nicholson微观经济理论（答案+ppt+习题库）-70-03-033593-0

MARKETDEMANDANDELASTICITYINCHAPTER5WESHOWEDHOWTOCONSTRUCTTHEINDIVIDUALSDEMANDCURVEFORAGOODBYEXAMININGCHANGESINTHEUTILITYMAXIMIZINGCHOICESFORTHEGOODINRESPONSETOCHANGINGPRICESINTHISCHAPTERWEWILLBECONCERNEDWITH“ADDINGUP”THESEINDIVIDUALDEMANDCURVESTOCREATEAMARKETDEMANDCURVE,ACONCEPTTHATPLAYSACRUCIALROLEINALLOFMICROECONOMICTHEORYCONSIDERABLEATTENTIONISDEVOTEDTOEXAMININGHOWTHEPOSITIONOFTHEMARKETDEMANDCURVEMIGHTSHIFTINRESPONSETOCHANGINGCONDITIONSWEWILLALSOBECONCERNEDWITHDENINGVARIOUS“ELASTICITY”MEASURES,BECAUSETHOSEMEASURESAREWIDELYUSEDINEMPIRICALWORK7CHAPTERMARKETDEMANDCURVESFOREASEOFEXPOSITION,ASSUMETHATTHEREAREONLYTWOGOODSXANDYANDONLYTWOPEOPLENUMBERED1AND2INANECONOMYTHERSTPERSONSDEMANDFUNCTIONFORGOODXISGIVENBYX1H11005D1XPX,PY,I171ANDTHESECONDPERSONSDEMANDFORXBYX2H11005D2XPX,PY,I272TWOFEATURESOFTHESEDEMANDFUNCTIONSSHOULDBENOTEDFIRST,BOTHINDIVIDUALSAREASSUMEDTOFACETHESAMEPRICESPXANDPYEACHPERSONISALSOASSUMEDTOBEAPRICETAKER,WHOMUSTACCEPTTHEPRICESPREVAILINGINTHEMARKETSECOND,EACHPERSONSDEMANDDEPENDSONHISORHEROWNINCOME,BECAUSEEACHISBOUNDBYABUDGETCONSTRAINTTHATDETERMINESHOWMUCHHEORSHECANBUYWITHINCOMEI1ORI2,RESPECTIVELYTHETOTALDEMANDFORXISSIMPLYTHESUMOFTHEAMOUNTSDEMANDEDBYTHETWOINDIVIDUALSOBVIOUSLY,THISMARKETDEMANDWILLDEPENDONTHEPARAMETERSPX,PY,I1,ANDI2MATHEMATICALLY,TOTALXH11005X1H11001X2H11005D1XPX,PY,I1H11001D2XPX,PY,I273ORTOTALXH11005DXPX,PY,I1,I2,WHERETHEFUNCTIONDXREPRESENTSTHEMARKETDEMANDFUNCTIONFORGOODXNOTICETHATINTHISCASE,MARKETDEMANDDEPENDSONTHEPRICESOFGOODXANDGOODYANDONTHEINCOMESOFEACHPERSONTOCONSTRUCTTHEMARKETDEMANDCURVE,PXISALLOWEDTOVARYWHILEPY,I1,ANDI2AREHELDCONSTANTIFWEASSUMETHATEACHINDIVIDUALSDEMANDFORGOODXISDOWNWARDSLOPING,THEMARKETDEMANDCURVEWILLALSOBETHATIS,ADECREASEINPXWILLCAUSETHEQUANTITYOFXDEMANDEDINTHEMARKETTOINCREASEBECAUSEEACHPERSONWILLDEMANDMOREAGRAPHICALCONSTRUCTIONFIGURE71SHOWSTHECONSTRUCTIONOFTHEMARKETDEMANDCURVEFORXFOREACHPRICE,THEPOINTONTHEMARKETDEMANDCURVEISFOUNDBYSUMMINGTHEQUANTITIESDEMANDEDBYEACHINDIVIDUALFOREXAMPLE,ATAPRICEOFPXINDIVIDUAL1DEMANDSX1ANDINDIVIDUAL2DEMANDSX2THETOTALQUANTITYDEMANDEDINTHEMARKETATPXISTHEREFORETHESUMOFTHESETWOAMOUNTSXH11005X1H11005X2CONSEQUENTLY,THEPOINTX,PXISONEPOINTONTHEMARKETDEMANDCURVEDXTHEOTHERPOINTSONTHECURVEAREDERIVEDINASIMILARWAYTHEMARKETCURVEISTHE“HORIZONTALSUM”OFEACHINDIVIDUALSDEMANDCURVE1SHIFTSINTHEMARKETDEMANDCURVETHEMARKETDEMANDCURVE,THEN,SUMMARIZESTHECETERISPARIBUSRELATIONSHIPBETWEENXANDPXITISIMPORTANTTOKEEPINMINDTHATTHECURVEISINREALITYA172PARTIICHOICEANDDEMAND1ALTHOUGHTHECONSTRUCTIONHEREAPPLIESTOUNCOMPENSATEDDEMANDCURVESTHATIS,NOMINALINCOMEISBEINGHELDCONSTANT,ANIDENTICALPROCEDURECOULDBEUSEDTOCONSTRUCTCOMPENSATEDMARKETDEMANDCURVESFROMCOMPENSATEDCONSTANTUTILITYINDIVIDUALDEMANDCURVESTWODIMENSIONALREPRESENTATIONOFAMANYVARIABLEFUNCTIONCHANGESINPXRESULTINMOVEMENTSALONGTHISCURVEBUTCHANGESINANYOFTHEOTHERDETERMINANTSOFTHEDEMANDFORXCAUSETHECURVETOSHIFTTOANEWPOSITIONAGENERALRISEININCOMESWOULD,FOREXAMPLE,CAUSETHEDEMANDCURVETOSHIFTOUTWARDASSUMINGXISANORMALGOODBECAUSEEACHINDIVIDUALWOULDCHOOSETOBUYMOREXATEVERYPRICESIMILARLY,ARISEINPYWOULDSHIFTTHEDEMANDCURVEFORXOUTWARDIFINDIVIDUALSREGARDEDXANDYASSUBSTITUTES,BUTSHIFTTHEDEMANDCURVEFORXINWARDIFTHEGOODSWEREREGARDEDASCOMPLEMENTSACCOUNTINGFORALLSUCHSHIFTSMAYSOMETIMESREQUIRERETURNINGTOEXAMINETHEINDIVIDUALDEMANDFUNCTIONSTHATCONSTITUTETHEMARKETRELATIONSHIP,ESPECIALLYWHENEXAMININGSITUATIONSINWHICHTHEDISTRIBUTIONOFINCOMECHANGES,THEREBYRAISINGSOMEINCOMESANDREDUCINGOTHERSTOKEEPMATTERSSTRAIGHT,ECONOMISTSUSUALLYRESERVETHETERMCHANGEINQUANTITYDEMANDEDFORAMOVEMENTALONGAXEDDEMANDCURVEINRESPONSETOACHANGEINPXALTERNATIVELY,ANYSHIFTINTHEPOSITIONOFTHEDEMANDCURVEISREFERREDTOASA“CHANGEINDEMAND”EXAMPLE71SHIFTSINMARKETDEMANDTHESEIDEASCANBEILLUSTRATEDWITHASIMPLESETOFLINEARDEMANDFUNCTIONSSUPPOSEINDIVIDUAL1SDEMANDFORORANGESXMEASUREDINDOZENSPERYEARISGIVENBY2X1H1100510H110022PXH110011I1H110015PY,74CHAPTER7MARKETDEMANDANDELASTICITY173CONSTRUCTIONOFAMARKETDEMANDCURVEFROMINDIVIDUALDEMANDCURVESAMARKETDEMANDCURVEISTHE“HORIZONTALSUM”OFEACHINDIVIDUALSDEMANDCURVEATEACHPRICETHEQUANTITYDEMANDEDINTHEMARKETISTHESUMOFTHEAMOUNTSEACHINDIVIDUALDEMANDSFOREXAMPLE,ATPXTHEDEMANDINTHEMARKETISX1H11001X2H11005XPXPXPXPXX1DXX1X2X2DX2XXDX1AINDIVIDUAL1BINDIVIDUAL2CMARKETDEMANDFIGURE712THISLINEARFORMISUSEDTOILLUSTRATESOMEISSUESINAGGREGATIONITISDIFCULTTODEFENDTHISFORMTHEORETICALLY,HOWEVERFOREXAMPLE,ITISNOTHOMOGENEOUSOFDEGREEZEROINALLPRICESANDINCOMEWHEREPXH11005PRICEOFORANGESDOLLARSPERDOZENI1H11005INDIVIDUAL1SINCOMEINTHOUSANDSOFDOLLARSPYH11