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∆
Π
∆
M
M
Y
Y
=
+
T
HE
U
NIVERSITY OF
T
ORONTO AT
S
CARBOROUGH
Division of Management
ECM B06H – Macroeconomic Theory and Policy: A Mathematical Approach
TUTORIAL #2

SOLUTIONS
Q1.
Consider an economy is such that real output is growing at 5% each
year, the real interest rate is constant at 4%, and the money supply is
growing at 5% each year. The demand for money is given by:
( M
d
/P ) = k
@
Y
(
Suppose
(
=1, and k = 1/V = a constant (where V is the income velocity of
money).
a)
Calculate the rate of inflation and the nominal interest rate.
We have the following information:
∆
∆
∆
Y
Y
M
M
r
V
V
=
=
=
=
5%
5%
4%,
0%
,
,
M
S
= M,
M
d
= k
@
P
@
Y
(
,
(
=1, and k = (1/V)
Money Market Equilibrium implies:
M
S
= M
d
M = k
@
P
@
Y
M
@
(1/k) =
M
@
V = P
@
Y
So money market equilibrium here yields the
Standard/Basic Quantity Equation
Clearly, the following relationship holds with respect to changes in the terms of the
quantity equation:
∆
∆
∆
∆
M
M
V
V
P
P
Y
Y
+
=
+
Π
∆
∆
=

M
M
Y
Y
A
= 5%  5% = 0%
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Page 2 of
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The
Fisher Equation
implies:
i = r +
A
Here
i = r + 0%
i = r = 4%
b)
Calculate the effect on the price level and the rate of inflation if the rate of growth of
the money supply changes to 10% each year. Represent your answer in a graph
(with horizontal axis=time).
Π
∆
∆
=

M
M
Y
Y
A
= 10%  5% = 5%
The rate of inflation rises oneforone with the increase in the rate of growth of the money
supply (i.e. the M
s
growth rate rose 5 percentage points as did
A
).
Here we have assumed that the policy change occurs at time t
1
and at that time the money
supply rises by a full 5 percent (this is why the P curve jumps from 1 to 1.05 immediately 
if the money supply did not rise by the full 5% initially then the P curve would still jump
upwards, be discontinuous, but would rise to a value less than 1.05 at time t
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