income and substitution effects: a graphical...

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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 decompos-ing 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 bud-get 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 substitu-tion 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 rel-ative 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 illus-trates 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 consump-tion 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.

Income and Substitution Effects: A Graphical Analysis

Chapter 18 Appendix

Z11_MISH4317_WEB_CH18App_pp001-004.indd 1 13/11/13 4:18 PM

2 Chapter 18 appendix

Consumptionin Period 2, C2

CI2

CI1CJ

1CS1

Consumption in Period 1, C1

Shift of IBLS to IBL2 andmovement from point S topoint J shows income effect.

CJ2

CS2

J

IC2

IC1

IBL1

IBL2

IBLS

ICS

S

I

Pivoting of IBL1 to IBLS andmovement from point I topoint S shows substitutioneffect.

Figure 18A1.1

income and Substitution effectsThe line marked as IBLs illustrates the response of consump-tion due solely to future consumption becom-ing cheaper relative to current consumption, that is, the substitu-tion 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 bud-get line from IBLs to IBL2, and the move-ment from point S to point J is the income effect in which con-sumption in period 1 and period 2 both rise.


consumption. The income effect from a rise in the real interest rate involves a parallel, out-ward shift of the intertemporal budget line and shows that as income rises, consumption in both periods rises.

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 con-sumption during the next period because future consumption is cheaper relative to current

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.

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 bor-rower 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 pres-ent and future consumption of an interest rate

rEvIEw QuEStIonS And ProblEmS

inCome and SubStitution effeCtS: a GraphiCal analySiS 3



IBL1

IC1

C2A

C1A

A


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?

b) Calculate the size of the income and sub-stitution effects on present consumption if this individual was consuming at point A before the change in the interest rate. Which effect is larger?



$780

$500

$720

$650 $700

IBL1

IC1

A

IBL2

B

$600 C

IC2


income and substitution effects: a graphical...

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