A TwoPeriod Economy (Part II)
Giacomo Rondina
Lecture Notes Prepared for Econ110B
Department of Economics
University of California, San Diego
Winter 2011
These notes build on Part I to show that consumption today
C
is a positive function of
the level of lifetime expected wealth
W
. In Part I we showed that income and consumption in
period
t
must be related to income and consumption in period
t
+ 1
according to the following
relationship
(
Y
−
C
)
=
1
(1 +
r
)
(
C
0
−
Y
0
)
.
(1)
If we rearrange this equation we get
Y
+
Y
0
(1 +
r
)
=
C
+
C
0
(1 +
r
)
.
(2)
This expression says that whatever is the income of an agent over her lifetime (today and in
the future) in terms of apples today, this must be equal to whatever the agent consumes over
her lifetime (today and in the future). The left hand side of this equation can be termed the
lifetime wealth of agent today and denote it by
W
=
Y
+
Y
0
(1 +
r
)
.
There are many combinations of current and future income
Y
and
Y
0
that would result in the
same level of lifetime wealth
W
for a given level of the real interest rate
r
. We can represent this
1
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W
0
(
1+r
)
Apples
in the
Future
W
1
(
1+r
)
Budget Constraint
Apples Today
W
0
W
1
Figure 1: Total Lifetime Wealth and the Budget Constraint
set of points in a diagram and call them the
budget constraint
for the agent. This is represented
by the straight line in Figure 1. Notice the axis of the diagram. The horizontal axis measure the
amount of goods (apples) today, while the vertical axis measure the among of goods (apples)
in the future.
Any point in the diagram corresponds to a combination of apples today and
apples in the future. All the points to the right of that line are combinations of apples today
and apples in the future that the economic agent cannot a
ff
ord as her wealth is not enough to
buy them. All the points to the left of that line are combinations of apples today and apples in
the future that the economic agent can a
ff
ord and, in addition, some wealth will be not spent
by the end of the two periods.
All the points on the budget constraint are combinations of
apples today and apples in the future that the economic agent can just a
ff
ord: no wealth will
be unspent at the end of the agent’s lifetime.
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 Summer '07
 Bansak
 Economics, Intertemporal Consumption Choice

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