Macroeconomics Chapter 71 Consumption, Saving and Investment Chapter 7

Macroeconomics Chapter 72 Consumption and Saving  Household budget constraint C + (1/P) · ∆B+ ∆K = π/P + ( w/P ) · L + i · ( B/P + K) π /P = 0 C+(1/P) · ∆B+∆K=(w/P) · L+i · (B/P+K) consumption+ real saving = real income

Macroeconomics Chapter 73 Consumption and Saving

Macroeconomics Chapter 74 Consumption and Saving  Consumption Over Two Years Year 1  C 1 + ( B 1 / P + K 1 ) − ( B 0 / P + K 0 ) = ( w/P) 1 · L + i 0 · ( B 0 / P + K 0 )  consumption in year 1 + real saving in year 1 = real income in year 1 Year 2  C 2 + ( B 2 / P + K 2 ) − ( B 1 / P + K 1 ) = ( w/ P) 2 · L + i 1 · ( B 1 / P + K 1 )  consumption in year 2 + real saving in year 2 = real income in year 2

Macroeconomics Chapter 75 Consumption and Saving  Consumption Over Two Years Combine the budget constraints to describe a household ’ s choice between consuming this year, C 1, and next year, C 2. B 1 /P + K 1 = B 0 /P + K 0 + i 0 · (B 0 /P + K 0 ) + ( w/P) 1 · L− C 1 Real assets end year 1 = real assets end year 0 + real income year 1 − consumption year 1

Macroeconomics Chapter 76 Consumption and Saving

Macroeconomics Chapter 77 Consumption and Saving

Macroeconomics Chapter 78 Consumption and Saving  Consumption Over Two Years B 1 /P + K 1 = (1+i 0 ) · (B 0 /P + K 0 ) + (w/P) 1 · L − C 1 B 2 /P + K 2 = (1+ i 1 ) · (B 1 /P + K 1 ) + (w/P) 2 · L − C 2 B 2 /P + K 2 = (1+i 1 ) · [(1+i 0 ) · ( B 0 /P + K 0 ) + (w/P) 1 · L − C 1 ] + (w/P) 2 · L − C 2

Macroeconomics Chapter 79 Consumption and Saving  Consumption Over Two Years C 2 +(1+i 1 ) · C 1 = (1+i 1 ) · (1+i 0 ) · (B 0 /P+K 0 ) +(1+i 1 ) · (w/P) 1 · L+(w/P) 2 · L - (B 2 /P + K 2 )  Two-year household budget constraint: C 1 + C 2 /(1+i 1 ) = (1+ i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L+(w/P) 2 · L/(1+i 1 )−(B 2 /P+K 2 )/(1+i 1 )

Macroeconomics Chapter 710 Consumption and Saving  Present value If the interest rate, i 1, 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+i 1 is called a discount factor.

Macroeconomics Chapter 711 Consumption and Saving Household chooses the time path of consumption — in this case, C 1 and C 2 — to maximize utility, subject to the budget constraint.

Macroeconomics Chapter 712 Consumption and Saving  Choosing consumption: income effects C 1 + C 2 /(1+i 1 ) = (1+ i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L+(w/P) 2 · L/(1+i 1 )−(B 2 /P+K 2 )/(1+i 1 ) p.v. of consumption = value of initial assets + p.v. of wage incomes − p.v. of assets end year 2 V = (1 + i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L + (w/P) 2 · L/(1+i 1 ) p.v. of sources of funds = value of initial assets + p.v. of wage incomes

Macroeconomics Chapter 713 Consumption and Saving  Choosing consumption: income effects C 1 + C 2 /(1+i 1 ) = V − (B 2 /P+K 2 )/(1+i 1 ) p.v. of consumption = p.v. of sources of funds − p.v. of assets end year 2

