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1、巴罗宏观经济学：现代观点第巴罗宏观经济学：现代观点第7章章Consumption 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 income2Macroeconomics Chapter 7Consumption and SavingConsumption Over Two Years C2+(1+i1) C1 = (1+i1)(1+i0)(B
2、0/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)9Macroeconomics Chapter 7Consumption and SavingPresent valuelIf the interest rate, i1, is greater than zero, $1 received or spent in year 1 is eq
3、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.10Macroeconomics Chapter 7Consumption and SavinglHousehold chooses the time path of consumptionin this case, C1 and C2to
4、 maximize utility, subject to the budget constraint.11Macroeconomics Chapter 7Consumption 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
5、year 2lV = (1 + i0)(B0/P+K0) + (w/P)1L + (w/P)2L/(1+i1) p.v. of sources of funds = value of initial assets + p.v. of wage incomes12Macroeconomics Chapter 7Consumption 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
6、. of assets end year 213Macroeconomics Chapter 7Consumption 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 a
7、mount as V. lSince households like to consume at similar 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.14Macroeconomics Chapter 7Consumption and SavingChoosing c
8、onsumption: the intertemporal-substitution effect.lC1 + 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 215Macroeconomics Chapter 7Consumption and SavingChoosing consumption: the intertemporal-substitution effect.lA higher i1 provides a greater r
9、eward for deferring consumption. Therefore, the household responds to an increase in i1 by lowering C1 and raising C2.lThis response is called the intertemporal-substitution effect.16Macroeconomics Chapter 7Consumption and SavingChoosing consumption: the intertemporal-substitution effect.lC1 + (B1/P
10、 + K1) ( B0/P+K0) = (w/P)1L + i0(B0/P +K0)lConsumption in year1 + real saving in year1 = real income in year 117Macroeconomics Chapter 7Consumption and SavingChoosing consumption: the intertemporal-substitution effect.lWe know from the intertemporal-substitution effect that an increase in the intere
11、st rate, i1, motivates the household to postpone consumption, so that this years consumption, C1, falls on the left-hand side. 18Macroeconomics Chapter 7Consumption and SavingChoosing consumption: the intertemporal-substitution effect.lSince year 1s real income is given, the decline in C1 must be ma
12、tched by a rise in year1s real saving, (B1/P + K1) (B0/P + K0).lThe intertemporal-substitution effect motivates the household to save more when the interest rate rises.19Macroeconomics Chapter 7Consumption and SavingThe income effect from a change in the interest ratelC2 + ( B2/ P + K2) ( B1/ P + K1
13、) = ( w/ P) 2 L + i1 ( B1/ P + K1)The income effect from i1li1(B1/P)li1K120Macroeconomics Chapter 7Consumption and SavingThe 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
14、from an increase in i1 is negative.For the economy as a whole, lending and borrowing must balancethe income effect from the term i1(B1/P) is zero.21Macroeconomics Chapter 7Consumption and SavingThe income effect from a change in the interest rateli1K1Average households holding of claims on capital,
15、K1, is greater than zero.The term i1K1, the income effect from an increase in i1 is positive.22Macroeconomics Chapter 7Consumption 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
16、) and a positive effect from the term i1K1.lThe full income effect from an increase in i1 is positive.23Macroeconomics Chapter 7Consumption and SavingCombining income and substitution effectslThe effect of an increase in the interest rate, i1, on year 1s consumption, C1The intertemporal substitution
17、 effect motivates the household to reduce C1. An increase in i1 also has a positive income effect, which motivates the household to raise C1. The overall effect from an increase in i1 on C1 is ambiguous.24Macroeconomics Chapter 7Consumption and Saving25Macroeconomics Chapter 7Consumption and SavingC
18、onsumption 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 simplifying assumption that the household could not change the present value of assets held at the end of year 226Macroeconomics Chapter 7Consumption and Sav
19、ingConsumption 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 = (w/P)1L + (w/ P)2L/(1+ i1) + (w/P)2L/(1+i1)(1+i2) + 27Macroeconomics Chapter 7Consumption and SavingMultiyear budget constraint: C1 + C2/(
20、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) + 28Macroeconomics Chapter 7Consumption and SavingMulti-Year budget constraint allows the comparison of the effects of temporary and permanent changes in income.29Macroeconomics Chapter 7Consumption and
21、 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 means, however, that consumption in any particular year, such as year 1, cannot increase very much. Therefor
22、e, 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 small when the extra income is temporary.30Macroeconomics Chapter 7Consumption and Savingtemporary
23、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-hand side.The propensity to save in year 1 out of an extra unit of year 1s income is n
24、early one when the extra income is temporary.31Macroeconomics Chapter 7Consumption 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 household to respond by increasing consumption by one unit in each year32Macroeconomic
25、s Chapter 7Consumption 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.The propensity to save in year 1 out of an extra unit of year 1s income is small when
26、the extra income is permanent.33Macroeconomics Chapter 7Consumption and SavingConsumption Over Many YearslPermanent income.Consumption depends on a long-term average of incomeswhich he called permanent incomerather than current income.34Macroeconomics Chapter 7Consumption, Saving, and Investment in
27、EquilibriumDetermine the aggregate quantities of consumption and saving.Determine the aggregate quantity of investment.35Macroeconomics Chapter 7Consumption, Saving, and Investment in EquilibriumBudget ConstraintlC + (1/P)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
28、 KlB = 0 and B = 036Macroeconomics Chapter 7Consumption, 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 product37Macroeconomics Chapter 7Consumption, S
29、aving, 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 investment, K.This choice of C d
30、etermines K38Macroeconomics Chapter 7Multiyear 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:ConsumptionandSaving39Macroeconomics Chapter 7Extra:ConsumptionandSaving1. A simple case with zero interest rate: Budge
31、t constraint: Lagrangian: 40Macroeconomics Chapter 7FOC: Extra:ConsumptionandSaving Implication: 1) Permanent income hypothesis The time pattern of income is not important to consumption, but to saving! 2) Saving is future consumption41Macroeconomics Chapter 7Extra:ConsumptionandSaving2. The constant interest rate and savingBudget constraint: 42Macroeconomics Chapter 7Extra:ConsumptionandSavingExample: 43Macroeconomics Chapter 7结束语结束语谢谢大家聆听！谢谢大家聆听！44
