Spring 2010
Sadler
Homework 6
Solutions
1.
Note that the “gross” growth rate for some variable like real GDP,
Y
, can be written as
షభ
ൌ1
݃
, where
݃
is the “net” growth rate (for example, 3 percent per year, so the gross growth rate
would be 1.03). Let the equation of exchange (or “quantity equation”) for year
t
as
ܯ
௧
ܸ
௧
ൌܲ
௧
ܻ
௧
.
a.
Noting that in the previous year the equation of exchange can be written as
M
୲ିଵ
V
୲ିଵ
ൌP
୲ିଵ
Y
୲ିଵ
,
write the quantity equation in terms of the growth rates of the four variables and show that the
approximate final answer is
g
m
g
v
ൌπg
y
.
Hint: for any economy under normal
circumstances, the product of two growth rates, such as
g
m
g
v
is approximately zero
.
For example,
assume that
g
m
ൌ.05
and
g
v
ൌ.02
, then
g
m
g
v
ൌ ሺ.05ሻሺ.02ሻ ൌ .001
,
which is very close to zero,
so we will assume that it is exactly zero.
Just divide the quantity equation for year t by that for year t
‐
1:
ି
ି
ൌ
۾
ܜି
܇
ܜି
ି
ି
ൌ
۾
ܜି
܇
ܜି
ሺ
ሻሺ
ሻ ൌ ሺሻሺ
ሻ
Where the gross growth rate in the price level
۾
ܜష
is one plus the rate of inflation,
.
ൌ
According to the hint given in the problem, the two product terms on each side of the equation are
approximately zero, so we set them to zero. Canceling the ones on both sides leaves
ൌ
b.
Imposing the assumptions of the quantity theory onto the equation, demonstrate Milton
Friedman’s dictum that “Inflation is always and everywhere a monetary phenomenon.”
According to the quantity theory as we discussed in class, velocity is constant, so its growth rate is
zero:
ൌ
so
ൌ
The quantity theory is part of the classical school of macroeconomics, which asserts that real
variables, such as real GDP,
Y
, cannot be influenced by nominal variables such as the money supply.
Therefore,