# Quantity Theory of money (Fisher’s): Assumptions and Criticism

Recently updated on April 13th, 2023 at 05:58 pm

The demand for money refers to how much assets individuals wish to hold in the form of money (as opposed to illiquid physical assets.) It is sometimes referred to as liquidity preference. The demand for money is related to income, interest rates and whether people prefer to hold cash(money) or illiquid assets like money.

Money performs two important functions:

(i) Medium of exchange

(ii) Store of value

It is due to these two functions that money is considered as indispensable by the society. Therefore, demand for money is a derived demand. Demand for money is a very crucial concept as the value of money depends on the demand for money. There are different concepts of the demand for money.

Classical View of Money

The Classical economists viewed that money does not have any inherent utility of its own but is demanded for transaction motive. Money serves as a medium of exchange. Irving Fisher’s version of the quantity theory of money which he developed in his book “Purchasing Power of Money” is the most famous version and represents the Classical approach to the analysis of the relationship between the quantity of money and the price level.

With V and T remaining constant, P changes proportionately to the changes in M, such that if M is doubled, P is also doubled but the value of money is halved.

Limitations

1. It does not explain how a change in M changes P
2. P is regarded as a passive factor which is unrealistic
3. Not only M determines P but also P determines M.

Quantity Theory of Money

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 development 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.

Quantity Theory of Money Fisher’s Version:

Like the price of a commodity, value of money is determinded by the supply of money and demand for money. In his theory of demand for money, Fisher attached emphasis on the use of money as a medium of exchange. In other words, money is demanded for transac­tion purposes.

As a truism, in a given time period, total money expenditure is equal to the total value of goods traded in the economy. In other words, national expenditure, i.e., the value of money, must be identically equal to national income or total value of the goods for which money is exchanged, i.e.,

MV = ∑ piqj = PT ….(4.1)

where

M = total stock of money in an economy;

V = velocity of circulation of money, that is, the number of times a unit of money changes its hand;

Pi = prices of individual goods;

∑P = p1q1 + p2q2 + … + pnqn are the prices and outputs of all individual goods;

qi = quantities of individual goods transacted;

P = average or general price level or index of prices;

T = total volume of goods transacted or index of physical volume of trans­actions.

This equation is an identity that always holds true: It tells us that the total stock of money used for transactions must equal to the value of goods sold in the economy. In this equation, supply of money consists of nomi­nal quantity of money multiplied by the ve­locity of circulation.

The average number of times that a unit of money changes its hand is called the velocity of circulation of money. The concept that provides the link between M and P x T is also called the velocity of money. V is, thus, defined as total expenditure, P x T, di­vided by the amount of money, M, i.e.,

V = P x T/M

Quantity Theory of Money: Cambridge Version

An alternative version, known as cash balance version, was developed by a group of Cam­bridge economists like Pigou, Marshall, Robertson and Keynes in the early 1900s. These economists argue that money acts both as a store of wealth and a medium of exchange. Here, by cash balance and money balance we mean the amount of money that people want to hold rather than savings.

According to Cambridge economists, people wish to hold cash to finance transactions and for security against unforeseen needs. They also sug­gested that an individual’s demand for cash or money balances is proportional to his in­come. Obviously, larger the incomes of the individual, greater is the demand for cash or money balances.

Thus, the demand for cash balances is specified by:

Md = kPY …(4.6)

where Y is the physical level of aggregate or national output, P is the average price and k is the proportion of national output or income that people want to hold. Let us assume that the supply of money, MS’ is determined by the monetary authority, i.e.,

MS = M …(4.7)

Equilibrium requires that the supply of money must equal the demand for money, or

k and Y are determined independently of the money supply. With k constant given by the transaction demand for money and Y constant because of full employment, increase or de­crease in money supply leads to a proportional

increase and decrease in price level. This con­clusion holds for Fisherian version also. Note that Cambridge ‘k’ and Fisherian V are reciprocals of one another, that is, 1/k is the same as V in Fisher’s equation.

The classical relationship between money supply and price level can be illustrated in terms of Fig. 1. This diagram is interesting in the sense that it first establishes the rela­tionship between money supply and national output or national income below the full em­ployment stage (YF). For this relationship, the origin ‘O’ is important.

