The quantity equation is an accounting identity. Move the sliders to see how M, V, P, and Y interact. The QTM adds the assumption that V is roughly constant.
M · V = P · Y
$5.0T
4.0
$20.0T
Nominal GDP (M·V)
$20.0T
Implied price level P
1.00
Real money M/P
$5.0T
Money / GDP ratio
25%
Try this
Hold V and Y constant; double M. P should also double — that's the heart of QTM. Now try dropping V (financial-crisis behavior). With M fixed, P falls — quantity equation still holds, but velocity, not money, is moving the price level.
Take logs and time-derivatives of M·V = P·Y to get π = gM − gY (when V is roughly constant). Adjust money growth and real growth.
π = gM − gY(if gV ≈ 0)
6.0%
3.0%
0.0%
gM
6.0%
+ gV
0.0%
− gY
−3.0%
= Inflation π
3.0%
QUICK SCENARIOS
Concept check
For the Fed to hit a 2% inflation target with gY ≈ 2%/year, money growth should be ≈ 4%/year (with stable V). When V drops (e.g., 2008–09), the same gM produces lower π — and policy needs to inject more M to compensate.
Cross-country data: countries with high money growth tend to have high inflation. The relationship is approximately one-for-one — confirming the QTM.
DATA TABLE
Country
gM (%/yr)
π (%/yr)
Comparison
Reading the chart
Each dot is one country averaged over 10–20 years. The dashed 45° line is "perfect Fisher" (π = gM exactly). Most points cluster near it. At low gM (advanced economies), the data scatter more — velocity moves matter. At high gM (Argentina, Venezuela), the relationship is tight.