Quantity Theory

The quantity theory of money asserts that the price of goods and services is proportional to the money supply in the economy, assuming everything else is held constant. Basically, if you double how much money exists in the economy, then prices will simply double in response over time due to inflation.

Velocity of Money

The ‘velocity’ of money is a measure of the rate at which mone circulates in the economy. It’s the number of times $1 is exchanged in a time period. A higher velocity of money is indicative of economic growth.

The velocity of money is calculated as the ratio of nominal GDP to the money supply,

$$\begin{array}{rl}V& \equiv \frac{Y_{\text{nominal}}}{M}\\ & \equiv \frac{P{Y}_{\text{real}}}{M},\end{array}$$

with $P$ being the aggregate price level.

When we assume that $Y$ and $M$ are exogenous, or in other words, constant, then we’ll have

$$P\propto M,$$ $$\Delta P=\pi =\Delta M.$$