Mechanism of Money Demand

To understand how money affects the economy, it is useful to
express the quantity of money in terms of the quantity of goods
and services it can buy which is the concept of real money
balances (M/P). Real money balances measure the purchasing
power of the stock of money.


Since V is rather stable, we can represent it as k = 1/V, and
therefore M can be written as:

M = k PY
The quantity theory of money is also a theory of the demand for
money. When the money market is in equilibrium, quantity of
money supplied (M) equals the quantity of money demanded
(Md)

Therefore:
Md = kPY


This means that the real demand for money (Md/P) is proportional
to real income or the level of output. Therefore according to the
Classical school, the demand for money is purely a function of
income.