Econ 352
YiLi Chien
Intermediate Macroeconomics
Spring 2011
Homework Assignment 4 Answer
Question 1 (35 pts):
Suppose Jill obeys the two-period model of consumption and earns
nothing in the first period and $210 in the second period. In addition, she can borrow or
lend at the interest rate
r
.
a.
(20 pts) What will happen to Jill’s consumption in the first period when the
interest rate increases? Is Jill better off or worse off than before the interest rate
increase? Show your result in graphs.
Jill’s initial choice is describe in the following graph:
Jill is a borrower. A higher interest rate makes her poorer, meaning that
the income effect contributes to lower both C
1
and C
2
. But this also means
that the relative price of consumption today is higher; according to the
substitution effect, C
1
goes down and C
2
goes up. Therefore, C
1
surely
decreases (income and substitution effects reinforce each other), but the
impact of C
2
is ambiguous. C
2
will go up (down) if the substitution
(income) effect is dominant. In the following graph, the substitution effect
is stronger.
C
1
C
2
Y
1
+
Y
2
/(1+
r
)
A
(1+
r
)
Y
1
+
Y
2
Y
1
= 0,
Y
2
= 210

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