PROBLEM SET 4 SOLUTIONS
(1) Consider a closed economy with the following data:
N
K
Y
=
K = 100
N
K
MPN
1
2
1
=
Labor supply is inelastic so that:
N = 10000
The money market clearing condition is given by
0
)
(
200
2
.
0
1
=
+
−
=
e
e
r
Y
P
M
π
π
High powered money: H = 4000
Currency/deposit ratio:
cu
= 0.5
Reserve/deposit ratio:
res
= 0.5
a)
Derive the FE line in this economy and compute the real wage
Solution: Since labor supply is inelastic, we can plug N = 10000 and K = 100 into the
equation for Y to get Y = 10000. This is the full employment output. The real wage is
equal to MPN. Plugging in we get W/P = 1/2
b) Suppose that the IS curve is given by
r = 10 - 0.0005Y.
Derive the LM curve as a
function of
Y
and
H/P
. [Express it in the form
r = f(Y,H/P)
] Hint: Use the formula
H
res
cu
cu
M
+
+
=
1
1
Solution: Set (1/1,000)M1/P = 0.0002Y - 0.2r
and solve for r. By definition:
H
H
res
cu
cu
M
5
.
1
1
1
=
+
+
=
Hence the LM curve is given by the equation
r = 0.001Y - 0.005M1/P
or
r = 0.001Y - 0.0075H/P

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