Microeconomic Theory
Econ 101A
Fall 2008
GSI: Eva Vivalt
Section Notes 5: Consumption Saving Decisions
1 Consumption Savings Decisions
Suppose a consumer has preferences of consumption of goods today,
C
1
and consumption of goods in the
next period,
C
2
, that can be expressed by the utility function
U
(
C
1
,C
2
) =
C
1
2
1
+
βC
1
2
2
where 0
< β <
1
reﬂects the degree to which the consumer prefers consumption today relative to consumption of goods next
period. Then the consumer’s utility maximization problem (UMP) can be expressed as:
max
C
1
,C
2
C
1
2
1
+
βC
1
2
2
s.t.
p
1
C
1
+
p
2
C
2
1 +
R
=
Y
1
+
Y
2
1 +
R
where
p
1
,p
2
are the price of the consumption goods in periods 1 and 2,
Y
1
,Y
2
are income in periods 1 and
2, and
R
is the net interest rate for borrowing or saving between periods 1 and 2. (Note: future income and
future expenditure are discounted by 1+R. This gives us the
present value
of that cash ﬂow. Another
way to see it is that one unit of consumption tomorrow is worth only
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 Fall '08
 Staff
 Economics, Utility, Eva Vivalt, s.t. p1 C1

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