Macroeconomics Chapter 714 Consumption and Saving  Choosing consumption: income effects Suppose that V increases due to a rise in wage incomes. Since we are holding fixed the term (B 2 /P+K 2 )/(1 + i 1 ), the total present value of consumption, C 1 + C 2 /(1 + i 1 ), 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 715 Consumption and Saving  Choosing consumption: the intertemporal-substitution effect. C 1 + C 2 /(1+i 1 ) = V − (B 2 /P+K 2 )/(1+i 1 ) p.v. of consumption = p.v. of sources of funds − p.v. of assets end year 2

Macroeconomics Chapter 716 Consumption and Saving  Choosing consumption: the intertemporal-substitution effect. A higher i 1 provides a greater reward for deferring consumption. Therefore, the household responds to an increase in i 1 by lowering C 1 and raising C 2. This response is called the intertemporal-substitution effect.

Macroeconomics Chapter 717 Consumption and Saving  Choosing consumption: the intertemporal-substitution effect. C 1 + (B 1 /P + K 1 ) − ( B 0 /P+K 0 ) = (w/P) 1 · L + i 0 · (B 0 /P +K 0 ) Consumption in year 1 + real saving in year 1 = real income in year 1

Macroeconomics Chapter 718 Consumption and Saving  Choosing consumption: the intertemporal-substitution effect. We know from the intertemporal- substitution effect that an increase in the interest rate, i 1, motivates the household to postpone consumption, so that this year ’ s consumption, C1, falls on the left-hand side.

Macroeconomics Chapter 719 Consumption and Saving  Choosing consumption: the intertemporal-substitution effect. Since year 1 ’ s real income is given, the decline in C1 must be matched by a rise in year 1 ’ s real saving, (B 1 /P + K 1 ) − (B 0 /P + K 0 ). The intertemporal-substitution effect motivates the household to save more when the interest rate rises.

Macroeconomics Chapter 720 Consumption and Saving  The income effect from a change in the interest rate C 2 + ( B 2 / P + K 2 ) − ( B 1 / P + K 1 ) = ( w/ P) 2 · L + i 1 · ( B 1 / P + K 1 )  The income effect from i 1 i 1 (B 1 /P) i 1 K 1

Macroeconomics Chapter 721 Consumption and Saving  The income effect from a change in the interest rate i 1 (B 1 /P)  For a holder of bonds, the income effect from an increase in i 1 is positive.  For an issuer of bonds, the income effect from an increase in i 1 is negative.  For the economy as a whole, lending and borrowing must balance  the income effect from the term i 1 · (B1/P) is zero.

Macroeconomics Chapter 722 Consumption and Saving  The income effect from a change in the interest rate i 1 K 1  Average household ’ s holding of claims on capital, K 1, is greater than zero.  The term i 1 K 1, the income effect from an increase in i 1 is positive.

Macroeconomics Chapter 723 Consumption and Saving  The income effect from a change in the interest rate In the aggregate, the income effect from an increase in i 1 consists of a zero effect from the term i 1 · (B 1 /P) and a positive effect from the term i 1 K 1. The full income effect from an increase in i 1 is positive.

Macroeconomics Chapter 724 Consumption and Saving  Combining income and substitution effects The effect of an increase in the interest rate, i 1, on year 1 ’ s consumption, C 1  The intertemporal substitution effect motivates the household to reduce C 1.  An increase in i 1 also has a positive income effect, which motivates the household to raise C 1.  The overall effect from an increase in i 1 on C 1 is ambiguous.

Macroeconomics Chapter 725 Consumption and Saving

Macroeconomics Chapter 726 Consumption and Saving  Consumption Over Many Years Two-year budget constraint  C 1 + C 2 /(1+i 1 ) = (1+ i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L + (w/P) 2 · L/(1+i 1 ) − ( B 2 /P+K 2 )/(1+i 1 ) Relax our simplifying assumption that the household could not change the present value of assets held at the end of year 2

Macroeconomics Chapter 727 Consumption and Saving  Consumption and income in future years.  overall present value of consumption = C 1 + C 2 /(1 + i 1 ) + C 3 /[(1 + i 1 ) · (1 + i 2 )] + · · ·  overall present value of wage incomes = (w/P) 1 · L + (w/ P) 2 · L/(1+ i 1 ) + (w/P) 2 · L/[(1+i 1 ) · (1+i 2 )] + · · ·

