Intertemporal Trade and Consumption Demand

Intertemporal Trade and Consumption Demand
We assume in the chapter that private consumption demand is a function of disposable
income, , with the property that when rises, consumption rises by less
(so that saving, , goes up too). This appendix interprets this assumption in the
context of the intertemporal model of consumption behavior discussed in the appendix to
Chapter 6.
The discussion in Chapter 6 assumed that consumers’ welfare depends on present consumption
demand and future consumption demand . If present income is and
future income is , consumers can use borrowing or saving to allocate their consumption
over time in any way consistent with the intertemporal budget constraint
where is the real rate of interest.
Figure 17A1-1 reminds you of how consumption and saving were determined in
Chapter 6. If present and future output are initially described by the point labeled 1 in the
figure, a consumer’s wish to pick the highest utility indifference curve consistent with his
or her budget constraints leads to consumption at point 1 as well.
We have assumed zero saving at point 1 to show most clearly the effect of a rise in
current output, which we turn to next. Suppose present output rises while future output
doesn’t, moving the income endowment to point , which lies horizontally to the right of
point 1. You can see that the consumer will wish to spread the increase in consumption
this allows her over her entire lifetime. She can do this by saving some of the present
2oe
r
DP + DF/(1 + r) = QP + QF/(1 + r),
QF
DP DF QP
Yd - C(Yd)
C = C(Y d) Yd
Future
consumption
Present
consumption
D2 2
1
F
Q1
F D1
F =
D2
P Q2
P
2'
Intertemporal
budget constraints
Indifference
curves
Q1
P D1
P =
Figure 17A1-1
Change in Output and Saving
A one-period increase in output
raises saving.
CHAPTER 17 Output and the Exchange Rate in the Short Run 459
income rise, , and moving up to the left along her budget line from her endowment
point to point 2.
If we now reinterpret the notation so that present output, , corresponds to disposable
income, , and present consumption demand corresponds to , we see that while
consumption certainly depends on factors other than current disposable income—notably,
future income and the real interest rate—its behavior does imply that a rise in lifetime income
that is concentrated in the present will indeed lead to a rise in current consumption
that is less than the rise in current income. Since the output changes we have been considering
in this chapter are all temporary changes that result from the short-run stickiness of
domestic money prices, the consumption behavior we simply assumed in the chapter does
capture the feature of intertemporal consumption behavior essential for the DD-AA model
to work.
We could also use Figure 17A1-1 to look at the consumption effects of the real interest
rate, which we mentioned in footnote 1. If the economy is initially at point 1, a fall in the
real interest rate causes the budget line to rotate counterclockwise about point 1, causing
a rise in present consumption. If initially the economy had been saving a positive amount,
however, as at point 2, this effect would be ambiguous, a reflection of the contrary pulls of
the income and substitution effects we introduced in the first part of this book on international
trade theory. In this second case, the endowment point is point , so a fall in the real
interest rate causes a counterclockwise rotation of the budget line about point .
Empirical evidence indicates that the positive effect of a lower real interest rate on consumption
probably is weak.
Use of the preceding framework to analyze the intertemporal aspects of fiscal policy
would lead us too far afield, although this is one of the most fascinating topics in macroeconomics.
We refer readers instead to any good intermediate macroeconomics text.14
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Yd