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Economics 3213
Answers to Problem Set 9:
Aladdin
Prof. Xavier SalaiMartin
1. Jafar
a.
If the firm buys real capital, it will receive the same amount as usual:
[MPK
t
+1
+ (1 
δ
)]
P
t
+1
.
b.
If the firm buys a bond, it will receive (1 +
R
)
P
t
.
c.
If the firm is optimizing, it will compare the returns to real investment
from part (a) and buying bonds from part (b). If one is higher than
the other, the firm will do more of the high return activity until the
returns are equalized:
[MPK
t
+1
+ (1 
δ
)]
P
t
+1
= (1 +
R
)
P
t
.
This is exactly the same relation that we found in class and simplifies
to
MPK
t
+1
+ (1 
δ
) = (1 +
R
)
P
t
/
P
t
+1
.
Remember that inflation is defined as
π
= (
P
t
+1

P
t
)/
P
t
=
P
t
+1
/
P
t
 1.
Hence, 1 +
π
=
P
t
+1
/
P
t
or
P
t
/
P
t
+1
= 1/(1 +
π
). Remember also that real and nominal interest
rates are linked by the Fisher equation:
R
=
r
+
π
+
r
π
or 1 +
R
= (1 +
r
)(1 +
π
). Substituting these in the above expression, we get:
MPK
t
+1
+ (1 
δ
) = (1 +
r
)(1 +
π
)/(1 +
π
)
MPK
t
+1
+ (1 
δ
) = 1 +
r
MPK
t
+1
=
δ
+
r
This is exactly the same relation that we obtained in class. The
amount of capital desired by firms and hence investment demand are
not
affected by whether firms borrow or use their own funds.
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a.
The credit crunch shifts the investment curve to the left. The
aggregate demand curve also shifts to the left because it is simply the
sum of investment demand and consumption demand:
Y
d
=
C
d
+
I
d
. In
the Keynesian model, the short run equilibrium is found at the
intersection of the aggregate demand and the LM curve (Diagram 1).
Thus real output and real interest rate both go down. Aggregate
supply is greater than aggregate demand at the new equilibrium;
therefore, prices begin to fall in the medium run. The LM curve shifts
downward until it reaches the intersection of the aggregate demand
and supply curves. Remember that the LM curve is given by
. The interest rate drops further, while output increases
a little. In the long run, the overall effect is the reduction of output,
interest rate, and prices compared with the initial equilibrium.
b.
To prevent output from declining, the Fed may want to increase the
money supply. Expansionary monetary policy can shift the LM curve
downwards, so that real interest rate goes down and output stays at
the initial level (LM
3
in Diagram 2). However, demand is greater than
supply at the new short run equilibrium, and prices will rise. The LM
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This note was uploaded on 06/02/2011 for the course ECONECON 3213 taught by Professor Martin during the Spring '11 term at Columbia.
 Spring '11
 MARTIN

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