# > Econ 100b Created 4/30/1996 Go to Brad De Long's Home Page 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

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:

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# Econ 100b

Created 4/30/1996
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