The concept of the quantity theory of money (QTM) began in the 16th century. As gold and silver inflows from the Americas into Europe were being minted into coins, there was a resulting rise in inflation.

This led economist Henry Thornton in 1802 to assume that more money equals more inflation and that an increase in money supply does not necessarily mean an increase in economic output. Here we look at the assumptions and calculations underlying the QTM, as well as its relationship to monetarism and ways the theory has been challenged.

Table of Contents

## Theories of Value of Money

- Quantity Theory
- Cambridge Theory
- Friedman Theory
- Keynesian Equations

### Quantity Theory

The quantity theory of money states that there is a direct relationship between the quantity of money in an economy and the level of prices of goods and services sold. According to QTM, if the amount of money in an economy doubles, price levels also double, causing inflation (the percentage rate at which the level of prices is rising in an economy). The consumer, therefore, pays twice as much for the same amount of the good or service.

Another way to understand this theory is to recognize that money is like any other commodity: increases in its supply decrease marginal value (the buying capacity of one unit of currency). So an increase in money supply causes prices to rise (inflation) as they compensate for the decrease in money’s marginal value.

**The Quantity Theory’s Calculations**

In its simplest form, the theory is expressed as:

**MV = PT (the Fisher Equation)**

Each variable denotes the following:

M = Money Supply

V = Velocity of Circulation (the number of times money changes hands)

P = Average Price Level

T = Volume of Transactions of Goods and Services

The original theory was considered orthodox among 17th-century classical economists and was overhauled by 20th-century economists Irving Fisher, who formulated the above equation, and Milton Friedman. It is built on the principle of “equation of exchange”.

**Amount of Money x Velocity of Circulation = Total Spending**

Thus if an economy has US$3, and those $3 were spent five times in a month, total spending for the month would be $15.

**Assumptions** **of Quantity Theory**

- Velocity of money in circulation (V) remains constant
- Total volume of transactions or trade remains constant
- Price level (P) is a passive factor
- Money is a medium of exchange
- Long period

**Velocity of money in circulation (V) remains constant:**According to Fisher the velocity of money in circulation (V) remains constant and the changes in the quantity of money cannot influence it (V).**Total volume of transactions or trade remains constant**: Total volume of transactions or trade (T) too, remain constant or unchanged and is not affected by the changes in the quantity of money.**Price level (P) is a passive factor**: According to Fisher, the price level (P) is a passive factor in the equation of exchange which is affected by the other factors of the equation.**Money is a medium of exchange**: The quantity theory of money assumed that money is used only as a medium of exchange.**Long period**: The cash transactions approach to the quantity theory of money is based on the assumption of long period.

### Cambridge Theory

The Cambridge cash-balance approach was based on the store of value function of money. According to cash-balance approach, the demand for money and supply of money determine the value of money. This approach, considers the demand for money and supply of money at a particular moment of time. Since, at a particular moment the supply of money is fixed, it is the demand for money which largely accounts for the changes in the price level. As such, the cash-balance approach is also called the demand theory of money.

The Cambridge cash-balance approach considers the demand for money not as a medium of exchange but as a store of value. The actual demand for money comes from those who want to hold want to exchange it for goods and services. Thus, according to Cambridge cash-balance approach, the demand for money implies demand for cash balances. According to Cambridge cashbalance approach for the given supply of money at a point of time, the value of money is determined by the demand for cash balances.

**Marshall’s Equation**

The Marshallian cash-balance equation is expressed as follows :

**MV = KPY**

Where

M is the supply of money (currency plus demand deposits)

P is the price level

Y is aggregate real income

K is the fraction of the real income which the people desire to hold in the form of money.

The value of money (1/p) (or, the purchasing power of money), in terms of this equation, can be found out by dividing the total quantity of goods which the people desire to hold out of the total income (KY) by the total supply of money (M). thus,

**1/P=KY/M**

Similarly, the price level (P) can be found out by dividing the total money supply (M) by the quantity of goods which the people desire to hold out of the total income (KY). thus,

**P=M/KY**

**The Cash Balance Approach States that :**

- The price level (P) is directly proportional to the money supply (M)
- The price level (P) is indirectly proportional to the aggregate real income (Y) and the proportion of the real income which people desire to keep in the form of money (K)
- M and Y being constant, with the increase in K price level (P) falls and with the decreases in K price level (P) rises.
- K and Y remaining unchanged, if supply of money (M) increases, price level (P) rises and if supply of money (M) decreases, price level (P) falls.

**Pigou’s Equation**

Pigou’s cash balance equation is as follows:

1/P=KR/M

Where

P is the price level and 1/p is the purchasing power;

R is the total real income or the real resources;

K is the proportion of real income held by the people in the form of money; and

M is the total money supply.

Since money is held by the community in the form of cash and in the form of bank deposits, According to Pigou, K was more significant than M in explaining changes in the purchasing power of money (value of money). This means that the value of money depends upon the demand of the people to hold money. Moreover, assuming K and R to be constant, the relationship between money supply (M) and price level (P) is direct and proportional.

