Chapter 18
Appendix
Income and Substitution
Effects: A Graphical Analysis
To more fully understand income and substitution effects in the intertemporal choice
model, here we do a more detailed analysis of Figure 18.5 in the chapter by decomposing the movement from point I to point J in two steps.
In the first step, we ask what happens in Figure 18A1.1 if the intertemporal budget line pivots clockwise around point I as a result of the new higher level of r2, which
causes the intertemporal budget line to have the steeper negative slope of -11 + r2).
We mark this line as IBLs ; it illustrates the response of consumption due solely to future
consumption becoming cheaper relative to current consumption, that is, the substitution effect. Because the slope of IBLs gets steeper, you can see that Carmencita can reach
a higher indifference curve ICs that is tangent to the IBLs at point S. The position of this
point above and to the left of point I implies that current consumption in period 1 falls,
while future consumption in period 2 rises. The substitution effect is then as described
in the text, where a higher interest rate that makes future consumption cheaper relative to current consumption leads to higher future consumption and lower current
consumption.
The next step is a parallel shift of the intertemporal budget line from IBLs to IBL2.
We have already analyzed this kind of shift in Figure 18.4 in the chapter, because it illustrates the response from an increase in lifetime resources due to an increase in income,
and is thus the income effect. Because of the increase in lifetime resources, the parallel
shift from IBLs to IBL2 leads to a movement from point S to point J, in which consumption in period 1 and period 2 both rise. We now see that the income effect for first-period
consumption that causes it to rise is opposite to the substitution effect that causes it to
fall. Thus, there is some ambiguity as to whether first-period consumption rises or falls
when interest rates rise. However, as the figure is drawn, the income effect is smaller
than the substitution effect and so the overall impact of a rise in the interest rate is a
fall in current consumption. On the other hand, the income and substitution effects for
consumption in period 2 both indicate a rise in second-period consumption, so there is
no ambiguity regarding second-period consumption, which clearly rises.
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2 Chapter 18 appendix
Figure 18A1.1
Income and
Substitution Effects
The line marked as
IBLs illustrates the
response of consumption due solely to future
consumption becoming cheaper relative to
current consumption,
that is, the substitution effect. Because
the slope of IBLs gets
steeper, Carmencita
can reach a higher
indifference curve ICs
that is tangent to IBLs
at point S, in which
current consumption
in period 1 falls while
future consumption in
period 2 rises. There is
then a parallel shift of
the intertemporal budget line from IBLs to
IBL2, and the movement from point S to
point J is the income
effect in which consumption in period 1
and period 2 both rise.
Z11_MISH4317_WEB_CH18App_pp001-004.indd 2
Consumption IBL2
in Period 2, C2
IBLS
CJ2
CS2
Pivoting of IBL1 to IBLS and
movement from point I to
point S shows substitution
effect.
J
S
Shift of IBLS to IBL2 and
movement from point S to
point J shows income effect.
IBL1
CI2
I
IC2
ICS
IC1
CS1 CJ1
CI1
Consumption in Period 1, C1
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Income and Substitution Effects: A Graphical Analysis 3 Summary
1. The substitution effect from a rise in the real
interest rate involves a clockwise pivoting of
the intertemporal budget line, and it leads to
a fall in consumption today and a rise in consumption during the next period because future
consumption is cheaper relative to current
consumption. The income effect from a rise in
the real interest rate involves a parallel, outward shift of the intertemporal budget line and
shows that as income rises, consumption in
both periods rises.
Review Questions and Problems
1. Why is the substitution effect characterized as
a pivoting of the intertemporal budget line?
2. Why is the income effect characterized as a
parallel shift of the intertemporal budget line?
3. If Carmencita is a lender rather than a borrower in period 1, what will be the effect on
consumption today if the real interest rate
rises?
4. Draw a graph to illustrate the effects on present and future consumption of an interest rate
increase when the income effect is larger than
the substitution effect.
5. Consider the following graph and assume that
the interest rate decreases.
a) Draw the new intertemporal budget line.
b) Assuming the income effect is smaller
than the substitution effect, draw the new
indifference curve at the point at which
optimal consumption takes place, and
denote that point as point B.
Consumption
in Period 2, C2
IBL1
C2A
A
IC1
C1A
Consumption in Period 1, C1
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4 Chapter 18 appendix
6. Consider the accompanying graph and answer
the following questions.
a) If the intertemporal budget line changes
from IBL1 to IBL2, is this the result of an
increase or a decrease in the interest rate?
Consumption
in Period 2, C2
$780
b) Calculate the size of the income and substitution effects on present consumption
if this individual was consuming at point
A before the change in the interest rate.
Which effect is larger?
IBL1
A
B
$720
IC1
C
$600
IC2
IBL2
$500
$650 $700
Consumption in Period 1, C1
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