lecture6.ppt

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1、IntermediateMicroeconomics,Economics4011Lecture6:IntertemporalChoice10IntertemporalChoiceIntertemporalChoicePersonsoftenreceiveincomein“lumps”;e.g.monthlysalary.Howisalumpofincomespreadoverthefollowingmonth(savingnowforconsumptionlater)?Orhowisconsumptionfinancedb

2、yborrowingnowagainstincometobereceivedattheendofthemonth?PresentandFutureValuesBeginwithsomesimplefinancialarithmetic.Takejusttwoperiods;1and2.Letrdenotetheinterestrateperperiod.FutureValueE.g.,ifr=0.1then$100savedatthestartofperiod1becomes$110atthestartofperiod2.

3、Thevaluenextperiodof$1savednowisthefuturevalueofthatdollar.FutureValueGivenaninterestraterthefuturevalueoneperiodfromnowof$1isGivenaninterestraterthefuturevalueoneperiodfromnowof$misPresentValueSupposeyoucanpaynowtoobtain$1atthestartofnextperiod.Whatisthemostyoush

4、ouldpay?$1?No.Ifyoukeptyour$1nowandsaveditthenatthestartofnextperiodyouwouldhave$(1+r)>$1,sopaying$1nowfor$1nextperiodisabaddeal.PresentValueQ:Howmuchmoneywouldhavetobesavednow,inthepresent,toobtain$1atthestartofthenextperiod?A:$msavednowbecomes$m(1+r)atthestartof

5、nextperiod,sowewantthevalueofmforwhichm(1+r)=1Thatis,m=1/(1+r),thepresent-valueof$1obtainedatthestartofnextperiod.PresentValueThepresentvalueof$1availableatthestartofthenextperiodisAndthepresentvalueof$mavailableatthestartofthenextperiodisPresentValueE.g.,ifr=0

6、.1thenthemostyoushouldpaynowfor$1availablenextperiodisAndifr=0.2thenthemostyoushouldpaynowfor$1availablenextperiodisTheIntertemporalChoiceProblemLetm1andm2beincomesreceivedinperiods1and2.Letc1andc2beconsumptionsinperiods1and2.Letp1andp2bethepricesofconsumptioninpe

7、riods1and2.TheIntertemporalChoiceProblemTheintertemporalchoiceproblem:Givenincomesm1andm2,andgivenconsumptionpricesp1andp2,whatisthemostpreferredintertemporalconsumptionbundle(c1,c2)?Forananswerweneedtoknow:theintertemporalbudgetconstraintintertemporalconsumptionp

8、references.TheIntertemporalBudgetConstraintTostart,let’signorepriceeffectsbysupposingthatp1=p2=$1.TheIntertemporalBudgetConstraintSupposethattheconsum