1、Macroeconomics Chapter 71Consumption and SavingHousehold budget constraintlC+(1/P)B+K=/P+(w/P)L+i(B/P+K)l/P=0lC+(1/P)B+K=(w/P)L+i(B/P+K)lconsumption+real saving=real incomeMacroeconomics Chapter 72Consumption and SavingMacroeconomics Chapter 73Consumption and SavingConsumption Over Two YearslYear1C1
2、+(B1/P+K1)(B0/P+K0)=(w/P)1 L+i0 (B0/P+K0)consumption in year1+real saving in year1=real income in year1lYear2 C2+(B2/P+K2)(B1/P+K1)=(w/P)2 L+i1 (B1/P+K1)consumption in year 2+real saving in year 2=real income in year 2Macroeconomics Chapter 74Consumption and SavingConsumption Over Two YearslCombine
3、the budget constraints to describe a households choice between consuming this year,C1,and next year,C2.lB1/P+K1=B0/P+K0+i0(B0/P+K0)+(w/P)1L C1lReal assets end year1=real assets end year0+real income year1 consumption year1Macroeconomics Chapter 75Consumption and SavingMacroeconomics Chapter 76Consum
4、ption and SavingMacroeconomics Chapter 77Consumption and SavingConsumption Over Two YearslB1/P+K1=(1+i0)(B0/P+K0)+(w/P)1 L C1lB2/P+K2=(1+i1)(B1/P+K1)+(w/P)2 L C2lB2/P+K2=(1+i1)(1+i0)(B0/P+K0)+(w/P)1L C1 +(w/P)2 L C2Macroeconomics Chapter 78Consumption and SavingConsumption Over Two Years C2+(1+i1)C1
5、=(1+i1)(1+i0)(B0/P+K0)+(1+i1)(w/P)1L+(w/P)2L-(B2/P+K2)Two-year household budget constraint:C1+C2/(1+i1)=(1+i0)(B0/P+K0)+(w/P)1L+(w/P)2L/(1+i1)(B2/P+K2)/(1+i1)Macroeconomics Chapter 79Consumption and SavingPresent valuelIf the interest rate,i1,is greater than zero,$1 received or spent in year 1 is eq
6、uivalent to more than$1 in year 2.lDollars received or spent in year 2 must be discounted to make them comparable to dollars in year 1.lThe term 1+i1 is called a discount factor.Macroeconomics Chapter 710Consumption and SavinglHousehold chooses the time path of consumptionin this case,C1 and C2to ma
7、ximize utility,subject to the budget constraint.Macroeconomics Chapter 711Consumption and SavingChoosing consumption:income effectslC1+C2/(1+i1)=(1+i0)(B0/P+K0)+(w/P)1L+(w/P)2L/(1+i1)(B2/P+K2)/(1+i1)lp.v.of consumption=value of initial assets+p.v.of wage incomes p.v.of assets end year 2lV=(1+i0)(B0/
8、P+K0)+(w/P)1L+(w/P)2L/(1+i1)p.v.of sources of funds=value of initial assets+p.v.of wage incomesMacroeconomics Chapter 712Consumption and SavingChoosing consumption:income effectslC1+C2/(1+i1)=V (B2/P+K2)/(1+i1)lp.v.of consumption=p.v.of sources of funds p.v.of assets end year 2Macroeconomics Chapter
9、 713Consumption and SavingChoosing consumption:income effectslSuppose that V increases due to a rise in wage incomes.Since we are holding fixed the term(B2/P+K2)/(1+i1),the total present value of consumption,C1+C2/(1+i1),must rise by the same amount as V.lSince households like to consume at similar
10、levels in the two years,we predict that C1 and C2 will rise by similar amounts.These responses of consumption to increases in initial assets or wage incomes are called income effects.Macroeconomics Chapter 714Consumption and SavingChoosing consumption:the intertemporal-substitution effect.lC1+C2/(1+
11、i1)=V (B2/P+K2)/(1+i1)lp.v.of consumption=p.v.of sources of funds p.v.of assets end year 2Macroeconomics Chapter 715Consumption and SavingChoosing consumption:the intertemporal-substitution effect.lA higher i1 provides a greater reward for deferring consumption.Therefore,the household responds to an
