Money, Velocity, and Inflation
(Economics 100b; Spring 1996)
Professor of Economics J. Bradford DeLong
601 Evans, University of California at Berkeley
Berkeley, CA 94720
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net
February 7, 1996
Products and Percentage Changes
There is a box on page 150 of Mankiw's textbook that--very
quickly--runs through "an arithmetic trick that is useful to know:
the percentage change of a product of two variables is approximately
the sum of the percentage changes in each of the variables."
It is worth going through this in somewhat more detail, as it is
the key to getting from the quantity equation:
M V = P Y
where M is the money stock, V is the velocity of circulation, P is
the overall price level, and Y is the level of output, to the
equation for the inflation rate:
Inflation (in % per year) = Money Growth (in % per year) + Velocity
Growth (in % per year) - Output Growth (in % per year)
First, a caveat:
- This "arithmetic trick" works only as long as all of the
percentage changes are small--say, twenty percent or less.
Second, let's run through the math:
ÿ