中级微观经济学 econ301_lab+answers

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1、Question1.Peter’sutilityforSmarties(x1)andSnickers(x2)isgivenby0.30.7U(x1,x2)=x1x2.1.IfSmartiescostp1dollarsarollandSnickerscostp2dollarsperbar,howshouldPeterspendhisincomeofmdollars?(Hint:ForCobb-Douglaspreferencesx⇤(p,p,m)=amand112a+bp1x⇤(p,p,m)=bm).212a+bp22.Assume

2、thatp1=2andp2=1.HowmuchSmartiesandSnickerswillPeterbuywithhisincomeof$100?(Denotethesequantitiesasx0andx0)123.Assumenowthatp1=1andp2=1.HowmuchSmartiesandSnickerswillPeterbuywithhisincomeof$100?(Denotethisamountasx00)WhatisthetotalchangeinthedemandforSmarties?14.Howmuc

3、hmoneyisneededtobuytheinitialbundlewiththenewprices?Denotethisamountasm0.5.WhatisthedemandforSmartieswithm0andthenewprices?Denotethisamountasx0.16.Decomposethetotalchangeinthedemandforsmartiesbetweenincomeandsubstitutioneffect.7.Graphyourresultsfromparts(2)to(6).Answe

4、r:1.Usingthehint,x⇤(p,p,m)=0.3mandx⇤(p,p,m)=0.7m.112p1212p22.Pluggingthevaluesofm,pandpintox⇤(p,p,m)andx⇤(p,p,m),wehavethatx0=15121122121andx0=70.23.Pluggingthenewvaluesofm,pandpintox⇤(p,p,m)andx⇤(p,p,m),wehavethatx00=30121122121andx00=70.Thetotalchangeinthedemandfors

5、martiesisx00x0=15.2114.m0=1⇥x0+1⇥x0=15+70=85.125.Pluggingthevalueofm0andthenewpricespandpintox⇤(p,p,m)andx⇤(p,p,m),we12112212havethatx0=25.5andx0=59.5.126.Thesubstitutioneffectinthiscaseisx0x0=10.5,andtheincomeeffectisx00x0=4.5.Note1111thatthetotaleffectisequaltoth

6、esumofthesubstitutionandincomeeffects.7.AgraphwithasummaryoftheresultsispresentedinFigure1.Question2.DavidN.gets$3perweekasanallowancetospendanywayhepleases.Becausehelikesonlypeanutbutterandjellysandwiches,hespendstheentireamountonpeanutbutter(at$0.05perounce)andjelly

7、(at$0.10perounce).Breadisprovidedfreeofchargebyaconcernedneighbor.Davidisaparticulareaterandmakeshissandwicheswithexactly1ounceofjellyand2ouncesofpeanutbutter.Heissetinhiswaysandwillneverchangetheseproportions.1.Howmuchpeanutbutter(b)andjelly(j)willDavidbuywithhis$3al

8、lowanceinaweek?2.Supposethepriceofjellyweretoriseto$0.15anounce.Howmuchofeachcommoditywouldbebought?13.Howmuchmoneyisneededt