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The purpose of this article is to make you known the different versions of quantity theory of money along with underlying assumptions and flaws. Italian economist Davanzatti developed the quantity theory of money, and American economist Irving Fisher popularized it after his influential book “The Purchasing Power of Money” in 1911.

## Statement of Theory

This theory postulates that there is direct and proportional relationship between money supply and price level, and inverse and proportional relationship between money supply and value of money (1/p). In terms of Fisher, “Any given percentage increase or decrease in money supply will lead to the same percentage increase or decrease in the general level of prices.”

## Assumptions

1. Price level is passive variable i.e. money supply determines the price level.
2. People use money only for the medium of exchange. That is, people do not hold money as idle cash balance. Because holding idle cash means to forego the interest earnings that could be earned by keeping in saving deposit and investing in securities. Even if people hold money, they hold it for the transaction purpose only. Hence, people spend all the accumulated money either via consumption or via spending on capital goods. Thus, all the money supplied is in circulation.
3. There is always full employment in the economy i.e. economy utilizes all resources fully.
4. Volume of goods and services, and velocity of money remain constant in the short run.
5. The supply of M1, credit money, depends on M and the ratio of M1 to M remains the same.

## Equation of Exchange

Fisher had given the equation named ‘Equation of Exchange’ to explain the quantity theory of money as

MV = PT

where,
M = money supply (currencies and notes in the hands of people),
V = transaction velocity of money. It is the average number of times that a currency passes through hands or changes hands during the certain time period specially a year,
P = general price level i.e. average price of goods and services, and
T = total volume of transacted goods and services.

Example of Velocity of Money: Suppose that a ten dollar bill changes hands five times to purchase 5 piece of journals costing \$10 each during a year. Then, M, V, P and T equal 10, 5, 10 and 5 respectively.

The value of V is associated to the nominal value of total transaction in an economy. This is why, V is transaction velocity. Fisher assumed that velocity of money depends on institutional and technological features (such as spending habits and introduction of debit card) in the economy which changes only gradually. So, velocity of money remains constant in short run.

Similarly, T is constant because there is full employment in the economy and economy utilized all resources – labor and capital- fully. In addition, output of an economy depends on the aggregate production function (technology) and the quantities of factors of production available. Thus, output is constant in short run because factors like technology, capital and labor are constant in the short run.

### Revised Version of Equation of Exchange

Later on, Fisher revised the ‘equation of exchange’ to include bank or credit money because of their increasing importance in later time period. Thus, the revised equation is MV + M1V1 = PT.
Where, M1 is the credit or bank money and V1 is the velocity of the Credit Money. Note that the assumption of constant ratio of M1 to M validates this form of ‘equation of exchange’ as well.

## Quantity Theory of Money

Given the constant V and T, and increase or decrease in the money supply (M) leads to the direct and proportional increase or decrease in the price level P. For example, 10 % increase in M leads to the 10% increase in the price level and 10% decrease in the value of money (1/P).

The assumption of constant V over a long time period transforms the equation of exchange to quantity theory of money. And, this theory states that quantity of money solely determines the nominal income (spending) in the economy. Doubling the money supply (M) doubles nominal income (Py) (see Cambridge version below).

### Tabular Presentation

Consider the following hypothetical example:

Money Supply (M) Price Level (P) Value of Money (1/P)
1000 2 0.5
2000 4 0.25
4000 8 0.125
Given, V=5 and T= 2500

The table shows that doubling the money supply has doubled the price level but the value of money has declined by half. Notice that all these changes are proportionate in that each changes by 100%.

### Graphical Presentation

In the figure above, increasing the money supply by 100% i.e. from 1000 to 2000, the price level also has increased from by 100% i.e. from 2 to 4 (Panel A). At the same time, the value of money (1/P) decreased by 100% i.e. from 0.5 to 0.25 as shown in the panel B. Similar situation has occurred when the money supply is doubled from 2000 to 4000. Hence, the figure shows the
direct and proportionate relationship between money supply and price level, but inverse and proportionate relationship between money supply and value of money.

## Cambridge Version of Quantity Theory of Money

It is Cambridge University’s economist Marshall to transform the ‘equation of exchange’ in this Cambridge version. Due to the double counting problem and difficulty in measuring nominal value of total number of transaction in an economy, it became impractical to measure T in Fisher’s equation. Thus, Marshall revised the Fisher’s ‘equation of exchange’ to include only final goods and services, y, in place of T.

Accordingly, the transaction equation of exchange turns out to be MV = Py,

where, y is final goods and services or aggregate output, and V is income velocity of money. The income velocity of money is the average number of times per year a dollar is spent. Moreover, V is income velocity of money as oppose to the transaction velocity because the total nominal income of an economy, Py, comes to play instead of total transaction, PT.

This Cambridge version of Quantity Theory of Money establishes the connection between country’s total nominal income and total money supply. Here, total nominal income refers to the total amount of spending on final goods and services in an economy within a period of year. Given the constant V and y, equation of exchange states that quantity of money multiplied by its velocity must equal nominal income. This analogy implies that proportionate change in money supply leads to the proportionate change in price level.

The equation of exchange can be written as M =1/v (Py) or M = k (Py), where k = 1/v. The right hand side of equation, k(Py) is the demand for money and left hand side, M, is the money supply. When money demand equals money supply, money market will be in equilibrium.

### Monetary Nutrality

As we just outlined that money supply only affects price level, quantity theory of money shows the neutrality of money. The phenomenon that money supply does not affect real variables is called monerary nutrality.

## Implications of Quantity Theory of Money

Let us present the following implications:

• Price Level – the changes in quantity of money lead to the directly proportionate changes in price level.
• Inflation – the quantity theory of money as the theory of inflation states that inflation is the difference between money supply growth and aggregate output growth. The justification rests upon the mathematical fact that percentage change of a product of variables is approximately equal to the sum of percentage changes of individual variables. Accordingly, we can write equation of exchange as,

%change in M + %change in V = %change in P + %change in y

Since V is constant, the percentage change is zero. So, %change in P (inflation) equals

%change in P = %change in M – %change in y.

• Real income – On the one hand, classical economists believe that wages and prices are flexible enough to restore economy to the full employment level of equilibrium. You can read Say’s Law of Market for the justification provided by classical economists. On the other hand, the full employment level of output depends on the economy’s aggregate production function and qualities of available resources. Both of these facts imply that changing money supply leads to directly proportionate change in price level, and thus nominal income; but it does not alter the real aggregate output because there is full employment level of output in the economy. This implies that there is a complete separation between nominal and real variables like money, income, wage and interest rate. Classical economists term this separation as classical dichotomy.

## Flaws or Criticisms of Quantiry Theory of Money

1. Price is not a passive factor but it is active because price tends to encourage the producer to produce more. Higher price is the incentive to the producer to produce more.
2. Not only people hold money as idle cash to meet the daily liquidity needs, but also for the purpose of precautionary motives.
3. There is not always full employment in the economy but less than full employment.
4. The value of V may rise at boom period and fall at recession period. So, we cannot expect the value of V to be constant.
5. The price level and value of money may not change proportionately as the money supply.

If you like this article, then also don’t miss to read Say’s Law of Market, another pillar of complete classical model.