12、 increase in i1 by lowering C1 and raising C2.lThis response is called the intertemporal-substitution effect.Macroeconomics Chapter 716Consumption and SavingChoosing consumption:the intertemporal-substitution effect.lC1+(B1/P+K1)(B0/P+K0)=(w/P)1L+i0(B0/P+K0)lConsumption in year1+real saving in year1
13、 =real income in year 1Macroeconomics Chapter 717Consumption and SavingChoosing consumption:the intertemporal-substitution effect.lWe know from the intertemporal-substitution effect that an increase in the interest rate,i1,motivates the household to postpone consumption,so that this years consumptio
14、n,C1,falls on the left-hand side.Macroeconomics Chapter 718Consumption and SavingChoosing consumption:the intertemporal-substitution effect.lSince year 1s real income is given,the decline in C1 must be matched by a rise in year1s real saving,(B1/P+K1)(B0/P+K0).lThe intertemporal-substitution effect
15、motivates the household to save more when the interest rate rises.Macroeconomics Chapter 719Consumption and SavingThe income effect from a change in the interest ratelC2+(B2/P+K2)(B1/P+K1)=(w/P)2 L+i1 (B1/P+K1)The income effect from i1li1(B1/P)li1K1Macroeconomics Chapter 720Consumption and SavingThe
16、 income effect from a change in the interest rateli1(B1/P)For a holder of bonds,the income effect from an increase in i1 is positive.For an issuer of bonds,the income effect from an increase in i1 is negative.For the economy as a whole,lending and borrowing must balancethe income effect from the ter
17、m i1(B1/P)is zero.Macroeconomics Chapter 721Consumption and SavingThe income effect from a change in the interest rateli1K1Average households holding of claims on capital,K1,is greater than zero.The term i1K1,the income effect from an increase in i1 is positive.Macroeconomics Chapter 722Consumption
18、and SavingThe income effect from a change in the interest ratelIn the aggregate,the income effect from an increase in i1 consists of a zero effect from the term i1(B1/P)and a positive effect from the term i1K1.lThe full income effect from an increase in i1 is positive.Macroeconomics Chapter 723Consu
19、mption and SavingCombining income and substitution effectslThe effect of an increase in the interest rate,i1,on year 1s consumption,C1The intertemporal substitution effect motivates the household to reduce C1.An increase in i1 also has a positive income effect,which motivates the household to raise
20、C1.The overall effect from an increase in i1 on C1 is ambiguous.Macroeconomics Chapter 724Consumption and SavingMacroeconomics Chapter 725Consumption and SavingConsumption Over Many YearslTwo-year budget constraintC1+C2/(1+i1)=(1+i0)(B0/P+K0)+(w/P)1 L +(w/P)2L/(1+i1)(B2/P+K2)/(1+i1)lRelax our simpli
21、fying assumption that the household could not change the present value of assets held at the end of year 2Macroeconomics Chapter 726Consumption and SavingConsumption and income in future years.overall present value of consumption =C1 +C2/(1+i1)+C3/(1+i1)(1+i2)+overall present value of wage incomes =
22、(w/P)1L +(w/P)2L/(1+i1)+(w/P)2L/(1+i1)(1+i2)+Macroeconomics Chapter 727Consumption and SavingMultiyear budget constraint:C1+C2/(1+i1)+C3/(1+i1)(1+i2)+=(1+i0)(B0/P+K0)+(w/P)1L +(w/P)2L/(1+i1)+(w/P)2L/(1+i1)(1+i2)+Macroeconomics Chapter 728Consumption and SavingMulti-Year budget constraint allows the
23、comparison of the effects of temporary and permanent changes in income.Macroeconomics Chapter 729Consumption and SavingTemporary change in incomeWe predict that the household would respond to a rise in(w/P)1 L by raising consumption by similar amounts in each year:C1,C2,C3,and so on.This response me