**Robertson’s Equation**

Robertson’s cash balance equation is as follows:

M = KPT

Where,

P is the price level;

M is the money supply;

T is the total amount of goods and services to be purchased during a year.

K is the proportion of T which people wish to hold in the form cash.

According to Robertson’s cash balance equation, P changes directly with M and inversely with K and T.

**Keyne’s Equation**

Keyne’s cash balance equation is as follows:

n=pk

p=n/k

Where

n is the cash held by the general public;

p is the price level of consumer goods;

k is the real balance or the proportion of consumer goods over which cash (n) is kept.

Assuming K to be constant, a change in ‘n’ causes a direct and proportional change in ‘p’. In other words, if the quantity of money in circulation is doubled the price level will also be doubled, provided k remains constant. In order to include bank deposits in money supply,

Keynes extended the equation as follows:

Where,

r is the cash reserve ratio of the banks.

k’ is the real balance held in the form of bank money.

Again, assuming k, k’ and r to be constant, a change in ‘n’ causes a direct and proportional change in ‘p’.

**Criticism of cash-balance approach:**

- Like Fisher’s transaction equation, MV = PT, the Cambridge equation, M = KPY, is also a simple truism.
- The cash-balance approach is based on the assumption that the demand for money has uniform unitary elasticity. (This means that an increase in the desire for holding cash balance (K) leads to equi-proportionate fall in the price level). This is an unrealistic assumption.
- The cash balance approach has not properly analyzed various motives for holding money. For example, it ignored the speculative motive for holding money which causes violent changes in the demand for money.
- A serious defect in the Cambridge equations (furnished by Pigou and Keynes) is that they seek to explain the value of money (or, the purchasing power of money) in terms of consumption goods only and ignored the investment goods altogether. Thus cash balance approach has unduly narrowed down the conception of the purchasing power of money.
- The cash-balance approach ignored the role of rate of interest in explaining the changes in the price level. The rate of interest has a definite influence on demand for money and, in turn, on the price level.
- The approach ignored the influence of real factors like, income, saving, investment, etc. on the price level.
- The cash balance approach ignored the real-balance effect which means that (i) An individual’s wealth is influenced by the changes in money balances and the price level; (ii) The changes in wealth further influence the expenditure on goods.
- The approach viewed the real income as the sole determinant of K. It has ignored the influence of price level, banking and business habits of the people, business integration, etc. on the value of K.
- The approach maintains that the value of money or the price level (P) is determined by K. But it has been pointed out that K not only influences P but K is also influenced by P.
- In terms of cash balance approach it is difficult to visualize, the extent to which prices and output will change as a result of a given change in the supply of money. Thus the approach lacks quantitative analysis.

**Superiority of Cambridge Quantity Theory of Money over Fisher’s Version**

The cash-balances approach represents an advance over the cash transactions approach in many respects:

- Humanistic Approach
- Better Mode of Thinking
- Integration of the Theory of Money with the General Theory of Value
- More Realistic Approach
- Foundation of Modern Theory of Interest and Demand for Money
- More Convenient Equation

**Humanistic Approach:**The Cambridge equations emphasize K or cash-balances and consider human motives as important factors affecting the price level, as opposed to the mechanistic nature of the cash-transactions equation. Fisher’s equation, on the other hand, is mechanistic in the sense that it does not explain how changes in the volume of money bring about alterations in the price level. The Cambridge equations attempt to bring out the causal factors involved; a change in the desire to hold money may bring about alterations in the price level, even without there being any change in the quantity of money.**Better Mode of Thinking:**The Cambridge version is concerned with the level of income as against Fisherian consideration of the total number of transactions. This notion has paved the way for a new mode of thinking in modern economics.**Integration of the Theory of Money with the General Theory of Value:**Fisher’s approach is only one-sided in the sense that it considers supply of money to be the only effective element in determining the value of money. The Cambridge equations, on the other hand, are stated in terms of supply and demand both following the general theory of value.**More Realistic Approach:**The cash-balances equation emphasizes the psychological factors or subjective valuations as chief determinants of the demand for money, in contrast to the Fisherian approach which stresses the institutional, objective and technological [factors only. Thus, the former is more realistic, because [the fundamental truth about money is that someone always holds it.**Foundation of Modern Theory of Interest and Demand for Money:**The cash-balances theory has sown the seeds of the Keynesian Liquidity Preference Theory of Interest as well as the modern concept of the demand for money. It points out two of the three liquidity motives, viz., the transactions and precautionary motives.**More Convenient Equation:**Kurihara states that the Cambridge equation P = KT/M is far better than the cash-transactions equation P = MV/T in explaining money value, because it is more convenient to know the amount of the cashbalances individuals hold relative to total expenditure than to know how much they spend for a multitude of transactions.

### Friedman Theory

As restated by Milton Friedman, the quantity theory emphasizes the following relationship of the nominal value of expenditures** PQ** and the price level **P** to the quantity of money M :

**(1) PQ=M**

(2) P=g(M)

The plus signs indicate that a change in the money supply is hypothesized to change nominal expenditures and the price level in the same direction (for other variables held constant).