Now the relationship between money supply and price level after the full employment stage can be established assuming O’ as the origin. Before the attain­ment of full employment state (YF), an increase in money supply (from OM1 to OM2 and to OYF) causes national income (shown by the steep output curve) to rise more rapidly than the price level.

By utilising its resources effi­ciently and fully, an economy can increase its output level by increasing the volume of in­vestment consequent upon an increase in money supply. Since there is a limit to output expansion due to full employment (i.e., be­yond which output will not increase), an in­crease in money supply from (M3 to M4) will cause price level to rise from (P3 to P4) pro­portionally (shown in the upper panel).

For stability in price level money supply should grow in proportion to increases in out­put.

Assumptions of the Theory:

Fisher’s theory is based on the following assumptions:

1. P is passive factor in the equation of exchange which is affected by the other factors.
2. The proportion of M’ to M remains constant.
3. V and V are assumed to be constant and are independent of changes in M and M’.
4. T also remains constant and is independent of other factors such as M, M, V and V.
5. It is assumed that the demand for money is proportional to the value of transactions.
6. The supply of money is assumed as an exogenously determined constant.
7. The theory is applicable in the long run.
8. It is based on the assumption of the existence of full employment in the economy.

Criticisms of the Theory:

1. Truism:

According to Keynes, “The quantity theory of money is a truism.” Fisher’s equation of exchange is a simple truism because it states that the total quantity of money (MV+M’V’) paid for goods and services must equal their value (PT). But it cannot be accepted today that a certain percentage change in the quantity of money leads to the same percentage change in the price level.

1. Other things not equal:

The direct and proportionate relation between quantity of money and price level in Fisher’s equation is based on the assumption that “other things remain unchanged”. But in real life, V, V and T are not constant. Moreover, they are not independent of M, M’ and P. Rather, all elements in Fisher’s equation are interrelated and interdependent. For instance, a change in M may cause a change in V.

Consequently, the price level may change more in proportion to a change in the quantity of money. Similarly, a change in P may cause a change in M. Rise in the price level may necessitate the issue of more money. Moreover, the volume of transactions T is also affected by changes in P. When prices rise or fall, the volume of business transactions also rises or falls. Further, the assumptions that the proportion M’ to M is constant, has not been borne out by facts. Not only this, M and M’ are not independent of T. An increase in the volume of business transactions requires an increase in the supply of money (M and M’).

1. Constants Relate to Different Time:

Prof. Halm criticises Fisher for multiplying M and V because M relates to a point of time and V to a period of time. The former is a static concept and the latter a dynamic. It is therefore, technically inconsistent to multiply two non-comparable factors.

1. Fails to Measure Value of Money:

Fisher’s equation does not measure the purchasing power of money but only cash transactions, that is, the volume of business transactions of all kinds or what Fisher calls the volume of trade in the community during a year. But the purchasing power of money (or value of money) relates to transactions for the purchase of goods and services for consumption. Thus the quantity theory fails to measure the value of money.

1. Weak Theory:

According to Crowther, the quantity theory is weak in many respects. First, it cannot explain ’why’ there are fluctuations in the price level in the short run. Second, it gives undue importance to the price level as if changes in prices were the most critical and important phenomenon of the economic system. Third, it places a misleading emphasis on the quantity of money as the principal cause of changes in the price level during the trade cycle.

Prices may not rise despite increase in the quantity of money during depression; and they may not decline with reduction in the quantity of money during boom. Further, low prices during depression are not caused by shortage of quantity of money, and high prices during prosperity are not caused by abundance of quantity of money. Thus, “the quantity theory is at best an imperfect guide to the causes of the trade cycle in the short period” according to Crowther.

1. Neglects Interest Rate:

One of the main weaknesses of Fisher’s quantity theory of money is that it neglects the role of the rate of interest as one of the causative factors between money and prices. Fisher’s equation of exchange is related to an equilibrium situation in which rate of interest is independent of the quantity of money.

1. Unrealistic Assumptions:

Keynes in his General Theory severely criticised the Fisherian quantity theory of money for its unrealistic assumptions. First, the quantity theory of money for its unrealistic assumptions. First, the quantity theory of money is unrealistic because it analyses the relation between M and P in the long run. Thus it neglects the short run factors which influence this relationship. Second, Fisher’s equation holds good under the assumption of full employment. But Keynes regards full employment as a special situation. The general situation is one of the under-employment equilibrium. Third, Keynes does not believe that the relationship between the quantity of money and the price level is direct and proportional.

