Cambridge Equation or Cash Balance Approach
Cambridge Equation or cash balance approach
There are two main lines of approach to the problem of relationship between the quantity of money and its value (or the price-level). This has given rise to two types of quantity theories. One is the Quantity Theory of Money proper, called the transactions type theory and which is represented by Fisher's Equation. This approach has been more popular in the U.S.A. The other approach, known as the cash balance type, which has been more popular in Europe, especially England, is represented by the Cambridge Equation.
The latter is an improvement on the former Quantity Equation in the sense that it is based on the National Income approach and takes into account the concept of liquidity, both of which form part of Keynesian Economics.
As mentioned above, the Cambridge Equation represents what has been called the cash-balance approach to the value of money. It simply says that the value of money depends on demand for cash-balance and the supply thereof, at any given time. Here we need draw attention to one point on the demand side. The demand for money does not merely depend on the physical quantity of resources or of the goods and services, which are sought to be exchanged, but it largely depends on the period of time which the transactions are intended to cover. Take the case of a consumer of wheat. Is it necessary for him to purchase his whole year's requirement of wheat at once or, what comes to the same thing, keep sufficient liquid cash to buy the whole year's requirement? No, it is unnecessary. Few consumers will do that unless they happen to be foolish. A consumer may decide to buy wheat from month to month. It will then be necessary for him to keep cash equal to 1/12 of his total requirement of wheat for the year. Similarly, he will keep liquid funds just enough to enable him to purchase his requirements of other goods and services for a certain period only and not for the whole year.
If the members of a community are in the habit of keeping cash to cover their purchases over a longer period, obviously their demand for cash will be greater. Only a fraction of the whole income is kept in cash, the rest is invested. The amount of cash held should not be too much, because to keep cash locked up idly means a loss besides being a danger, although a large cash balance makes business smooth and easy, nor should be amount of cash held be too small, because it may be risky from the business point of view.
An individual has thus to keep only a fraction of his income in titles to legal tender (i.e., liquid cash) to carry on his business smoothly and to guard against emergencies. Let this fraction be denoted by k.
The equation is usually put in the form:
Where M is the quantity of money and is the same as M of Fisher's Equation of Exchange. R is the real national income, i.e., it is the sum total of goods and services finally brought to the market and sold for money, e.g., cotton is not part of R but a suit of clothes made by a tailor is a part of R. Similarly, wheat is not included in R but bread is.
p is the average price-level of the real national income. That is, it is the average of prices of clothes, food, shelter and other goods and services consumed by the public.
Thus, pR is the monetary national income.
Now a proportion of the monetary national income is held by the Community in cash. This proportion is k and represents the desire of the public to have liquid resources. This is called the liquidity factor for buying it. If all money circulated only once, then the amount of money required would be the same as the monetary national income. If money circulated twice in a year, then obviously half pR will be required to purchase the national product, i.e., to create the monetary national income which is shown as pR above. The number of times money circulates for buying the national product in a year is V1 i.e., Home velocity of circulation of money; k is the proportion of the monetary national income which the community desires to hold in cash. pR then is the demand for money for purchasing the national product. This must be equal to the money supply.
M X velocity of circulation of money = MV.
M=kpR where K= I/ V1
We have seen that in the Fisher's Equation of Exchange in its simplest form
M= PT/ Vt
By Cambridge Equation M= kpR
Now as k= I/ V1
M= I* pR/ V1
The differences between the two equations are as follows: —
(i) T in the Fisher Equation is the sum total of all transactions, whereas R is only the final product which comes to the market. For example, Fisher will include in T the transactions of production and sale of cotton, sale of yarn, sale of cloth and finally sale of tailored clothes, whereas R includes only the goods finally brought to the market, e.g., tailored clothes.
(ii) Similarly, Pin the first equation is the average of the price level of each good and service at each stage of production and includes the average price-level of all transactions, p in the Cambridge Equation is the price-level of only the good finally brought to the market. They may tend to move up and down in the same direction, but are not the same.
(iii) The meaning of V and V1 i.e., velocity of circulation, also differs between them. In the Fisher Equation it takes the form Vt i.e., Transactions Velocity of circulation. It represents the number of times a unit of money circulates for performing all the transactions taking place in the economy in a year. V., on the other hand, is only Income Velocity of circulation and represents the number of times a unit of money circulates for buying the final national product.