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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