6. 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
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
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9. Consumption and Saving
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
– Real assets end year1 =
real assets end year0 + real income year1
− consumption year1
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13. Consumption and Saving
Present value
If the interest rate, i1, is greater than zero, €1
received or spent in year 1 is equivalent to more
than €1 in year2.
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14. Consumption and Saving
Euros received or spent in year2 must be
discounted to make them comparable to euros in
year1.
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16. Consumption and Saving
Choosing consumption: income effects
Household chooses the time path of consumption
—in this case, C1 and C2—to maximize utility,
subject to the budget constraint.
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18. Consumption and Saving
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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19. Consumption and Saving
Choosing consumption: income effects
– 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
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20. Consumption and Saving
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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21. Consumption and Saving
Choosing consumption: income effects
Since households like to consume at similar levels in the
two years, we predict that C1 and C2 will rise by similar
amounts.
The responses of consumption to increases in initial assets
or wage incomes are called income effects.
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22. Consumption and Saving
Choosing 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
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23.
24. 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.
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25. Consumption and Saving
Choosing consumption: the intertemporal-
substitution effect.
– 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 year 1
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26. Consumption and Saving
Choosing 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 year’s consumption, C1,
falls on the left-hand side.
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27. Choosing consumption: the
intertemporal-substitution effect.
Since year 1’s real income, (w/P)1 · L+ i0 · (B0/P +
K0) on the right-hand side of equation (7.2), is
given, the decline in C1 must be matched by a rise
in year1’s s real saving, (B1/P + K1) − (B0/P + K0).
The intertemporal-substitution effect motivates the
household to save more when the interest rate
rises.
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28. 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)
The income effect from i1, [i1·(B1/P + K1)]
– i1(B1/P)
– i1K1
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