24、ans,however,that consumption in any particular year,such as year 1,cannot increase very much.Therefore,if(w/P)1 L rises by one unit,we predict that C1 increases by much less than one unit.To put it another way,the propensity to consume in year 1 out of an extra unit of year 1s income tends to be sma
25、ll when the extra income is temporary.Macroeconomics Chapter 730Consumption and Savingtemporary change in incomeIf(w/P)1L rises by one unit on the right-hand side,C1 rises by much less than one unit on the left-hand side.Year 1s real saving,(B1/P+K1)(B0/P+K0),must rise by nearly one unit on the left
26、-hand side.The propensity to save in year 1 out of an extra unit of year 1s income is nearly one when the extra income is temporary.Macroeconomics Chapter 731Consumption and SavingPermanent increase in wage income(w/P)1L,(w/P)2L,(w/P)3L,and so on each rise by one unit.It would be possible for the ho
27、usehold to respond by increasing consumption by one unit in each yearMacroeconomics Chapter 732Consumption and SavingPermanent increase in wage incomeThe prediction is that the propensity to consume out of an extra unit of year 1s income would be highclose to onewhen the extra income is permanent.Th
28、e propensity to save in year 1 out of an extra unit of year 1s income is small when the extra income is permanent.Macroeconomics Chapter 733Consumption and SavingConsumption Over Many YearslPermanent income.Consumption depends on a long-term average of incomeswhich he called permanent incomerather t
29、han current income.Macroeconomics Chapter 734Consumption,Saving,and Investment in EquilibriumDetermine the aggregate quantities of consumption and saving.Determine the aggregate quantity of investment.Macroeconomics Chapter 735Consumption,Saving,and Investment in EquilibriumBudget ConstraintlC+(1/P)
30、B+K=(w/P)L+i(B/P)+iKi=(R/P )lC+(1/P)B+K=(w/P)L+i(B/P)+(R/P)K KlB=0 and B=0Macroeconomics Chapter 736Consumption,Saving,and Investment in EquilibriumBudget ConstraintlC+K=(w/P)L+(R/P)K K(w/P)L+(R/P)K=Y(Real GDP).lC+K=Y KlConsumption+net investment =real GDP depreciation =real net domestic productMacr
31、oeconomics Chapter 737Consumption,Saving,and Investment in EquilibriumThe left-hand side of the equation implies that the economys net investment,K,is determined by households choices of consumption,C.Given the real net domestic product,one unit more of consumption,C,means one unit less of net inves
32、tment,K.This choice of C determines KMacroeconomics Chapter 738Multiyear budget constraint:C1+C2/(1+i1)+C3/(1+i1)(1+i2)+=(1+i0)(B0/P+K0)+(w/P)1L +(w/P)2L/(1+i1)+(w/P)2L/(1+i1)(1+i2)+Extra:Consumption and SavingTttstsTttstsYiACi11101111111Macroeconomics Chapter 739Extra:Consumption and Saving1.A simp
33、le case with zero interest rate:0,0,)(1uuCuUTtt Budget constraint:TttTttYAC101Lagrangian:TttTttTttCYACuL1101)(Macroeconomics Chapter 740FOC:Extra:Consumption and Saving)(tCutYATCTt101 Implication:1)Permanent income hypothesis The time pattern of income is not important to consumption,but to saving!2
34、)Saving is future consumptionMacroeconomics Chapter 741Extra:Consumption and Saving2.The constant interest rate and saving0,0,)(111uuCuUTtttBudget constraint:TtttTtttYrACr1011111TtttTtttTtttCrYrACuL11011111)(11Macroeconomics Chapter 742Extra:Consumption and SavingtttrCu11)(11trCuCutt111tRttttCuuRCuCuCCu 1)(111111rCCttExample:更多精品资请访问更多精品资请访问 更多品资源请访问更多品资源请访问
