Cash Balance Theory

Cash Balance Theory | Income Theory, Criticisms

The Cash Balance Theory otherwise known as the Cambridge equation had its origin in Britain at about the same time that the transactions theory was reigning in America. The theory like the transactions approach is based on the supply and demand analysis even thought the definitions of these basic concept differ somewhat markedly.

To the Cash Balance Theory or theorist, the supply of money is simply the average quantity of money available in a given period of time. It is thus the quantity held in the cash balance of the people and at the same time necessary the quantity available for spending. The velocity of money is not explicitly recognized as an immediate determinant of the value of money.

Although the concept of velocity is admitted by the backdoor, the cash balance theorist do not multiply average quantity of money by the magnitude representing velocity to get the total supply of money. Rather they hold that the averaged quantity is total supply. Cash Balance Theory describe demand for money in terms of the decision of the people to retain the power to purchase certain volumes commodities, service and property rights.

As increase in the demand for money is thus found in the determination of the people to retain the power to purchase a larger quantity of the commodity, services and property rights than formerly and a decrease in the demand for money is found in their decision to retain the power to purchase a smaller in their of commodities, service and property rights than formerly.

Almost everybody decides to retain a cash balance so that he may have available the power to purchase a  certain quantity of goods in the future. A worker who earns wages of $4000 per month does not ordinarily spend the entire amount immediately on receiving it. Early in the month, he probably retains most of it as a cash balance and spends it. Little by little as the month progresses to the end.

Business men, banks, government bodies, individuals and organizations also find it highly desirable to maintain to guarantee the solvency of the holder. At other times it is because the holder plans to use them in acquiring commodities, services and property rights in the future.

At any given amount or moment therefore, the aggregate of the cash balance of wages earners, businessman, government bodies and other individuals and organisation, represent the quantity of commodities, services and property rights over which the people of the nation as a whole desire to retain purchasing  power.

Let T represent the total quantity of these items that will be bought in a given time period say one year. The Cash Balance Theory or the cash balance school then introduced a symbol K to stand for that proportion of the year’s volume of trade over which the people hence the demand for money is given as KT.

Using M to stand for average quantity of money available and P as an average of the prices of commodities, services property rights, the cash balance theorist constructed their equation as;


The equation like transaction theory of equation is a truism because it states an obvious fact. It merely tells us that purchasing power of the available quantity of money held as cash balance is equal to the commodity, service and property right over which the people retains purchasing power. In conclusion they postulate, that based on the equation and other things being equal the general price level varies in direct proportion to the supply of money and in inverse proportion to the demand for money. So that once more;

We have – M/KT = P

M is the numerator of the fraction and KT the demand for money as the denominator. If KT remains uncharged and M increases, P will also increase while if KT increase and M remains unchanged, the factor P will fall.

Cash Balance Theory Criticism

The assumption of the advanced by the Cash Balance Theory or the cash balance school does not hold because nothing remains constant. For instance an increase in K may be offset by an increase in M or an increase in T may be partially or wholly offset by decrease in K o decrease in T may wholly or partially offset by a decrease in M. Other combinations of changes are possible. Due to the size of cash balance and the demand for purchasing power, the Cash Balance Theory holds that the total quantity of money available is equal to the total quantity that people decide to hold as cash.

For instance if $900,000 is in circulation, the people must have that amount in their cash balance. They can have neither more nor less. If only $900,000 is in circulation, how can total cash balances amount to more than $900,000, in essence how can demand for money exceed $900,000. The difficulty suggested by this question arises because of a failure to think of the demand for money as a demand for purchasing power over specific quantity of money or commodities, services and property rights, for it is possible for the people regardless of the quantity of money available to decide to retain the power to purchase larger or smaller quantities of commodities than they have retained previously.

In some, therefore, a change in the demand for money is reflected not in an increase or decrease in the quantity of money held cash balances, but in a change in the purchasing power of the total cash balances. Changes in the demand for money are translated into changes in the general price level through the actions of people take in order to retain purchasing power over larger or smaller quantities of goods if the demand for money is increasing , the buyers of goods are less willing to give money for goods and the sellers are most anxious than before to exchange their goods for money.

The reduced demand for goods and the increased supply of the same, cause the general price level to fall. And though the total quantity of money available is not affected  the objective of holding purchasing power over large  quantities of goods is achieved. If the demand for money is decreasing buyers who have money in their possession are more willing to offer money in exchange for good while the sellers are anxious to exchange their goods for money.

This situation means an expansion in the demand for goods and a reduction in the supply. The result is a rising price level hence the purchasing powers of the cash balances fall although there is no need for a charge in the size of the cash balances.

Relationship Between K and V In The Two Schools

Why do people make decisions to retain more or less purchasing power than they retain before

People are less anxious to hold purchasing power, in essence;

  1. More willing to spend, if they expect prices to rise
  2. If they feel secures in their jobs
  3. If they find an abundance of favorable investment opportunities
  4. If they can borrow readily to meet extra ordinary expenditures,
  5. If their income is received regularly etc

But they are more anxious to hold purchasing power, in essence less willing to spend if they anticipate that prices will fall, if they are afraid of losing their jobs. If they think that holding of money is better investment and if they find it difficult to obtain loans etc.

But these are the very factor that we had identified the determinants of the velocity of money. IF K and V are determined by exactly the same forces, they must necessarily be closely related. In fact they must amount to the same thing different expressed, in short each is a reciprocal of the other

Transaction Theory


V = PT/M

K=I/V……. V= I/K from both sides of the equation

Cash Balance Theory


M/PT = K

Income Theory (Cash Balance Theory)

Many monetary theorist prefer to cast the transactions and cash balance theorist in terms of transactions in newly produced goods and services and decision to hold cash sufficient to buy given quantities of commodities and services currently being produced or to be produced in the future.

It is their contention that changes in the value of money influence the tempo of economic activity, this influence  services from its purchasing power over new goods and not in any significant way from its purchasing power over existing houses, firms, factory buildings, used cars and other second hand equipment, stocks and bonds etc.

If prices rise because people are increasing their spending for new goods currently being produced. And if idle factors of production are available, entered prize will surely be inclined to hire these factors and expand output to meet the increase demand, but if people increase spending for existing houses, used book, and used car and second hand facilities of other kinds with resulting increase in the prices of these goods, enterprise receive no direct stimulus to expand output.

Moreover the prices of used card will generally depend on the prices of new cars. The prices of old buildings will depend on the cost of new constructions. The prices of securities upon the sales of corporate enterprises from current production etc.

Mvy = PyTy

Where ……………….. M = Money

Vy = Income velocity

Py = Prices index for all final goods produced in the period (current productions)

Ty = Physical volume of final goods currently produced in the period

By a process of transformation

Pv = MVy/Ty

The argument of the income theorist as against the Cash Balance Theory is that if Mvy is increased while output, Ty remains unchanged, Py will increase. And if the output Ty increased while Mvy remains unchanged< Py will fall. With exposition, the income school tried to postulate that time own proposition is theoretically better than that of the transaction and cash balance schools. The reason include that the data needed to fill in the equations above can be obtained thus;

PyTy = GNP

M = Money supply from Central bank

VY = Ratio of GNP to the average estimated money in circulation during the same period.

These they say cannot obtain in the transaction approach because it will be difficult under that system to determine the volume of trade. Thus in designing a policy, the policy is at pains over what data to use.

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