Friedman described the empirical regularity of substantial changes in the quantity of money and in the level of prices as perhaps the most-evidenced economic phenomenon on record. Empirical studies have found relations consistent with the models above and with causation running from money to prices.

The short-run relation of a change in the money supply in the past has been relatively more associated with a change in real output **Q** than the price level **P** in (1) but with much variation in the precision, timing, and size of the relation. For the long-run, there has been stronger support for (1) and (2) and no systematic association of **Q** and **M**.

**The Theory above is based on the following hypotheses:**

- The source of inflation is fundamentally derived from the growth rate of the money supply.
- The supply of money is exogenous.
- The demand for money, as reflected in its velocity, is a stable function of nominal income, interest rates, and so forth.
- The mechanism for injecting money into the economy is not that important in the long run.
- The real interest rate is determined by non-monetary factors: (productivity of capital, time preference).

Milton Friedman (another Nobel Prize winner) developed a model for money demand based on the general theory of asset demand. Money demand, like the demand for any other asset, should be a function of wealth and the returns of other assets relative to money. His money demand function is as follows:

Where

Yp = permanent income (the expected long-run average of current and future income)

rb = the expected return on bonds

rm = the expected return on money

re = the expected return on stocks

pi(e) = the expected inflation rate (the expected return on goods, since inflation is the increase in the price (value) of goods.

Money demand is positively related to permanent income. However, permanent income, since it is a long-run average, is more stable than current income, so this will not be the source of a lot of fluctuation in money demand.

The other terms in Friedman’s money demand function are the expected returns on bonds, stocks and goods relative the expected return on money. These items are negatively related to money demand: the higher the returns of bonds, equity and goods relative the return on money, the lower the quantity of money demanded. Friedman did not assume the return on money to be zero. The return on money depended on the services provided on bank deposits (check cashing, bill paying, etc) and the interest on some checkable deposits.

**Friedman vs. Keynes**

When comparing the money demand frameworks of Friedman and Keynes, several differences arise

- Friedman considers multiple rates of return and considers the relative returns to be important.
- Friedman viewed money and goods and substitutes.
- Friedman viewed permanent income as more important than current income in determining money demand.

### Keynesian Equations

In monetary economics, the quantity theory of money is the theory that money supply has a direct, proportional relationship with the price level. For example, if the currency in circulation increased, there would be a proportional increase in the price of goods.

The theory was challenged by Keynesian economics, but updated and reinvigorated by the monetarist school of economics. While mainstream economists agree that the quantity theory holds true in the long run, there is still disagreement about its applicability in the short run. Critics of the theory argue that money velocity is not stable and, in the short-run, prices are sticky, so the direct relationship between money supply and price level does not hold.

Equation of exchange in its modern form, the quantity theory builds upon the following definitional relationship:

Where

**M** is the total amount of money in circulation on average in an economy during the period, say a year. **VT** is the transactions velocity of money, that is the average frequency across all transactions with which a unit of money is spent. This reflects availability of financial institutions, economic variables, and choices made as to how fast people turn over their money.

**Pi** and **Qi** are the price and quantity of the i-th transaction.**P** is a column vector of the **pi** , and the superscript T is the transpose operator.**Q** is a column vector of the **qi**.

Mainstream economics accepts a simplification, the equation of exchange:

**M.VT=PT.T**

Where

**PT** is the price level associated with transactions for the economy during the period**T** is an index of the real value of aggregate transactions.

The previous equation presents the difficulty that the associated data are not available for all transactions. With the development of national income and product accounts, emphasis shifted to national-income or final-product transactions, rather than gross transactions. Economists may therefore work with the form

**M.V=P.Q**

Where

**V** is the velocity of money in final expenditures.**Q** is an index of the real value of final expenditures.

As an example, **M** might represent currency plus deposits in checking and savings accounts held by the public, **Q** real output (which equals real expenditure in macroeconomic equilibrium) with P the corresponding price level, and **P.Q** the nominal (money) value of output. In one empirical formulation, velocity was taken to be “the ratio of net national product in current prices to the money stock”.

**Criticisms of Keynes Thesis of Money and Prices**

Keynes views on money and prices have been criticized by the monetarists on the following causes:

- Direct Association
- Stable Demand for Money
- Nature of Money
- Effect of Money

**Direct Association:**Keynes misguidedly took prices as unchangeable and that the effect of money materializes in his scrutiny in terms of quantity of goods exchanged somewhat than their average prices. That is why Keynes adopted an indirect mechanism through bond prices, interest rates and investment of the effects of fiscal variations on monetary performance. But the actual effects of monetary variations are direct somewhat than meandering.**Stable Demand for Money:**Keynes believed that monetary variations are largely absorbed by variations in the demand for money. But Friedman has depicted on the basis of his pragmatic examines that the demand for money is hugely invariable.**Nature of Money:**Keynes was unsuccessful in understanding the true nature of money. He assumed that money could be exchanged for bonds only. Actually, money can be exchanged for many diverse kinds of like wealth like bonds, physical assets, securities human wealth etc.**Effect of Money:**Because Keynes wrote for a depression period, this led him to conclude that money had little effect on earnings. According to Friedman, it was the retrenchment of money that impetuous the depression.