Rather, it is an indirect one via the rate of interest and the level of output. According to Keynes, “So long as there is unemployment, output and employment will change in the same proportion as the quantity of money, and when there is full employment, prices will change in the same proportion as the quantity of money.” Thus Keynes integrated the theory of output with value theory and monetary theory and criticised Fisher for dividing economics “into two compartments with no doors and windows between the theory of value and theory of money and prices.”

1. V not Constant:

Further, Keynes pointed out that when there is underemployment equilibrium, the velocity of circulation of money V is highly unstable and would change with changes in the stock of money or money income. Thus it was unrealistic for Fisher to assume V to be constant and independent of M.

1. Neglects Store of Value Function:

Another weakness of the quantity theory of money is that it concentrates on the supply of money and assumes the demand for money to be constant. In order words, it neglects the store-of-value function of money and considers only the medium-of-exchange function of money. Thus the theory is one-sided.

1. Neglects Real Balance Effect:

Don Patinkin has critcised Fisher for failure to make use of the real balance effect, that is, the real value of cash balances. A fall in the price level raises the real value of cash balances which leads to increased spending and hence to rise in income, output and employment in the economy. According to Patinkin, Fisher gives undue importance to the quantity of money and neglects the role of real money balances.

1. Static:

Fisher’s theory is static in nature because of its such unrealistic assumptions as long run, full employment, etc. It is, therefore, not applicable to a modern dynamic economy.

1. Keynesian Quantity theory of Money

Keynes believed that changes in the money supply affect aggregate demand because of the relationship between the rate of interest and planned invest­ment. The link remains on the basis of how today’s Keynesians view the impact of monetary changes on GNP.

The Keynesians’ view of the transmission of changes in the money supply can be stated thus:

An increase in money supply lowers the interest rate. Thus planned investment increases. This causes the aggregate expenditure (C+I+G) sched­ule to shift up. This addition to aggregate expenditure increases equilibrium GNP by shifting the aggregate derived expenditure (C+I+G) schedule to the right.

1. Friedman Quantity Theory of Money

Friedman in his essay, “The Quantity Theory of Money—A Restatement” published in 1956 beautifully restated the old quantity theory of money. In his restatement he says that “money does matter”. For a better understanding and appreciation of Friedman’s modern quantity theory, it is necessary to state the major assumptions and beliefs of Friedman.

First of all Friedman says that his quantity theory is a theory of demand for money and not a theory of output, income or prices.

Secondly, Friedman distinguishes between two types of demand for money. In the first type, money is demanded for transaction purposes. It serves as a medium of exchange. This view of money is the same as the old quantity theory. But in the second type, money is demanded because it is considered as an asset. Money is more basic than the medium of exchange. It is a temporary abode of purchasing power and hence an asset or a part of wealth. Friedman treats the demand for money as a part of the wealth theory.

Thirdly, Friedman treats the demand for money just like the demand for any durable consumer good.

The demand for money depends on three factors:

(a) The total wealth to be held in various forms

(b) The price or return from these various assets and

(c) Tastes and preferences of the asset holders.

Friedman considers five different forms in which wealth can be held, namely, money (M), bonds (B), equities (E), physical non-human goods (G) and human capital (H). In a broad sense, total wealth consists of all types of “income”. By “income” Friedman means “aggregate nominal permanent income” which is the average expected yield from wealth during its life time.

The wealth holders distribute their total wealth among its various forms so as to maximise utility from them. They distribute the assets in such a way that the rate at which they can substitute one form of wealth for another is equal to the rate at which they are willing to do.

Accordingly the cost of holding various assets except human capital can be measured by the rate of interest on various assets and the expected change in their prices. Thus Friedman says there are four factors which determine the demand for money. They are: price level, real income, rate of interest and rate of increase in the price level.

Friedman’s quantity theory of money can be explained diagrammatically in the following figure (fig.2)

In the figure while the X-axis shows the demand and supply of money, Y-axis measures the income level. MD is the demand curve for money which changes along with income. MS is the supply curve for money. These two curves intersect at point E and the equilibrium income level OY is determined. If there is an increase in money supply, the supply curve shifts to M1S1. At this level the supply is greater than demand and a new equilibrium is established at E1. At the new equilibrium level the income increases to OY1.

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