# Macroeconomics Chapter 71 Consumption, Saving and Investment Chapter 7

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Consumption, Saving and Investment

Chapter 7

Macroeconomics Chapter 7

Consumption and SavingHousehold budget constraintC + (1/P) B+ K = /P + ( w/P )L + i( B/P + K) /P = 0C+(1/P)B+K=(w/P)L+i(B/P+K)consumption+ real saving = real income

Macroeconomics Chapter 7

Consumption and Saving

Macroeconomics Chapter 7

Consumption and SavingConsumption Over Two YearsYear1C1 + ( B1/ P + K1) ( B0/ P + K0) = ( w/P)1 L + i0 ( B0/ P + K0)consumption in year1 + real saving in year1 = real income in year1Year2 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 2

Macroeconomics Chapter 7

Consumption and SavingConsumption Over Two YearsCombine the budget constraints to describe a households choice between consuming this year, C1, and next year, C2.B1/P + K1 = B0/P + K0 + i0(B0/P + K0) + ( w/P)1L C1

Real assets end year1 = real assets end year0 + real income year1 consumption year1

Macroeconomics Chapter 7

Consumption and Saving

Macroeconomics Chapter 7

Consumption and Saving

Macroeconomics Chapter 7

Consumption and SavingConsumption Over Two YearsB1/P + K1 = (1+i0) (B0/P + K0) + (w/P)1 L C1B2/P + K2 = (1+ i1) (B1/P + K1) + (w/P)2 L C2B2/P + K2 = (1+i1) [(1+i0)( B0/P + K0) + (w/P)1L C1] + (w/P)2 L C2

Macroeconomics Chapter 7

Consumption and SavingConsumption Over Two Years C2+(1+i1) C1 = (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 7

Consumption and SavingPresent valueIf the interest rate, i1, is greater than zero, $1 received or spent in year 1 is equivalent to more than $1 in year 2. Dollars received or spent in year 2 must be discounted to make them comparable to dollars in year 1.The term 1+i1 is called a discount factor.

Macroeconomics Chapter 7

Consumption and SavingHousehold chooses the time path of consumptionin this case, C1 and C2to maximize utility, subject to the budget constraint.

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: income effectsC1 + C2/(1+i1) = (1+ i0)(B0/P+K0) + (w/P)1L+(w/P)2L/(1+i1)(B2/P+K2)/(1+i1)

p.v. of consumption = value of initial assets + p.v. of wage incomes p.v. of assets end year 2

V = (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 incomes

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: income effectsC1 + C2/(1+i1) = V (B2/P+K2)/(1+i1)p.v. of consumption = p.v. of sources of funds p.v. of assets end year 2

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: income effectsSuppose 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.

Since 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.

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: the intertemporal-substitution effect.

C1 + C2/(1+i1) = V (B2/P+K2)/(1+i1)p.v. of consumption = p.v. of sources of funds p.v. of assets end year 2

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: the intertemporal-substitution effect.A higher i1 provides a greater reward for deferring consumption. Therefore, the household responds to an increase in i1 by lowering C1 and raising C2.This response is called the intertemporal-substitution effect.

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: the intertemporal-substitution effect.C1 + (B1/P + K1) ( B0/P+K0) = (w/P)1L + i0(B0/P +K0)

Consumption in year1 + real saving in year1 = real income in year 1

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: the intertemporal-substitution effect.We know from the intertemporal-substitution effect that an increase in the interest rate, i1, motivates the household to postpone consumption, so that this years consumption, C1, falls on the left-hand side.

Macroeconomics Chapter 7

Consumption and SavingChoosing consumption: the intertemporal-substitution effect.Since 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).

The intertemporal-substitution effect motivates the household to save more when the interest rate rises.

Macroeconomics Chapter 7

Consumption and SavingThe income effect from a change in the interest rateC2 + ( B2/ P + K2) ( B1/ P + K1) = ( w/ P) 2 L + i1 ( B1/ P + K1)

The income effect from i1i1(B1/P)i1K1

Macroeconomics Chapter 7

Consumption and SavingThe income effect from a change in the interest ratei1(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 term i1(B1/P) is zero.

Macroeconomics Chapter 7

Consumption and SavingThe income effect from a change in the interest ratei1K1Average 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 7

Consumption and SavingThe income effect from a change in the interest rateIn 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.The full income effect from an increase in i1 is positive.

Macroeconomics Chapter 7

Consumption and SavingCombining income and substitution effectsThe 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 C1. The overall effect from an increase in i1 on C1 is ambiguous.

Macroeconomics Chapter 7

Consumption and Saving

Macroeconomics Chapter 7

Consumption and SavingConsumption Over Many YearsTwo-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)

Relax our simplifying assumption that the household could not change the present value of assets held at the end of year 2

Macroeconomics Chapter 7

Consumption 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 = (w/P)1L + (w/ P)2L/(1+ i1) + (w/P)2L/[(1+i1)(1+i2)] +

Macroeconomics Chapter 7

Consumption 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 7

Consumption and SavingMulti-Year budget constraint allows the comparison of the effects of temporary and permanent changes in income.

Macroeconomics Chapter 7

Consumption 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 means, 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 small when the extra income is temporary.

Macroeconomics Chapter 7

Consumption 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-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 7

Consumption 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 year

Macroeconomics Chapter 7

Consumption 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 the extra income is permanent.

Macroeconomics Chapter 7

Consumption and SavingConsumption Over Many YearsPermanent income.Consumption depends on a long-term average of incomeswhich he called permanent incomerather than current income.

Macroecono

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