The quantity theory of money
The equation of exchange M·V = P·Y is an identity. Read in growth rates it says inflation tracks money growth net of real output growth, with velocity as the swing term: π = gM + gV − gY. The gold line has slope 1, shifted off the 45° reference π = gM by the velocity-and-output offset gV − gY.
Implied inflation π2.9%
Approximate π = gM + gV − gY 3.0%Velocity + output offset gV − gY −3.0%
Money growth gM6.0%
Velocity growth gV+0.0%
Real output growth gY3.0%
Exact form 1 + π = (1 + gM)(1 + gV) / (1 + gY) gives 2.9%; the additive approximation gives 3.0%. They diverge as the growth rates get large.
Hold velocity and output fixed and inflation moves one-for-one with money growth. A velocity rise (gV > 0) adds to inflation; faster real growth (gY) absorbs money growth and subtracts from it.
Read carefully.M·V = P·Y always holds, by definition. Constant velocity and the long-run independence of real output are assumptions, not facts. So “inflation is a monetary phenomenon” is a long-run, sustained claim, not a one-period mechanical law. In the short run velocity (gV) shifts and absorbs the link.
Try this. Push gM to 10%: fast money growth feeds straight into high inflation. Then lift gV to +3%: a velocity pickup adds to inflation on top of money growth.