Quantity Theory of Money
Why QTM is important?
Quantity Theory of Money is a theory that suggests that, in the long-run, a change in money supply results in a proportional change in price level.
Deriving Aggregate Demand from Fisher Identity
Fisher Identity
The theory begins from Irving Fisher’s simple identity. The product of money supply and velocity of money is the same with the product of price and output.
Expenditure, which is spent by consumers, equals to the Recipes, which is received by producers. Dividing an equation into P, we are able to derive the following:
We call k ‘real money balance’ as a fraction of real output. I therefore can equate fisher identity and definition of k to derive real money balance.
Real Money Balance
We finally have an equation for aggregate demand:
We finally find that aggregate demand equals real money balance multiplied by V (velocity).
Two Assumptions
There are two assumptions underlying this theory. They are very important assumptions not only because it supports the basic framework of theory but also explains why the theory is only used in the long-run, not short-run.
Monetary Neutrality
In the long-run, Y is entirely determined by real variables, not nominal variables. Therefore, it stays the same in the long-run. An increase in M increases real money balance, which means Y also increases. Because supply of real money balance exceeds its demand, people spend more, and it raises P by the same proportion in the long-run.
The attribute that Y is entirely determined by real variables is called Monetary Neutrality. However, in the short-run, this rule fails. In the short-run, M is dependent on Y; for instance, a sharp decline in M always has been followed by sharp decline in real output. (i.e. Great Depression, Volcker Disinflation). In accordance with aggregate demand, Y increases when M increases in the short-run. This is the reason why the Federal Reserve’s prints tons of dollars in monetary policy, which spreads a large amount of dollars across the globe (increase in M) to fight against recession.
Stable Velocity
Another assumption behind the quantity theory of money is “stable velocity”.
Assume that velocity of money is stable, we are able to derive the following equation:
However, V varies in the short-run, and hence money demand does not have a simple proportional relation to output. Holding money in hand incurs the opportunity cost, which is the forgone nominal interest rate r, which is also relevant. Suppose W as nominal wealth, it is the sum of bond (B) and Money Supply.
Because r represents portfolio motive (interest rate), M varies inversely with r.
V varies positively with r, being pro-cyclical as r is pro-cyclical. With nominal rigidity, r adjusts to change in M, not P (If M increases, r decreases). Therefore, stable velocity is also failed, which means QTM does not work in the short-run.