Macroeconomics Chapter 728 Consumption and Saving  Multiyear budget constraint: C 1 + C 2 /(1 + i 1 ) + C 3 /[(1+i 1 ) · (1+i 2 )] + · · · = (1+ i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L + (w/P) 2 · L/(1+ i 1 ) + (w/P) 2 · L/[(1+i 1 ) · (1+i 2 )] + · · ·

Macroeconomics Chapter 729 Consumption and Saving  Multi-Year budget constraint allows the comparison of the effects of temporary and permanent changes in income.

Macroeconomics Chapter 730 Consumption and Saving  Temporary change in income  We predict that the household would respond to a rise in (w/P) 1 · L by raising consumption by similar amounts in each year: C 1, C 2, C 3, 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 1 ’ s income tends to be small when the extra income is temporary.

Macroeconomics Chapter 731 Consumption and Saving  temporary change in income  If (w/P) 1 · L rises by one unit on the right- hand side, C 1 rises by much less than one unit on the left-hand side.  Year 1 ’ s 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 1 ’ s income is nearly one when the extra income is temporary.

Macroeconomics Chapter 732 Consumption and Saving  Permanent increase in wage income  (w/P) 1 · L, (w/P) 2 · L, (w/P) 3 · L, 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 733 Consumption and Saving  Permanent increase in wage income  The prediction is that the propensity to consume out of an extra unit of year 1 ’ s income would be high — close to one — when the extra income is permanent.  The propensity to save in year 1 out of an extra unit of year 1 ’ s income is small when the extra income is permanent.

Macroeconomics Chapter 734 Consumption and Saving  Consumption Over Many Years Permanent income.  Consumption depends on a long-term average of incomes — which he called permanent income — rather than current income.

Macroeconomics Chapter 735 Consumption, Saving, and Investment in Equilibrium  Determine the aggregate quantities of consumption and saving.  Determine the aggregate quantity of investment.

Macroeconomics Chapter 736 Consumption, Saving, and Investment in Equilibrium  Budget Constraint C + (1/P) · ∆B+ ∆K = (w/P) · L + i · (B/P) + iK  i = (R/P − δ ) C+ (1/P) · ∆B+ ∆K = (w/P) · L + i · (B/P) + (R/P) · K − δ K B = 0 and ∆B = 0

Macroeconomics Chapter 737 Consumption, Saving, and Investment in Equilibrium  Budget Constraint C+ ∆K = (w/P) · L + (R/P) · K − δ K  (w/P) · L + (R/P) · K = Y (Real GDP). C + ∆K = Y −δK Consumption + net investment = real GDP − depreciation = real net domestic product

Macroeconomics Chapter 738 Consumption, Saving, and Investment in Equilibrium  The left-hand side of the equation implies that the economy ’ s 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 determines ∆K

Macroeconomics Chapter 739  Multiyear budget constraint: C 1 + C 2 /(1 + i 1 ) + C 3 /[(1+i 1 ) · (1+i 2 )] + · · · = (1+ i 0 ) · (B 0 /P+K 0 ) + (w/P) 1 · L + (w/P) 2 · L/(1+ i 1 ) + (w/P) 2 · L/[(1+i 1 ) · (1+i 2 )] + · · · Extra: Consumption and Saving

Macroeconomics Chapter 740 Extra: Consumption and Saving 1. A simple case with zero interest rate: Budget constraint: Lagrangian:

Macroeconomics Chapter 741  FOC: Extra: Consumption and Saving Implication: 1) Permanent income hypothesis The time pattern of income is not important to consumption, but to saving! 2) Saving is future consumption

Macroeconomics Chapter 742 Extra: Consumption and Saving 2. The constant interest rate and saving Budget constraint:

Macroeconomics Chapter 743 Extra: Consumption and Saving Example: