Problem Set 2 Answers - Marc Teignier

1 ProblemSet2 AnswersIntermediateMicro economics(22014)Group13-Fall2011 DueonWednesday,9/28 (c1,c2) = (c1)1/2(c2)1/2wherec1denotestheamountcon sumedinp erio d1andc2theamountconsumedinp erio osethatp erio d1incomeexpressedinunitsofgo o d1ism1= 20000andp erio d2incomeexpressedinunitsofgo o d2ism2= osealsothatp1=p2= or-rower?Answer:c 1= ,c 2= 'sequationandagraphtoexplainwhatwouldhap p :c1increasesb ecauseofb oththeincomeandthesubstitutione ,andletp1=p2= 1andr= osetheconsumerisaskedtocho oseb etweentwobundles,(c1,c2) = (25,16)and(c1,c2) = (9,36).Whichonewouldshecho ose?Answer:The rstone,b ecauseu(25,16) = 20>18 =u(9,36). osenowsheisaskedtocho oseb etweentheincomevectors(m1,m2) = (25,16)and(m1,m2) = (9,36).Whichonewouldshecho ose?

2 Answer:Theso condone,b ecauseithashigherpresentvalue:25 +161+ <39 =9 +361+ ,whatwouldtheoptimalintertemp oralconsumptionbundle?Answer:c 1= ,c 2= ationConsideragainoncemoreourconsumerfromexercise1,andsupp osethat(m1,m2) =(110,100),p1= 1,andr= ationratesthatmakeherb easaverandwhataretheonesthatmakeherb eab orrower?Answer:If < ,saver;if > ,b (m1,m2) = (5000,4200).Iftheinterestrateisequalto5% ,whatisthepresentvalueoftheincomestream? Whatishighestp ossibleconsumptionlevelinthesecondp erio :PV(m1,m2) = 5000 +42001+ ;cmax2= 5000 (1 + ) + 4200 = ossibilityofinvestinganamounttinp erio d1inafundthatgivesanamountsinp erio ositive,whatwouldb ethesmallestssothatitisoptimalforthecons umertoacceptthatinvestment?Answer:s=t(1 +r).

3 100ands= 115,whatisthehighestinterestrateatwhicht heindividualiswillingtoinvestinthatfund? Answer:r=st 1 = ,whocansaveattheinterestrater >0andb orrowattheinterestrateR > (atree,forinstance)thatgives121eurosatth eendofnextp erio dayforthatasset?Answer:1211+ +121(1+ )2= ectsofpensionsConsideranindividualwhoisa livefortwop erio dsandhasanincomestream(m1,m2).Atsomep ointthegovernmentdecidestointerveneinthe economy:inthe rstp erio dtheindividualhastopayafraction0 1ofitsincomeastaxes,andinthesecondp erio dhereceivesatransferequaltoqasp eforeandafterthegovernmentintervention?A nswer:q= m1(1 +r). ndthee erentiatethecasewhentheindividualisiniti allyasaverandthecasewhentheindividualisi nitiallyab :Ifinitiallyb orrower,nowstillb orrower;ifinitiallysaver, ectsofaninterestratefal lShowgraphicallythee ectsofadeclineintheinterestrateonthecons umptioninthe rstandsecondp erio