DerivingtheDividendDiscountModelintheIntermediate跨期消費(fèi)模型研究不同時(shí)間人們的消費(fèi)行為，涉及時(shí)間因素的的消費(fèi)和儲(chǔ)蓄。即消費(fèi)者不必將每期的收入用光，他可以選擇儲(chǔ)蓄，也可以選擇貸款。其預(yù)算約束線的斜率與利率有關(guān)，為-(1+R)，R是利率，然后再此預(yù)算約束現(xiàn)的情況下研究消費(fèi)者偏好。分析的結(jié)果一般為：利率提高，人們選擇少消費(fèi)，更傾向于儲(chǔ)蓄，利率降低，人們會(huì)多消費(fèi)，傾向于借貸。那它的方程是什么樣子的？假設(shè)只有兩期,C是消費(fèi)，M是收入：C2=M2+(1+R)(m1-c1)1，2都是角標(biāo)。weemployedastandard

two-periodmodelwithconsumersmaximizingutility

U(C1,C2).Income(I)inbothperiods

isknown,thepriceofaunitof

consumption(C)inbothperiodsisequaltoone,andtheindividual

canborroworlendatthesamerisk-freeinterestrate(rf).Themaximizingagenthastwobudgetconstraintsoverthetwoperiods.Inthefirstperiod,

I1=C1+BwhereBisthedollarvalueofthebondspurchased.Inthesecondperiod,

I2+(1+rf)B=C2Fromthefirstbudgetconstraint,B=I1?C1andsubstitutingthatintothesecondbudget

constraint,thisgivestheequationforthebudgetconstraintlineas

C2=I2+(1+rf)(I1?C1)Theequilibriumconditionisthenstraightforwardtoderiveasfollows:Themarginalrateofsubstitution(MRS)isthetradeoffofcurrentconsumptionforfuture

consumptionthatleavestheindividualindifferent;putdifferently,theminimumamountnecessary

toreceiveinthefuturetogiveupaunitofconsumptiontoday.Aslongasthereturn(1+rf)isgreater

thantheMRSofcurrentandfutureconsumption,theindividualwillpostponeconsumptionand

increasehisutility.Theindividualwillcontinuegivingupcurrentconsumptionpreciselytothe

pointwherethereturnofthebondisjustsufficienttocompensatehimforwaiting.Theimportant

aspectistheconceptofdiminishingMRS,thatwitheachadditionalunitofpostponedcurrent

consumptiontheindividualrequiresahigherreturn(slopeofindifferencecurvegetssteeperas

onemovesfromrighttoleft).Ina

financeclass,thestudenttypicallylearnsthenetpresentvalue(NPV)criteriaforinvestment

projectsasevaluatingallprojects,rankedfromhighesttolowestrateofreturn(ROR),againstthe

opportunitycostofcapital,whichisassumedtobeconstant.Todirectlycomparetheintertemporal

consumptionmodeltoconceptsinfinancerequiresconsiderationofastandardconcaveinvestment

opportunitysetthatranksinvestmentprojectsfromrighttoleftbyhighesttolowestratesofreturn.Theslopeoftheinvestmentopportunitysetis1plustheRORofaproject.Investmentisviewed

asforegonecurrentconsumption.Assuch,thecostofcapitalistheslopeoftheindifference

curve.Thisisshowninfigure2.Theindividualwill

continuetoinvestaslongastheproject’sRORisgreaterthantheMRS(costofcapital);in

otherwords,NPV>0.UtilityismaximizedwhentheRORisjustequaltotheMRS,where

NPV=0.Inthismodel,profitmaximizationisthesameasutilitymaximization,andzero

economicprofit(NPV=0)iswherethereturnofaprojectisjustequaltothevalueofforegone

current

consumption.thetwo-periodmodelhastwoconstraintsthatarecombinedintoonetorepresentthegraph’s

budgetconstraintline.Theconstraintforperiod1is

I1=C1+P1N(whereNisthenumberofsharesofastockandP1isthepriceofashare.)Thebudgetconstraint

forperiod2is

I2+(d2+P2)N=C2(whered2istheper-sharedividendandP2isthepriceofthesh