIGINALINDIFFERENCECURVEU1THEDASHEDLINEINFIGURE53HASTHESAMESLOPEASTHENEWBUDGETCONSTRAINTIH11005P2XXH11001PYY,BUTISDRAWNTOBETANGENTTOU1BECAUSEWEARECONCEPTUALLYHOLDING“REAL”INCOMETHATIS,UTILITYCONSTANTARELATIVELYLOWERPRICEFORXCAUSESAMOVEFROMX,YTOBIFWEDONOTALLOWTHISINDIVIDUALTOBEMADEBETTEROFFASARESULTOFTHELOWERPRICETHISMOVEMENTISAGRAPHICDEMONSTRATIONOFTHESUBSTITUTIONEFFECTTHEFURTHERMOVEFROMBTOTHEOPTIMALPOINTX,YISANALYTICALLYIDENTICALTOTHEKINDOFCHANGEEXHIBITEDEARLIERFORCHANGESININCOMEBECAUSETHEPRICEOFXHASFALLEN,THISPERSONHASAGREATER“REAL”INCOMEANDCANAFFORDAUTILITYLEVELU2THATISGREATERTHANTHATWHICHCOULDPREVIOUSLYBEATTAINEDIFXISANORMALGOOD,MOREOFITWILLBECHOSENINRESPONSETOTHISINCREASEINPURCHASINGPOWERTHISOBSERVATIONEXPLAINSTHEORIGINOFTHETERMINCOMEEFFECTFORTHEMOVEMENTOVERALLTHEN,THERESULTOFTHEPRICEDECLINEISTOCAUSEMOREXTOBEDEMANDEDITISIMPORTANTTORECOGNIZETHATTHISPERSONDOESNOTACTUALLYMAKEASERIESOFCHOICESFROMX,YTOBANDTHENTOX,YWENEVEROBSERVEPOINTBONLYTHETWOOPTIMALPOSITIONSAREREFLECTEDINOBSERVEDBEHAVIORHOWEVER,THENOTIONOFINCOMEANDSUBSTITUTIONEFFECTSISANALYTICALLYVALUABLEBECAUSEITSHOWSTHATAPRICECHANGEAFFECTSTHEQUANTITYOFXTHATISDEMANDEDINTWOCONCEPTUALLYDIFFERENTWAYSWEWILLSEEHOWTHISSEPARATIONOFFERSMAJORINSIGHTSINTHETHEORYOFDEMANDGRAPHICALANALYSISOFANINCREASEINPRICEIFTHEPRICEOFGOODXWERETOINCREASE,ASIMILARANALYSISWOULDBEUSEDINFIGURE54THEBUDGETLINEHASBEENSHIFTEDINWARDBECAUSEOFANINCREASEINTHEPRICEOFXFROMP1XTOP2XTHEMOVEMENTFROMTHEINITIALPOINTOFUTILITYMAXIMIZATIONX,YTOTHENEWPOINTX,YCANBEDECOMPOSEDINTOTWOEFFECTSFIRST,EVENIFTHISPERSONCOULDSTAYONTHEINITIALINDIFFERENCECURVEU2,THEREWOULDSTILLBEANINCENTIVETOSUBSTITUTEYFORXANDMOVEALONGU2TOPOINTBHOWEVER,BECAUSEPURCHASINGPOWERHASBEENREDUCEDBYTHERISEINTHEPRICEOFX,HEORSHEMUSTMOVETOALOWERLEVELOFUTILITYTHISMOVEMENTISAGAINCALLEDTHEINCOMEEFFECTNOTICEINFIGURE54THATBOTHTHEINCOMEANDSUBSTITUTIONEFFECTSWORKINTHESAMEDIRECTIONANDCAUSETHEQUANTITYOFXDEMANDEDTOBEREDUCEDINRESPONSETOANINCREASEINITSPRICEEFFECTSOFPRICECHANGESFORINFERIORGOODSSOFARWEHAVESHOWNTHATSUBSTITUTIONANDINCOMEEFFECTSTENDTOREINFORCEONEANOTHERFORAPRICEDECLINE,BOTHCAUSEMOREOFTHEGOODTOBEDEMANDED,WHEREASFORAPRICEINCREASE,BOTHCAUSELESSTOBEDEMANDEDALTHOUGHTHISANALYSISISACCURATEFORTHECASEOFNORMALNONINFERIORGOODS,THEPOSSIBILITYOFINFERIORGOODSCOMPLICATESTHESTORYINTHISCASE,INCOMEANDSUBSTITUTIONEFFECTSWORKINOPPOSITEDIRECTIONS,ANDTHECOMBINEDRESULTOFAPRICECHANGEISINDETERMINATEAFALLINPRICE,FOREXAMPLE,WILLALWAYSCAUSEANINDIVIDUALTOTENDTOCONSUMEMORE122PARTIICHOICEANDDEMANDOFAGOODBECAUSEOFTHESUBSTITUTIONEFFECTBUTIFTHEGOODISINFERIOR,THEINCREASEINPURCHASINGPOWERCAUSEDBYTHEPRICEDECLINEMAYCAUSELESSOFTHEGOODTOBEBOUGHTTHERESULTISTHEREFOREINDETERMINATETHESUBSTITUTIONEFFECTTENDSTOINCREASETHEQUANTITYOFTHEINFERIORGOODBOUGHT,WHEREASTHEPERVERSEINCOMEEFFECTTENDSTOREDUCETHISQUANTITYUNLIKETHESITUATIONFORNORMALGOODS,ITISNOTPOSSIBLEHERETOPREDICTEXACTLYHOWTHEPRICECHANGEWILLAFFECTTHEQUANTITYCHOSENCHAPTER5INCOMEANDSUBSTITUTIONEFFECTS123DEMONSTRATIONOFTHEINCOMEANDSUBSTITUTIONEFFECTSOFANINCREASEINTHEPRICEOFXWHENTHEPRICEOFXINCREASES,THEBUDGETCONSTRAINTSHIFTSINWARDTHEMOVEMENTFROMTHEINITIALUTILITYMAXIMIZINGPOINTX,YTOTHENEWPOINTX,YCANBEANALYZEDASTWOSEPARATEEFFECTSTHESUBSTITUTIONEFFECTWOULDBEDEPICTEDASAMOVEMENTTOPOINTBONTHEINITIALINDIFFERENCECURVEU2THEPRICEINCREASE,HOWEVER,WOULDCREATEALOSSOFPURCHASINGPOWERANDACONSEQUENTMOVEMENTTOALOWERINDIFFERENCECURVETHISISTHEINCOMEEFFECTINTHEDIAGRAM,BOTHTHEINCOMEANDSUBSTITUTIONEFFECTSCAUSETHEQUANTITYOFXTOFALLASARESULTOFTHEINCREASEINITSPRICEAGAIN,THEPOINTI/PYISNOTAFFECTEDBYTHECHANGEINTHEPRICEOFXTOTALREDUCTIONINXSUBSTITUTIONEFFECTINCOMEEFFECTQUANTITYOFXQUANTITYOFYXXBXYYIPYU2U2U1U1BIH11005PXXH11001PYY2IH11005PXXH11001PYY1FIGURE54GIFFENSPARADOXIFTHEINCOMEEFFECTOFAPRICECHANGEISSTRONGENOUGH,THECHANGEINPRICEANDTHERESULTINGCHANGEINTHEQUANTITYDEMANDEDCOULDACTUALLYMOVEINTHESAMEDIRECTIONLEGENDHASITTHATTHEENGLISHECONOMISTROBERTGIFFENOBSERVEDTHISPARADOXINNINETEENTHCENTURYIRELANDWHENTHEPRICEOFPOTATOESROSE,PEOPLEREPORTEDLYCONSUMEDMOREOFTHEMTHISPECULIARRESULTCANBEEXPLAINEDBYLOOKINGATTHESIZEOFTHEINCOMEEFFECTOFACHANGEINTHEPRICEOFPOTATOESPOTATOESWERENOTONLYINFERIORGOODS,BUTALSOUSEDUPALARGEPORTIONOFTHEIRISHPEOPLESINCOMEANINCREASEINTHEPRICEOFPOTATOESTHEREFOREREDUCEDREALINCOMESUBSTANTIALLYTHEIRISHWEREFORCEDTOCUTBACKONOTHERLUXURYFOODCONSUMPTIONINORDERTOBUYMOREPOTATOESEVENTHOUGHTHISRENDERINGOFEVENTSISHISTORICALLYIMPLAUSIBLE,THEPOSSIBILITYOFANINCREASEINTHEQUANTITYDEMANDEDINRESPONSETOANINCREASEINTHEPRICEOFAGOODHASCOMETOBEKNOWNASGIFFENSPARADOX2LATERWEWILLPROVIDEAMATHEMATICALANALYSISOFHOWGIFFENSPARADOXCANOCCURASUMMARYHENCE,OURGRAPHICALANALYSISLEADSTOTHEFOLLOWINGCONCLUSIONSSUBSTITUTIONANDINCOMEEFFECTSTHEUTILITYMAXIMIZATIONHYPOTHESISSUGGESTSTHAT,FORNORMALGOODS,AFALLINTHEPRICEOFAGOODLEADSTOANINCREASEINQUANTITYPURCHASEDBECAUSE1THESUBSTITUTIONEFFECTCAUSESMORETOBEPURCHASEDASTHEINDIVIDUALMOVESALONGANINDIFFERENCECURVEAND2THEINCOMEEFFECTCAUSESMORETOBEPURCHASEDBECAUSETHEPRICEDECLINEHASINCREASEDPURCHASINGPOWER,THEREBYPERMITTINGMOVEMENTTOAHIGHERINDIFFERENCECURVEWHENTHEPRICEOFANORMALGOODRISES,SIMILARREASONINGPREDICTSADECLINEINTHEQUANTITYPURCHASEDFORINFERIORGOODS,SUBSTITUTIONANDINCOMEEFFECTSWORKINOPPOSITEDIRECTIONS,ANDNODENITEPREDICTIONSCANBEMADETHEINDIVIDUALSDEMANDCURVESOFARWEHAVESHOWNTHATANINDIVIDUALSDEMANDFORAGOODSAY,X1DEPENDSONHISORHERPREFERENCESANDONALLPRICESANDINCOMEX1H11005D1P1,P2,PN,I57FREQUENTLY,ITISCONVENIENTTOGRAPHX1ASSIMPLYAFUNCTIONOFITSOWNPRICEP1,WITHTHEUNDERSTANDINGTHATALLOTHERPRICESANDINCOMEAREBEINGHELDCONSTANTOPTIMIZATIONPRINCIPLE124PARTIICHOICEANDDEMAND2AMAJORPROBLEMWITHTHISEXPLANATIONISTHATITDISREGARDSMARSHALLSOBSERVATIONTHATBOTHSUPPLYANDDEMANDFACTORSMUSTBETAKENINTOACCOUNTWHENANALYZINGPRICECHANGESIFPOTATOPRICESINCREASEDBECAUSEOFTHEPOTATOBLIGHTINIRELAND,THENSUPPLYSHOULDHAVEBECOMESMALLER,SOHOWCOULDMOREPOTATOESPOSSIBLYHAVEBEENCONSUMEDALSO,SINCEMANYIRISHPEOPLEWEREPOTATOFARMERS,THEPOTATOPRICEINCREASESHOULDHAVEINCREASEDREALINCOMEFORTHEMFORADETAILEDDISCUSSIONOFTHESEANDOTHERFASCINATINGBITSOFPOTATOLORE,SEEGPDWYERANDCMLINDSEY,“ROBERTGIFFENANDTHEIRISHPOTATO,”AMERICANECONOMICREVIEWMARCH1984188192TOSHOWTHECONSTRUCTIONOFSUCHAGRAPH,WEASSUMETHATTHEREAREONLYTWOGOODSXANDYANDTHATTHEDEMANDFUNCTIONFORGOODXISGIVENBYXH11005DXPX,PY,I58FIGURE55ASHOWSUTILITYMAXIMIZINGCHOICESOFXANDYASTHISINDIVIDUALISPRESENTEDWITHSUCCESSIVELYLOWERPRICESOFGOODXWHILEHOLDINGPYANDICONSTANTITISASSUMEDTHATTHEQUANTITIESOFXCHOSENINCREASEFROMXH11032TOXH11033TOXH11032H11033ASTHATGOODSPRICEFALLSFROMPH11032XTOPH11033XTOPXH11032H11033SUCHANASSUMPTIONISINACCORDWITHOURGENERALCONCLUSIONTHAT,EXCEPTINTHEUNUSUALCASEOFGIFFENSPARADOX,H11128X/H11128PXISNEGATIVEINFIGURE55BINFORMATIONABOUTTHEUTILITYMAXIMIZINGCHOICESOFGOODXISTRANSFERREDTOADEMANDCURVE,HAVINGPXONTHEVERTICALAXISANDSHARINGTHESAMEHORIZONTALAXISASTHEGUREABOVEITTHENEGATIVESLOPEOFTHECURVEAGAINREECTSTHEASSUMPTIONTHATH11128X/H11128PXISNEGATIVEHENCE,WEMAYDENEANINDIVIDUALDEMANDCURVEASFOLLOWSINDIVIDUALDEMANDCURVEANINDIVIDUALDEMANDCURVESHOWSTHERELATIONSHIPBETWEENTHEPRICEOFAGOODANDTHEQUANTITYOFTHATGOODPURCHASEDBYANINDIVIDUALASSUMINGTHATALLOTHERDETERMINANTSOFDEMANDAREHELDCONSTANTTHEDEMANDCURVEILLUSTRATEDINFIGURE55STAYSINAXEDPOSITIONONLYSOLONGASALLOTHERDETERMINANTSOFDEMANDREMAI