005PRICEOFGRAPEFRUITAGROSSSUBSTITUTEFORORANGESDOLLARSPERDOZENINDIVIDUAL2SDEMANDFORORANGESISGIVENBYX2H1100517H11002PXH1100105I2H110015PY75HENCETHEMARKETDEMANDFUNCTIONISDXPX,PY,I1,I2H11005X1H11001X2H1100527H110023PXH110011I1H1100105I2H11001PY76HERETHECOEFFICIENTFORTHEPRICEOFORANGESREPRESENTSTHESUMOFTHETWOINDIVIDUALSCOEFFICIENTS,ASDOESTHECOEFFICIENTFORGRAPEFRUITPRICESTHISREFLECTSTHEASSUMPTIONTHATORANGEANDGRAPEFRUITMARKETSARECHARACTERIZEDBYTHELAWOFONEPRICEBECAUSETHEINDIVIDUALSHAVEDIFFERINGCOEFFICIENTSFORINCOME,HOWEVER,THEDEMANDFUNCTIONDEPENDSONTHEDISTRIBUTIONOFINCOMEBETWEENTHEMTOGRAPHEQUATION76ASAMARKETDEMANDCURVE,WEMUSTASSUMEVALUESFORI1,I2,ANDPYBECAUSETHEDEMANDCURVEREECTSONLYTHETWODIMENSIONALRELATIONSHIPBETWEENXANDPXIFI1H1100540,I2H1100520,ANDPYH110054,THEMARKETDEMANDCURVEISGIVENBYXH1100527H110023PXH110014H110011H110014H1100536H110023PX,77WHICHISASIMPLELINEARDEMANDCURVEIFTHEPRICEOFGRAPEFRUITWERETORISETOPYH110056,THECURVEWOULD,ASSUMINGINCOMESREMAINUNCHANGED,SHIFTOUTWARDTOXH1100527H110023PXH110014H110011H110016H1100538H110023PX,78WHEREASANINCOMETAXTHATTOOK10THOUSANDDOLLARSFROMINDIVIDUAL1ANDTRANSFERREDITTOINDIVIDUAL2WOULDSHIFTTHEDEMANDCURVEINWARDTOXH1100527H110023PXH110013H1100115H110014H11005355H110023PX79BECAUSEINDIVIDUAL1HASALARGERMARGINALEFFECTOFINCOMECHANGESONORANGEPURCHASESALLOFTHESECHANGESSHIFTTHEDEMANDCURVEINAPARALLELWAYBECAUSE,INTHISLINEARCASE,NONEOFTHEMAFFECTSEITHERINDIVIDUALSCOEFCIENTFORPXINALLCASES,ARISEINPXOF10TENCENTSWOULDCAUSEXTOFALLBY30DOZENPERYEARQUERYFORTHISLINEARCASE,WHENWOULDITBEPOSSIBLETOEXPRESSMARKETDEMANDASALINEARFUNCTIONOFTOTALINCOMEI1H11001I2ALTERNATIVELY,SUPPOSETHEINDIVIDUALSHADDIFFERINGCOEFFCIENTSFORPYWOULDTHATCHANGETHEANALYSISINANYFUNDAMENTALWAYGENERALIZATIONSALTHOUGHOURCONSTRUCTIONCONCERNSONLYTWOGOODSANDTWOINDIVIDUALS,ITISEASILYGENERALIZEDSUPPOSETHEREARENGOODSDENOTEDBYXI,IH110051,NWITHPRICESPI,IH110051,NASSUMEALSOTHEREAREMINDIVIDUALSINSOCIETYTHENTHEJTHINDIVIDUALS174PARTIICHOICEANDDEMANDDEMANDFORTHEITHGOODWILLDEPENDONALLPRICESANDONIJ,THEINCOMEOFTHISPERSONTHISCANBEDENOTEDBYXIJH11005DIJP1,PN,IJ,710WHEREIH110051,NANDJH110051,MUSINGTHESEINDIVIDUALDEMANDFUNCTIONS,MARKETDEMANDCONCEPTSAREPROVIDEDBYTHEFOLLOWINGDENITIONSMARKETDEMANDTHEMARKETDEMANDFUNCTIONFORAPARTICULARGOODXIISTHESUMOFEACHINDIVIDUALSDEMANDFORTHATGOODXIH11005H20913MJ1XIJH11005DIP1,PN,I1,IM711THEMARKETDEMANDCURVEFORXIISCONSTRUCTEDFROMTHEDEMANDFUNCTIONBYVARYINGPIWHILEHOLDINGALLOTHERDETERMINANTSOFXICONSTANTASSUMINGEACHINDIVIDUALSDEMANDCURVEISDOWNWARDSLOPING,THISMARKETDEMANDCURVEWILLALSOBEDOWNWARDSLOPINGOFCOURSE,THISDENITIONISJUSTAGENERALIZATIONOFOURPRIORDISCUSSION,BUTTHREEFEATURESWARRANTREPETITIONFIRST,THEFUNCTIONALREPRESENTATIONOFEQUATION711MAKESCLEARTHATTHEDEMANDFORXIDEPENDSNOTONLYONPI,BUTALSOONTHEPRICESOFALLOTHERGOODSACHANGEINONEOFTHOSEOTHERPRICESWOULDTHEREFOREBEEXPECTEDTOSHIFTTHEDEMANDCURVETOANEWPOSITIONSECOND,THEFUNCTIONALNOTATIONINDICATESTHATTHEDEMANDFORXIDEPENDSONTHEENTIREDISTRIBUTIONOFINDIVIDUALSINCOMESALTHOUGHINMANYECONOMICDISCUSSIONSITISCUSTOMARYTOREFERTOTHEEFFECTOFCHANGESINAGGREGATETOTALPURCHASINGPOWERONTHEDEMANDFORAGOOD,THISAPPROACHMAYBEAMISLEADINGSIMPLICATION,BECAUSETHEACTUALEFFECTOFSUCHACHANGEONTOTALDEMANDWILLDEPENDONPRECISELYHOWTHEINCOMECHANGESAREDISTRIBUTEDAMONGINDIVIDUALSFINALLY,ALTHOUGHTHEYAREOBSCUREDSOMEWHATBYTHENOTATIONWEHAVEBEENUSING,THEROLEOFCHANGESINPREFERENCESSHOULDBEMENTIONEDWEHAVECONSTRUCTEDINDIVIDUALSDEMANDFUNCTIONSWITHTHEASSUMPTIONTHATPREFERENCESASREPRESENTEDBYINDIFFERENCECURVEMAPSREMAINXEDIFPREFERENCESWERETOCHANGE,SOWOULDINDIVIDUALANDMARKETDEMANDFUNCTIONSHENCE,MARKETDEMANDCURVESCANCLEARLYBESHIFTEDBYCHANGESINPREFERENCESINMANYECONOMICANALYSES,HOWEVER,ITISASSUMEDTHATTHESECHANGESOCCURSOSLOWLYTHATTHEYMAYBEIMPLICITLYHELDCONSTANTWITHOUTMISREPRESENTINGTHESITUATIONAWORDONNOTATIONOFTENINTHISBOOKWESHALLBELOOKINGATONLYONEMARKETINORDERTOSIMPLIFYTHENOTATION,INTHESECASESWESHALLUSETHELETTERQTOREFERTOTHEQUANTITYOFTHEPARTICULARGOODDEMANDEDINTHISMARKETANDPTODENOTEITSPRICEASALWAYS,WHENWEDRAWADEMANDCURVEINTHEQPPLANE,THECETERISPARIBUSASSUMPTIONISINEFFECTIFANYOFTHEFACTORSMENTIONEDINTHEPREVIOUSSECTIONOTHERPRICES,INDIVIDUALSDEFINITIONCHAPTER7MARKETDEMANDANDELASTICITY175INCOMES,ORPREFERENCESSHOULDCHANGE,THEQPDEMANDCURVEWILLSHIFT,ANDWESHOULDKEEPTHATPOSSIBILITYINMINDWHENWETURNTOCONSIDERRELATIONSHIPSAMONGTWOORMOREGOODS,HOWEVER,WEWILLRETURNTOTHENOTATIONWEHAVEBEENUSINGUPUNTILNOWTHATIS,DENOTINGGOODSBYXANDYORBYXIELASTICITYECONOMISTSOFTENWISHTOSUMMARIZETHEWAYINWHICHCHANGESINONEVARIABLE,SAY,A,AFFECTSOMEOTHERVARIABLE,SAY,BFOREXAMPLE,ANECONOMISTMIGHTBEINTERESTEDINMEASURINGHOWTHECHANGEINTHEPRICEOFAGOODAFFECTSTHEQUANTITYDEMANDEDORHOWACHANGEININCOMEAFFECTSTOTALEXPENDITURESONEPROBLEMTHATARISESINATTEMPTINGTODEVELOPSUCHSUMMARYMEASURESISTHATQUITEOFTENAANDBARENOTMEASUREDINTHESAMEUNITSTHEQUANTITYOFSTEAKPURCHASEDISMEASUREDINPOUNDSANDOUNCESPERYEAR,ANDTHEPRICEOFSTEAKISMEASUREDINDOLLARSWEMIGHTTHENSPEAKOFANINCREASEOF10CENTSINTHEPRICEOFSTEAK,LEADINGTOAFALLOF2POUNDSPERYEAROFSTEAKPURCHASESSIMILARLY,WECOULDSPEAKOFAFALLINTHEPRICEOFORANGESBY10CENTSPERDOZEN,LEADINGTOANINCREASEINORANGEPURCHASESOF30DOZENPERYEARASWASTHECASEINEXAMPLE71HOWEVER,THERENOWWOULDBENOEASYWAYTOANSWERTHEQUESTIONOFWHETHERSTEAKISMOREORLESSRESPONSIVETOPRICECHANGESTHANAREORANGESTHEPROBLEMEXISTSBECAUSETHECOMMODITIESAREMEASUREDINDIFFERENTUNITSASASOLUTIONECONOMISTSHAVEDEVELOPEDTHECONCEPTOFELASTICITY,WHICHWILLBEINTRODUCEDINTHISSECTIONAGENERALDENITIONSUPPOSETHATAPARTICULARVARIABLEBDEPENDSONANOTHERVARIABLEAANDTHATTHISDEPENDENCEISDENOTEDBYBH11005FA,712WHERETHEDOTSINTHEEQUATIONINDICATETHATBMAYDEPENDONOTHERVARIABLESASWELLWEDENETHEELASTICITYOFBWITHRESPECTTOADENOTEDBYEB,AASEB,AH11005H11005H11005H11080713THISEXPRESSIONSHOWSHOWTHEVARIABLEBRESPONDS,CETERISPARIBUS,TOA1PERCENTCHANGEINVARIABLEAALTHOUGHTHEPARTIALDERIVATIVEH11128B/H11128AALSOSHOWSHOWBCHANGESWHENACHANGES,ITISNOTASUSEFULASTHEELASTICITYBECAUSEITISMEASUREDINUNITSOFBPERUNITCHANGEINAINTHEELASTICITY,MULTIPLICATIONOFTHATPARTIALDERIVATIVEBYA/BCAUSESTHEUNITSTO“DROPOUT,”ANDTHEREMAININGEXPRESSIONISPURELYINTERMSOFPROPORTIONSINOURORANGESTEAKEXAMPLE,WEMIGHTKNOWTHATA1PERCENTCHANGEINTHEPRICEOFSTEAKLEADSTOA2PERCENTCHANGEINTHEQUANTITYBOUGHT,WHEREASA1PERCENTCHANGEINTHEPRICEOFORANGESLEADSTOA1PERCENTCHANGEINTHEQUANTITYBOUGHTCONSEQUENTLY,WECOULDCONCLUDETHATSTEAKPURCHASESWEREMORERESPONSIVETOPRICETHEFACTTHATSTEAKANDORANGESAREMEASUREDINDIFFERENTUNITSNOLONGERPRESENTSAPROBLEMBECAUSEWEAREDEALINGONLYINRELATIVEPERCENTAGECHANGESAH5007BH11128BH5007H11128AH9004B/BH5007H9004A/APERCENTAGECHANGEINBH5007H5007H5007PERCENTAGECHANGEINA176PARTIICHOICEANDDEMANDPRICEELASTICITYOFDEMANDALTHOUGHWESHALLCOMEACROSSMANYDIFFERENTAPPLICATIONSOFTHECONCEPTOFELASTICITYINTHISBOOK,PROBABLYTHEMOSTIMPORTANTISTHATOFTHEPRICEELASTICITYOFDEMANDCHANGESINTHEPRICEOFAGOODPWILLLEADTOCHANGESINTHEQUANTITYPURCHASEDQ,ANDTHEPRICEELASTICITYOFDEMANDISINTENDEDTOMEASURETHISRESPONSEAPPLYINGEQUATION713,THEPRICEELASTICITYOFDEMANDWOULDBEDENEDASFOLLOWSPRICEELASTICITYOFDEMANDEQ,PEQ,PH11005H11005H11080714THISELASTICITY,THEN,RECORDSHOWQCHANGESINPERCENTAGETERMSINRESPONSETOAPERCENTAGECHANGEINPBECAUSEH11128Q/H11128PISUSUALLYNEGATIVETHATIS,PANDQMOVEINOPPOSITEDIRECTIONS,EXCEPTINTHECASEOFGIFFENSPARADOX,EQ,PUSUALLYWILLBENEGATIVE3FOREXAMPLE,AVALUEOFEQ,POFH110021WOULDMEANTHATA1PERCENTRISEINPRICELEADSTOA1PERCENTDECLINEINQUANTITY,WHEREASAVALUEOFEQ,POFH110022WOULDRECORDTHEFACTTHATA1PERCENTRISEINPRICECAUSESQUANTITYTODECLINEBY2PERCENTADISTINCTIONISOFTENMADEAMONGVALUESOFEQ,PTHATARELESSTHAN,EQUALTO,ORGREATERTHANH110021SPECICALLY,THETERMINOLOGYUSEDISASSHOWNINTABLE71FORANELASTICCURVE,APRICEINCREASEISMETBYAMORETHANPROPORTIONATEQUANTITYDECREASEFORAUNITELASTICCURVE,THEPRICEINCREASEANDTHEQUANTITYDECREASEAREOFIDENTICALPROPORTIONALMAGNITUDESFORANINELASTICCURVE,PRICEINCREASESPROPORTIONALLYMORETHANQUANTITYDECREASESIFACURVEISELASTIC,PRICEAFFECTSQUANTITY“ALOT”IFACURVEISINELASTIC,PRICEDOESNOTHAVEASMUCHOFANEFFECTONQUANTITYDEMANDEDONEWAYTOCLASSIFYGOODSISBYTHEIRPRICEELASTICITIESOFDEMANDFOREXAMPLE,THEQUANTITYOFMEDICALSERVICESDEMANDEDISUNDOUBTEDLYVERYINELASTICTHEMARKETDEMANDCURVEMAYBEALMOSTVERTICALINTHISCASE,INDICATINGTHATTHEQUANTITYDEMANDEDISNOTRESPONSIVETOPRICEONTHEOTHERHAND,ITISLIKELYTHATPH5007QH11128QH5007H11128PPERCENTAGECHANGEINQH5007H5007H5007PERCENTAGECHANGEINPDEFINITIONCHAPTER7MARKETDEMANDANDELASTICITY1773SOMETIMESTHEELASTICITYOFDEMANDISDENEDASTHEABSOLUTEVALUEOFTHEDENITIONINEQUATION714CONSEQUENTLY,UNDERTHISALTERNATIVEDENITION,ELASTICITYISNEVERNEGATIVECURVESARECLASSIEDASELASTIC,UNITELASTIC,ORINELASTIC,DEPENDINGONWHETHERH20919EQ,PH20919ISGREATERTHAN,EQUALTO,ORLESSTHAN1YOUSHOULDRECOGNIZETHISDISTINCTIONINEXAMININGEMPIRICALWORK,BECAUSETHEREISNOCONSISTENTUSAGEINECONOMICLITERATURETERMINOLOGYFORADEMANDCURVETODISTINGUISHVALUESOFEQ,PTERMINOLOGYOFCURVEVALUEOFEQ,PATAPOINTATTHISPOINTEQ,PH11021H110021ELASTICEQ,PH11005H110021UNITELASTICEQ,PH11022H110021INELASTICTABLE71PRICECHANGESWILLHAVEAGREATEFFECTONTHEQUANTITYOFCANDYBOUGHTTHEDEMANDISELASTICHERETHEMARKETDEMANDCURVEWOULDBERELATIVELYATIFMARKETPRICEWERETOCHANGEEVENSLIGHTLY,THEQUANTITYDEMANDEDWOULDCHANGESIGNICANTLYPRICEELASTICITYANDTOTALEXPENDITURETHETOTALEXPENDITUREONANYGOODISTHEPRODUCTOFTHEPRICEOFTHEGOODPTIMESTHEQUANTITYCHOSENQBYUSINGTHECONCEPTOFPRICEELASTICITYOFDEMAND,ITISPOSSIBLETOEXAMINEHOWTOTALEXPENDITURECHANGESWHENTHEPRICEOFAGOODCHANGESBECAUSEQISITSELFAFUNCTIONOFP,DIFFERENTIATINGPQWITHRESPECTTOPYIELDSH11005QH11001PH11080715DIVIDINGBOTHSIDESBYQ,WEHAVEH110051H11001H11080H110051H11001EQ,P716BECAUSEQISPOSITIVE,THESIGNOFH11128PQ/H11128PWILLDEPENDONWHETHEREQ,PISGREATERTHANORLESSTHANH110021IFEQ,PH11022H110021,DEMANDISINELASTICANDTHEDERIVATIVEISPOSITIVEPRICEANDTOTALEXPENDITURESMOVEINTHESAMEDIRECTIONFOREXAMPLE,ANINCREASEINPRICEWOULDRAISETOTALEXPENDITURES,BECAUSEPWOULDRISEPROPORTIONALLYMORETHANQWOULDFALLTHATSITUATIONHASBEENOBSERVEDINTHEDEMANDFORAGRICULTURALPRODUCTSBECAUSETHEDEMANDFORFOODISPRICEINELASTIC,ANINCREASEINITSPRICE,PERHAPSDUETOBADWEATHER,ACTUALLYINCREASESTOTALEXPENDITURESONFOODONTHEOTHERHAND,IFEQ,PH11021H110021,PRICEANDTOTALEXPENDITURESWILLMOVEINOPPOSITEDIRECTIONSFOREXAMPLE,ANINCREASEINPRICEWILLREDUCETOTALEXPENDITURES,BECAUSEQUANTITYPURCHASEDWILLFALLPROPORTIONATELYMORETHANPRICERISESTABLE72WHICHISCONSTRUCTEDFROMEQUATION716SUMMARIZESTHESERESPONSESOFTOTALEXPENDITURETOACHANGEINPRICETHESERESULTSWILLBEUSEFULFOROUREXAMINATIONOFTHEBEHAVIOROFRMSINCOMEELASTICITYOFDEMANDANOTHERTYPEOFELASTICITYOFTENENCOUNTEREDINECONOMICSISTHEINCOMEELASTICITYOFDEMANDEQ,ITHISCONCEPTRECORDSTHERELATIONSHIPBETWEENINCOMECHANGESANDQUANTITYCHANGESANDISANOTHERAPPLICATIONOFTHEGENERALDENITIONGIVENINEQUATION713PH5007QH11128QH5007H11128PH11128PQ/H11128PH5007QH11128QH5007H11128PH11128PQPH5007H11128P178PARTIICHOICEANDDEMANDRESPONSESOFTOTALEXPENDITURETOPRICECHANGESRESPONSESOFPQPRICEPRICEDEMANDINCREASEDECREASEELASTICFALLSRISESUNITELASTICNOCHANGENOCHANGEINELASTICRISESFALLSTABLE72INCOMEELASTICITYOFDEMANDEQ,IEQ,IH11005H11005H11080717FORANORMALGOOD,EQ,IISPOSITIVEBECAUSEH11128Q/H11128IISPOSITIVEFORANINFERIORGOOD,ONTHEOTHERHAND,EQ,IISNEGATIVEAMONGNORMALGOODSTHEREISCONSIDERABLEINTERESTABOUTWHETHEREQ,IISGREATERTHANORLESSTHAN1GOODSFORWHICHEQ,IH110221MIGHTBECALLEDLUXURYGOODSINTHESENSETHATPURCHASESOFTHESEGOODSINCREASEMORERAPIDLYTHANINCOMEFOREXAMPLE,IFTHEINCOMEELASTICITYOFDEMANDFORAUTOMOBILESIS20,THENTHEIMPLICATIONISTHATA10PERCENTRISEININCOMEWILLLEADTOA20PERCENTINCREASEINAUTOMOBILEPURCHASESONTHEOTHERHAND,AGOODSUCHASFOODPROBABLYHASANINCOMEELASTICITYOFLESSTHAN1IFTHEINCOMEELASTICITYOFDEMANDFORFOODWERE05,THEIMPLICATIONISTHATA10PERCENTRISEININCOMEWOULDRESULTINONLYA5PERCENTINCREASEINFOODPURCHASES4THENALCONCEPTOFELASTICITYWEINTRODUCEINTHISCHAPTERMEASURESTHEREACTIONOFQUANTITYPURCHASEDQTOCHANGESINTHEPRICEOFSOMEOTHERGOODPH11032WEDENETHISCROSSPRICEELASTICITYOFDEMANDASFOLLOWSCROSSPRICEELASTICITYOFDEMANDEQ,PH11032EQ,PH11032H11005H11080718IFQANDTHEOTHERGOODAREGROSSSUBSTITUTES,H11128Q/H11128PH11032WILLBEPOSITIVE,ASWILLEQ,PH11032WHENTHEGOODSAREGROSSCOMPLEMENTS,H11128Q/H11128PH11032ANDEQ,PH11032WILLBENEGATIVERELATIONSHIPSAMONGELASTICITIESWEHAVEDEVELOPEDELASTICITYCONCEPTSASTHEYAPPLYTOTHEMARKETDEMANDFORAPRODUCTBECAUSETHESEPROVIDECONVENIENT,MEASURABLESUMMARIESOFTHERESPONSIVENESSOFQUANTITYDEMANDEDTOCHANGESINVARIOUSFACTORSBYTREATINGMARKETDEMANDASBEINGCOMPOSEDOFTHEDEMANDSOFMANY“TYPICAL”INDIVIDUALS,ITISPOSSIBLETODERIVESOMEIMPORTANTRELATIONSHIPSAMONGTHESEELASTICITIESFORTHISPURPOSE,SUPPOSETHATTHEREAREONLYTWOGOODSXANDYFORTHETYPICALINDIVIDUALPH11032H5007QH11128QH5007H11128PH11032DEFINITIONIH5007QH11128QH5007H11128IPERCENTAGECHANGEINQUANTITYH5007H5007H5007H5007PERCENTAGECHANGEININCOMEDEFINITIONCHAPTER7MARKETDEMANDANDELASTICITY1794INLIGHTOFOURPREVIOUSDISCUSSION,THESEDENITIONSOFINCOMEELASTICITYMIGHTBEGENERALIZEDTOINCLUDEPOSSIBLECHANGESINTHEDISTRIBUTIONOFINCOMEASWELLINPRACTICE,HOWEVER,THEDISTINCTIONISOFTENDISREGARDEDTOCHOOSEFROMINMAXIMIZINGUTILITYANDTHAT,ASBEFORE,THEBUDGETCONSTRAINTISGIVENBY5PXXH11001PYYH11005I719THETYPICALINDIVIDUALSDEMANDFUNCTIONSFORXANDYAREGIVENBYXH11005DXPX,PY,IYH11005DYPX,PY,I,720ANDTHESEDEMANDFUNCTIONSAREHOMOGENEOUSOFDEGREEZEROINALLPRICESANDINCOMEWESHALLNOWDERIVESOMERELATIONSHIPSAMONGTHEDEMANDELASTICITIESFORTHISTYPICALINDIVIDUALTHATCANTHENBETAKENTOHOLDFORTHEMARKETDEMANDFUNCTIONASAWHOLESUMOFINCOMEELASTICITIESFORALLGOODSDIFFERENTIATIONOFTHEBUDGETCONSTRAINTEQUATION719WITHRESPECTTOIYIELDSPXH11001PYH110051721OR,MULTIPLYINGEACHITEMBYACOMPLEXFORMOF1,H11080H11080H11001H11080H11080H110051722NOWPXH11080X/IISSIMPLYTHEPROPORTIONOFINCOMESPENTONGOODX,ANDPYH11080Y/IISASIMILAREXPRESSIONFORGOODYUSINGSXTODENOTETHEPROPORTIONOFINCOMESPENTONX,SYFORTHEPROPORTIONOFINCOMESPENTONY,ANDTHEDENITIONOFINCOMEELASTICITYOFDEMANDEQUATION717,W