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Econ 3131
TA: Tian Liang
Solutions to Problem Set 6
1.
(a)
i. If a consumer saved
$1
in period 1, he would have
$(1 +
r
)
in the following
period. This interest on dollar amounts is called a
nominal interest rate.
ii. If the price of a good in period 1 is
$1
;
and the price of a good in period 2 is
$(1 +
)
then we say that
is the rate of
iii. If by giving up a unit of the consumption good in period 1, one can purchase
(1 +
±
)
units of consumption good in the next period then we say
±
is the
real interest rate.
iv. Suppose the price of the good in period 1 is
p
1
= 1
and the price of the good
in period 2 is
p
2
= (1 +
)
;
and the interest on dollar amounts is
r:
By giving
up one unit of consumption in period 1, the consumer will be able to save $
1
in period 1, this saving will give him
$(1 +
r
)
in period 2, which means that
he will be able to by
(1 +
r
)
=
(1 +
)
units of consumption good in period 2
at the price
(1 +
)
:
Therefore,
1 +
±
=
1 +
r
1 +
:
(b)
±
=
r
1 +
=
5%
2%
1 + 2%
=
1
34
So the utility maximization problem is
max
c
1
;c
2
u
(
c
1
;c
2
)
s.t.
c
1
>
0
; c
2
>
0
1 +
1
34
±
c
1
+
c
2
=
1 +
1
34
±
m
1
+
m
2
(c) Approximated real interest rate:
r
= 5%
2% = 3%
Exact real interest rate:
r
1 +
=
5%
2%
1 + 2%
= 2
:
94%
The approximated real interest rate is larger and easier to compute.
1
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View Full Document 2.
(a) A bond is a debt security, in which the authorized issuer owes the holders a debt
and is obliged to make interest payments (the coupons) and repay the principal
(the face value) at a later date (the maturity date).
(b)
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This note was uploaded on 06/27/2008 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell University (Engineering School).
 Spring '06
 MASSON

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