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exam1solf01
Name
DavidsonCollegeMarkC.Foley
DepartmentofEconomicsFall2001
IntermediateMicroeconomicTheory
Review#1
SelectedSuggestedSolutions
SectionI:
MultipleChoice
Indicatethebestanswerinthespaceprovidedtotherightofeachquestion.
1.Ifbothsupplyanddemanddecreaseatthesametime,whichofthefollowingB
mustalsodecrease?
(a)theequilibriumprice
(b)theequilibriumquantity
(c)theuseofsubstitutes
(d)theuseofcomplements
(e)noneoftheabove
2.TheassumptionofnonsatiationsaysthatC
(a)toconsumemoreofonegood,wemustgiveupconsumptionofasecondgood.
(b)moreconsumptionwilldecreasetotalutility.
(c)moreofanythingisalwaysbetter.
(d)moreconsumptionwillnotleadtoachangeintotalutility.
(e)consumersreachapointwheretheycannotconsumemoreofanything.
3.Janeconsumesonlyxylophonesandyams.IfwegraphJane’sindifferenceD
curveswithxylophonesonthehorizontalaxisandyamsontheverticalaxis,
thenwhenevershehasmoreyamsthanxylophones,theslopeofherindifference
curvesare–2.Whenevershehasmorexylophonesthanyams,theslopeis–1/2.
Janewouldbeindifferentbetweenabundlewith24xylophonesand36yamsand
anotherbundlewith34xylophonesand
(a)28yams.
(b)32yams.
(c)22yams.
(d)25yams.
(e)26.50yams.
4.Whichofthefollowingstatementsaboutdemand-elasticityiscorrect?
E
(a)ifdemandisprice-inelastic,anincreaseinpricewilllowertotalexpenditures.
(b)ifdemandisprice-elastic,anincreaseinpricewillincreasetotalexpenditures.
(c)ifdemandisprice-elastic,anincreaseinpricewillleavetotalexpendituresunchanged.
(d)Ifdemandisunit-elastic,adecreaseinpricewilldecreasetotalexpenditures.
(e)ifdemandisprice-inelastic,adecreaseinpricewilldecreasetotalexpenditures.
5.AnindividualconsidersgoodsXandYtobeperfectcomplements.Thus,D
(a)theHicksiandemandcurveforXissteeperthantheMarshalliandemandcurve.
(b)theMarshalliandemandcurveforXissteeperthantheHicksiandemandcurve.
(c)theMarshallianandHicksiandemandcurvesarecoincident.
(d)theHicksiandemandcurveisvertical.
(e)Noneoftheabove.
SincetheHicksiandemandcurveindicatesonlysubstitutioneffectsandtherearenosubstitutioneffectsforperfectcomplements,theHicksiandemandcurveisverticalinthisspecialcase.
6.Inthegraphbelow,theshockisadecreaseinthepriceofyams.E
(a)YamsareanormalgoodandsubstitutesforXeroxes.
(b)YamsareaninferiorgoodandsubstitutesforXeroxes.
(c)YamsareaGiffengood.
(d)YamsareanormalgoodandcomplementsforXeroxes.
(e)YamsareaninferiorgoodandcomplementsforXeroxes.
Labeltheinitial,intermediate,andfinalpoints“A”,“B”,and“C”,respectively.
ThemovefromBtoCrepresentstheincomeeffect.Therefore,sinceYB>YC,yamsareinferior–consumptionofyamsfellwhenincome(purchasingpower)rose.Theansweriseither(b)or(e).Thequestionbecomes,areyamsandXeroxessubstitutesorcomplements?
BecausethedemandforXeroxesincreased(XC>XA)whenthepriceofyamsdecreased,theyarecomplements.Answer=(e).
7.ForaCobb-Douglasutilityfunction,
D
(a)preferencesarehomothetic.
(b)theshareofincomespentongoodYisunrelatedtothepriceofgoodX.
(c)theincome-consumptioncurveislinear.
(d)(a),(b),&(c)aretrue
(e)only(a)&(b)aretrue
WehaveshownthatC-Dpreferencesarehomothetic.WehaveshownthatexpendituresharesareconstantforC-Dpreferences.(a)&(b)aretrue.
For(c),X*=I/PX,andifIincreasesbyt%,thensodoesX*.Inotherwords,ifanICistangenttothebudgetlineat(x1,y1),thentheICwhichpassesthrough(tx1,ty1)willbetangenttothe“tI”budgetline.Thatisthedefinitionofanincome-consumptioncurve.
8.If,atagivenconsumptionbundleonthebudgetline,themarginalutilityC
ofyamsistwicethemarginalutilityofxylophones,andthepriceofyamsis
one-thirdthepriceofxylophones,theutility-maximizingconsumershould
(a)makenochangeinherconsumptionbundle.
(b)consumemorexylophonesandfeweryams.
(c)consumemoreyamsandfewerxylophones.
(d)consumemoreyamsandthesamenumberofxylophones.
(e)Noneoftheabove.
WearetoldthatMUY=2MUXandPY=1/3PX.Weknowthatattheoptimalconsumptionbundle,
musthold.Substituting,wefind
whichimpliesthattheMRSislessthantheslopeofthebudgetline(inabsolutevalue),orequivalently,theMUperdollarspentonYisgreaterthantheMUperdollarspentonX.Therefore,theoptimalconsumptionbundlewillcontainfewerxylophonesandmoreyamsthanthecurrentbundle.
9.If,whenincomedoubles,thepricesoftwogoods,XandY,increaseby50%C
and100%respectively,theconsumer’sbudgetlinewill
(a)remainthesame.
