The term i1K1, the income effect from an increase in i1 is positive.
Real assets end year1 = real assets end year0 + real income year1 − consumption year1
5
Consumption and Saving
6
Consumption and Saving
7
Consumption and Saving
V = (1 + i0)·(B0/P+K0) + (w/P)1·L + (w/P)2·L/(1+i1)
p.v. of sources of funds = value of initial assets + p.v. of wage incomes
12
Consumption and Saving
2
Consumption and Saving
3
Consumption and Saving
Consumption Over Two Years
Year1 C1 + ( B1/ P + K1) − ( B0/ P + K0) = ( w/P)1 ·L + i0 ·( B0/ P + K0) consumption in year1 + real saving in year1 = real income in year1
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 balance
the income effect from the term i1·(B1/P) is zero.
The income effect from i1 i1(B1/P) i1K1
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Consumption and Saving
The income effect from a change in the interest rate
i1(B1/P)
For a holder of bonds, the income effect from an increase in i1 is positive.
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.
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Consumption and Saving
Year2 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
4
Consumption and Saving
Consumption Over Two Years
B1/P + K1 = (1+i0) ·(B0/P + K0) + (w/P)1 ·L − C1
B2/P + K2 = (1+ i1) ·(B1/P + K1) + (w/P)2 ·L − C2
B2/P + K2 = (1+i1) ·[(1+i0)·( B0/P + K0) + (w/P)1·L − C1] + (w/P)2 ·L − C2
The intertemporal-substitution effect motivates the household to save more when the interest rate rises.
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Consumption and Saving
The income effect from a change in the interest rate C2 + ( B2/ P + K2) − ( B1/ P + K1) = ( w/ P) 2 ·L + i1 ·( B1/ P + K1)
Consumption in year1 + real saving in year1 = real income in year 1
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Consumption and Saving
Choosing consumption: the intertemporalsubstitution effect.
Choosing consumption: income effects
C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1·L+(w/P)2·L/(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
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Consumption and Saving
Choosing consumption: the intertemporalsubstitution 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.
Consumption Over Two Years
Combine the budget constraints to describe a household’s choice between consuming this year, C1, and next year, C2.
B1/P + K1 = B0/P + K0 + i0·(B0/P + K0) + ( w/P)1·L− C1
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Consumption and Saving
Choosing consumption: the intertemporalsubstitution effect.
Since year 1’s real income is given, the decline in C1 must be matched by a rise in year1’s real saving, (B1/P + K1) − (B0/P + K0).
We know from the intertemporal-substitution effect that an increase in the interest rate, i1, motivates the household to postpone consumption, so that this year’s consumption, C1, falls on the left-hand side.
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Consumption and Saving
Choosing consumption: the intertemporalsubstitution 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
Choosing consumption: income effects
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
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Consumption and Saving
Consumption Over Two Years
C2+(1+i1)·C1 = (1+i1)·(1+i0)·(B0/P+K0) +(1+i1)·(w/P)1·L+(w/P)2·L - (B2/P + K2)
Two-year household budget constraint:
This response is called the intertemporalsubstitution effect.
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Consumption and Saving
Choosing consumption: the intertemporalsubstitution effect.
C1 + (B1/P + K1) − ( B0/P+K0) = (w/P)1·L + i0·(B0/P +K0)
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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 (B2/P+K2)/(1 + i1), the total present value of consumption, C1 + C2/(1 + i1), must rise by the same amount as V.