THE QUANTITY THEORY OF MONEY (QTM)

The theory was first build up by people like Copernicus and Jean Bodin in as early as 1566. This theory according to me is more like an econophysics model which received its popularity from Irving Fisher in 1911 and other economists like J.S Mill. There were a lot of argument on the reality of the existence of the QTM, and many theory related to the QTM came in. However, the basic conclusion of each theory even though they deviated and restated the original Quantity Theory of Money equation, remained unchanged, i.e. they all explained that price level is directly related to the money supply. Let's discuss everything one-by-one. Even though not everything is there to study for your exam, but you can always prefer to know and get knowledge.

1. The Quantity Theory Of Money - In accordance with Irving Fisher.

Also known as the Cash Transaction approach, In its simplest form, it states that the general price level (P) in an economy is directly dependent on the money supply (M), P = f(M)

If M doubles, P will also double. If M falls by half, then P will also decline by the same amount. This is the logic behind the quantity theory of money. In his theory of demand for money, Fisher attached emphasis on the use of money as a medium of exchange (this is important, if you remember I have taught you how Keynes was different from Classical economists, in the way that the classical economists only thought of money as a medium of exchange, from which came a vague definition as “Money is what money does”. But Keynes said that money also has a function of store of value, where you can always save money for future use). Demand for money is a function of income. The rate of interest has no effect on the demand for money. Fisher emphasized on the supply of money, assuming demand for money is constant. 

Fisher has explained his theory in terms of his equation of exchange: According to Fisher, the equation for QTM is given as follows:

P x T = M x V

Where P = price level, or 1/P = the value of money;
M = the total money supply in the economy;
V = the velocity of Money;
T = the total amount of goods and services exchanged for money or the transactions taken place.

The total volume of transactions multiplied by the price level (PT)
represents the demand for money.
This equation equates the demand for money (PT) to supply of money
(MV).

The truth of this proposition is evident from the fact that if M is doubled, while V, and T remain constant, P is also doubled.

Assumptions of the Theory:

1. V is assumed to be constant and is independent of changes in M.
2. T also remains constant and is independent of other factors such as M, and V.
3. It is assumed that the demand for money is proportional to the value of transactions.
4. The supply of money is exogenously given from outside the system and is a constant.
5. The theory is applicable in the long run.

This whole thing was argued by Prof. Karl Marx, where he explained that whatever is being determined should be in terms of labor theory of value, where it should be determined by the socially necessary labor time needed to produce the commodity and that the QTM is a function of quantity of commodities, the price of the commodities and the velocity. After all, it is labor who determines how much production will happen. He didn't reject Fisher's theory, but just changed the function and said that the volume of money depends on labor basically.

Likewise, Keynes came in and argued that the amount of money was determined by the purchasing power or aggregate demand.

2. The Cambridge Version of the QTM - given by Alfred Marshall, Pigou, Robertson and Keynes.

Also known as the Cash Balance approach. We shall only discuss the original Cambridge version of the QTM and would avoid the functions given by each economist in specific.

M x V = P x Y

The whole concept is the same. I have mentioned it previously as well. The only difference is that everyone who has argued has just taken a different route to explain the same thing which was first explained by prof. Irving Fisher: As Money supply increases, Price level also goes up, other things remaining intact.

Thus, the % change in M x % change in Velocity = % change in P x % change in Y

Assuming velocity and income constant, we see that the change in the constant doesn't matter and the value becomes zero. Therefore, implying the direct relation between change in M and change in P. Thus, as Money supply in the economy increases, the price level also increases.

Let's take an example to explain how the model looks like.

Suppose, M = 1000, V = 4, P = 2, and Y = 2000

Then, according to the formula,  M x V = P x Y

                                                 ⟹ 1000 x 4 = 2 x 2000
                                                 ⟹ 4000 = 4000
Now, if M rises by 50%, i.e. it increases by 1000 + 50% of 1000 = 1500, then P will also increase by 50%, i.e. from 2 to 3, i.e. now P = 3 and M = 1500, then again, 

       M x V = P x Y
⟹  1500 x 4 = 3 x 2000 
⟹  6000 = 6000

This is what happens in reality. If the govt. of India increases the money supply which has happened earlier as well, then prices in the economy rise up fast. 

Thus, as M ↑ , V constant, (M x V)↑ ⇒ P↑, Y remaining constant.