The Quantity Theory of Money

The Quantity Theory of Money (QTM) explains what determines the value of money and the price level. In its simplest form it states that, other things remaining equal, the general price level varies directly and proportionately with the quantity of money in circulation — double the money supply and prices roughly double, so the value of money halves. There are two classic ways of expressing this theory.

Fisher's Equation of Exchange (Transactions approach)

The American economist Irving Fisher expressed the theory as an accounting identity:

where

• $M$ = total quantity of money in circulation,
• $V$ = velocity of circulation (the average number of times a unit of money changes hands in a period),
• $P$ = the general price level, and
• $T$ = the total volume of goods and services transacted.

The left side ($MV$) is the total money spent; the right side ($PT$) is the total money value of goods sold. They must be equal because every purchase is also a sale. Solving for the price level:

Fisher assumed that in the short run $V$ (which depends on habits and payment institutions) and $T$ (which depends on the economy's real output and resources) are fairly constant. With $V$ and $T$ fixed, $P$ becomes directly proportional to $M$: if the money supply doubles, the price level doubles and the value of money is halved. When bank deposits and their velocity are included, Fisher wrote the fuller version $MV + M'V' = PT$, where $M'$ is credit (bank) money and $V'$ its velocity.

The Cambridge (Cash-Balance) approach

Economists at Cambridge — Marshall, Pigou, Keynes and Robertson — approached the same idea from the demand side. They asked why people hold money: people wish to keep a fraction of their real income in the form of ready cash to meet transactions. The cash-balance equation is usually written:

where

• $M$ = the quantity of money,
• $P$ = the price level,
• $Y$ = real national income (real output), and
• $k$ = the fraction of real income that the community wishes to hold in the form of money.

Rearranged, $P = \dfrac{M}{kY}$, so the price level again varies directly with the money supply, other things equal.

Contrasting the two approaches

Both versions conclude that prices move with the quantity of money, but they emphasise different things:

• Focus: Fisher stresses the flow of money in transactions (its velocity $V$); Cambridge stresses the stock of money people choose to hold (the cash balance fraction $k$). The two are linked because $k$ is essentially the reciprocal of velocity, $k \approx 1/V$.
• Money's role: in Fisher, money is purely a medium of exchange (something to spend); in Cambridge, money is also a store of value — people demand it for the convenience and security of holding cash. …