ECO 301 Intermediate Macroeconomics,
Spring 2010
Instructor: Yangyi Shan
Homework Assignment 3
Answer Key
1. (40 points)
Consider two consumers, A and B. A and B both want perfect consumption
smoothing (c = c
f
) and both have no current wealth. However, the two consumers have
different income streams. Person A’s current income, y
A
, = 100, and future income, y
f
A
, =
121. Person B’s current income, y
B
, is 120, and future income, y
f
B
, = is 99. The real
interest rate is 10% (0.10).
a. Calculate the present value of lifetime resources (PVLR) for consumer A and B. (4
points)
PVLR
A
= 100 + 121/(1 + .1) = 210
PVLR
B
= 120 + 99/(1 + .1) = 210
b. How does the budget constraint of consumer A compare to the budget constraint of
consumer B? Explain. Draw consumer A’s budget constraint. (4 points)
Since both consumers face the same real interest rate, both budget constraints have the
same slopes. Since both consumers have the same PVLR, both budget constraints have
the same horizontal intercept. So the two budget constraints are the same.
c). Find consumer A’s optimal lifetime consumption plan, (c
A
, c
f
A
). How does consumer
B’s optimal lifetime consumption plan, (c
B
, c
f
B
), compare to consumer A’s lifetime
consumption plan? Explain. (6 points)
Consumer A’s budget constraint is
c
f
A
= 1.1c
A
+ 231
Using
the perfect consumption smoothing assumption, we can substitute c
A
= c
f
A
into the
budget constraint and solve for c
A
:
210
231
c
A
Slope = –1.1
c
f
A
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c
A
= 1.1c
A
+ 231
2.1 c
A
= 231
c
A
= 231/2.1 = 110.
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