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1、CentralUniversityofFinanceandEconomicsSchoolofEconomicsIntermediateMicroeconomics,Spring2011Homework2（DueDate:Wednesday,March23,2011）1.(16points)Inthisproblemwereviewyourknowledgeofcalculus.a)FilloutthefollowingtableU(x1,x2)MRS(x1,x2)MRS(2,3)1/32/3U=x1x23U
2、=x1x2U=lnx1+3lnx23b)ConsiderutilityfunctionU=x1x2.InterpretthevalueoftheMRSat(2,3)(seelastcolumnofthetableina).Isgood1moreorless“valuable”thangood2?Howmuch(approximately)ofgood2wouldyouhavetogivetoaconsumer,aftertakingaway0.0001ofgood1,tokeephimindifferent
3、?αβc)Knowingthatln(x)isastrictlyincreasefunctionandthatln(xy)=αlnx+βlny,explainwhytheMRSoffunctionsinthelasttworowsinthetablecoincide.2.(9points)Georgeisastamp(x1)collector,buthealsolikesfancyclothes(x2).Hisutilityfunctionisgivenby2U(x1,x2)=x1+10x2-0.5x2Ea
4、chstampcostsp1=1andapieceofhisfavoriteclothingcostsp2=3.a)Assumingthathistotalincomeisgivenbym=$15,findhisoptimalchoiceofx1andx2.Isitinterior?b)SupposenextyearGeorge’ssalarydoubles,resultinginhishigherincomem=$30.Findhisnewdemandedquantitiesofstampsandclot
5、hes.Isitinterior?c)Inpointa)andb)whatisthemarginalutilityfromonedollarinvestedinstamps,andinclothing(attheoptimaldemand).Aretheyequal?3.(14points)Timconsumestwogoods,xandy,whosepricesarerespectivelypxandpy.HisincomeisI.Tim’sutilityfunctioncanberepresenteda
6、s:0.60.4U=xya)IfTimgivesuponeunitofgoody,howmuchmoreofgoodxmustheconsumetoholdhisutilityconstant?Explain.b)DeriveexpressionsforTim’sdemandforeachofthegoodsintermsofpricesandincome.c)IfTim’sincomeequals$200,px=4andpy=2,howmuchxandywillheconsume?d)WhatisTim’
7、smarginalutilityofincome?Explainwhatitmeansintuitively,andsolveforthenumber.e)Showthattheutilityfunctiongivenby:U=0.6lnx+0.4lnyresultsinthesamedemandfunctionasinpartb).f)Isgoodynormalorinferior?Explain,usinganEngelcurveinyourexplanation.4.(15points)Asinthe
8、previousproblem,Benjamin’spreferencesarenowdescribedbyU(x1,x2)=4lnx1+lnx2Histotalincomeism=$100,thepriceofMP3isonedollar(pereachsong)(p2=$1).Supposethatthepriceofamoviedropsfromp1=$10top1=$5.a)Byhowmuchthe“co