(b)shiftoutfromtheorigin,withitsslopeunchanged.
(c)becomeflatter.
(d)becomesteeper.
(e)Noneoftheabove.
y-interceptx-interceptslope
Old:
I/PYI/PX-PX/PY
New:
2I/2PY=I/PYsame!
2I/1.5PXgreater!
-3PX/4PYflatter!
Thebudgetsetbecomeslargersinceincomerisesfasterthantheprices,2I/1.5PY>I/PY.
10.ThecompensateddemandfunctioniswhereB
(a)relativepricesareheldconstant.
(b)theconsumer’sincomeisadjustedforpricechangesinordertokeeputilityconstant.
(c)thesubstitutioneffectisoffsetbytheincomeeffect.
(d)relativepriceisadjustedforchangesinaconsumer’sincomeinordertokeeppurchasingpowerconstant.
(e)theconsumer’sindifferencecurvesareadjustedforchangesinpricesinordertokeepconsumerincomeconstant.
11.Whenanearmarkedgrantof$HisgiventoconsumerswhohaveanA
initialinterioroptimum,
(a)privatespendingonthesubsidizedgooddecreases.
(b)everyconsumerisstrictlyworseoffthaniftheyhadreceivedanequalcashgrant.
(c)theywillpurchaseanadditional$Hofthesubsidizedgood.
(d)consumptionofallothergoodswilldecrease.
(e)Noneoftheabove.
12.AlongaMarshalliandemandcurveforagivengood,A
(a)theconsumer’sutilityisincreasingasquantityofthegoodincreases.
(b)theheightofthedemandateachquantitylevelequalsthemarginalcostbenefitofthegood.
(c)thepricesofothergoodsarenotconstant.
(d)thequantitiespurchasedofothergoodsarenotconstant.
(e)theconsumer’sutilitydoesnotchangeasquantityofthegoodincreases.
13.Whichstatementbelowistrue?
C
(a)Someinferiorgoodsare(normals/bsuperior)goods.
(b)SomeGiffengoodsareinferiorgoods,butallinferiorgoodsareGiffengoods.
(c)AllGiffengoodsareinferiorgoods,butallinferiorgoodsarenotGiffengoods.
PoorEnglishhere,mybad,thisisfalseaswrittenbecause,whilethefirstclauseistrue,thesecondisnot.“Allinferiorgoodsare[notGiffen]goods”isfalsesincesomeinferiorgoodsareofcoursenon-Giffen.…rewritetosay
AllGiffengoodsareinferiorgoods,butsomeinferiorgoodsarenotGiffengoods.
(d)Some(normals/bsuperior)goodsareinferiorgoods.
(e)Noneoftheabove.
14.AcompletelyverticaldemandcurvewouldrepresentwhichtypeofelasticityB
ofdemand?
(a)perfectlyelastic
(b)perfectlyinelastic
(c)unit-elastic
(d)highly-elastic
(e)needmoreinformation.
15.Inusingexperimentationtoestimatethecross-priceelasticityofdemandD
foradoublecheeseburgerwithrespecttothepriceofBiggie®fries,Wendy’s
facestheproblemof:
(a)generalizabilityoftheestimate
(b)holdingthecustomers’incomeconstant
(c)holdingMcDonald’sandBurgerKing’spricesconstant
(d)alloftheabove
(e)noneoftheabove
SectionII:
ProblemsDothese2questions(Nochoice).
1.Considerthefollowingutilityfunction:
.
(a)Arethepreferencesrepresentedbythisutilityfunctionhomothetic?
Whyorwhynot?
Homotheticutilityfunctionshaveamarginalrateofsubstitutionwhichdependsonlyontheratioofthequantitiesofthetwogoods,nottheabsolutetotalamounts.Thisisusefulsinceindifferencecurvesofhigherutilityaresimplycopiesofthoseatlowerutilitylevels,thusresultsobtainedbyfocusingone(orafew)indifferencecurvewilllikelynotdiffergreatlyifadifferentindifferencecurve(orrangeofcurves)wasstudied.Homotheticpreferenceshavedrawbackshowever.Theincome-consumptioncurvesareallstraightlinesthroughtheorigin.Thatis,whenincomeisincreased(ordecreased)bys%,theoptimalconsumptionbundleincreases(ordecreases)bys%.
WhatistheMRS?
whichisnotafunctionoftheratioofXtoY
isnothomothetic.
(b)UsingtheLagrangianmethodofoptimization,derivetheuncompensated(Marshallian)demandfunctionsforXandY.Let
representtheindividual’sincome,
thepriceofgoodX,and
thepriceofgoodY.Explainintuitivelywhatthefirstorderconditionsmean.
Thefirstorderconditions(F.O.C.)arenecessaryconditionsformaximizingutility.Theyarenotsufficienttoensureutilitymaximization.SatisfactionoftheF.O.C.’sidentifiesapotentialoptimalconsumptionbundle.Intuitively,ifoneofthepartialderivativeswerenotequaltozero(moreorlessthanzero),thenutilitycouldstillbeincreasedbyincreasing(ordecreasing)theamountofXandY.
Combining&yields,
Substitutingintoandsolvingfor
yields:
(c)ShowthatincreasesinthepriceofgoodYwillnotaffectthequantityofgoodXthattheconsumerbuys,butthatincreasesinthepriceofgoodXwillaffectthequantityofgoodYthattheconsumerbuys.
(d)Iftheconsumer’s
=$11,
=$1,
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