Inflation and money supply

A question from Yahoo! Answers:

How can inflation be 3 % but the growth in the money supply have increased by 13.8% ?

First of all, where are you getting your data? Between end of May 2006 and end of May 2007, the M2 increased from $6,766.9 billion to $7,215.8 billion:

http://www.federalreserve.gov/releases/h…

which, if I am doing the math correctly, is a 6.63% increase…

However, 6.63% still does not equal 3%, so the mystery remains… 🙂 Let’s try to demystify…

Recall the Hume-Fisher equation of exchange:

MV = PQ

where
M is money supply,
V is money velocity,
P is price level, and
Q is real GDP

Now let’s rewrite the equation:

P = MV / Q

and differentiate it (approximately, of course):

dP = dM + dV – dQ

It is very easy to see that change in price level dP (aka inflation) is determined not only by change in money supply dM, but also by change in money velocity dV and change in real GDP dQ. More specifically to the present-day U.S., inflation is about 3%, growth in real GDP is a little over 2%, change in money supply is just under 7%, so money velocity must have decreased by about 2% (probably as a result of the slowdown in the housing market)…

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