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Economics 3213
Answers to Problem Set 8:
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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View Full Document2. King of the Thieves
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
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 Fall '06
 XAVIER
 Economics

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