#### Cambridge Equations in Cash Balance Approach:

The cash balance version of the quantity theory of money, though found in earlier writings of Locke, Petty and Cantillon became popular only in the twentieth century.

Following the lead of Dr. Marshall, some Cambridge economists, specially Pigou, Robertson, Keynes including R.G. Hawtrey, popularized and adhered to a slightly different version of the quantity theory of money, known as the cash balance approach, on account of its emphasis on cash balance (instead of transactions).

According to cash-balance approach, the value of money depends upon the demand for money. But the demand for money arises not on account of transactions but on account of its being a store of value. Money has two characteristics—flatness and roundness—money sitting and money on wings— to serve as a store of value and as a medium of exchange. “In the one use money piles up, in the other it runs round.”

Thus, according to the advocates of this theory the real demand for money comes from those who-want to hold it on account of various motives and not from those who simply want to exchange it for goods and services: just as the real demand for houses comes from those who want to live in them and not from those who simply want to construct and sell them.

The cash balance approach relates the process of determination of the value of money to cash the subjective valuations of individuals who are the real force behind all economic activities. Such an approach enables us to throw more light on the somewhat puzzling phenomenon of the velocity of circulation of money, by enquiring more deeply into the nature of the demand for money, as the demand for the money in the cash-balance approach has reference to the store of value function of money.

This type of demand for money arises from the fact that holding of money has great utility, as when it is held (hoarded) it acquires wealth value. Hence, instead of interpreting the ‘demand for money’ with reference to its ‘medium of exchange’ function as is done in the transactions approach; it is interpreted with reference to the ‘store of value’ function of money in the cash balance. It is, thus, the demand for ‘money sitting’ rather than money ‘on wings’ that matters.

It may, however, be made clear that in determining the amount of these cash balances the individuals and institutions are guided only by their real value. Thus, an individual is concerned with the extent of his liquid command over real resources. The community’s total demand of money balances constitutes a certain proportion of its annual real national income which the community seeks to hold in the form of money (liquid cash).

The community’s demand for real cash balances in this sense varies from time to time. Thus, given the state of trade (T) and the volume of planned transactions over a period of time, the community’s total demand for real money balances can be represented as a certain fraction (K) of the annual real national income (R). The following lines from Marshall explain clearly the substance of the cash-balance version of the quantity theory, “In every state of society there is some fraction of their income which people find it worthwhile to keep in the form of currency; it may be a fifth or a tenth or a twentieth.”

Holding of money involves a sacrifice because when we hold (save), we spend less. To have too little holding of money may mean inconvenience, to have too much may mean unnecessary stinting. Somewhere between the two extremes every person, every family, every community fixes the amount of money it will keep. “It is convenient to think of this amount as given proportion of the person’s or the family’s or the community’s annual income.”

Whatever this proportion may be, it is always the result of a deliberate decision; none of us has the money holding, we have, quite by accident. This is, in the most real sense, the demand for money. Suppose at one time people want to possess cash balances worth one-tenth of the annual income. Now, they want to have cash balances representing one-seventh of the national income. This means they want to have more cash with them, which is possible only by curtailing expenditure on goods and services, which, in turn, means less demand for them and hence a fall in their prices. Similarly, if they want to have less cash balances, they will spend more and the prices will be pushed up.

Thus, according to cash balance approach, the value of money depends upon the demand for money to be kept as cash. If one puts the problem as one of the amount of money an individual will choose to hold, the framework of this approach that suggests itself is one in which constraints and opportunity costs are the central factors, interacting with individual’s tastes.

As far as the Cambridge approach is concerned, the principal determinant of people’s taste for money holding is the fact that it is a convenient asset to have, being universally acceptable in exchange for goods and services. The more transactions an individual has to undertake the more cash will be he want to hold.

To this extent the approach is similar to Fisher’s, but the emphasis is on want to hold, rather than on have to hold. This is the basic difference between the Cambridge monetary theory and Fisher’s framework. The essence of this theory is that the demand for money, in addition to depending on the volume of transactions that an individual might be planning to undertake, will also vary with the level of his wealth, and with the opportunity cost of holding money, the income foregone by not holding other assets.

Let us illustrate it with an example:

(i) Suppose money supply in cash and bank deposits (M) = Rs. 1,000.

(ii) The total annual national income (R) = 10,000 units.

(iii) The goods (income) which the community wants to hold in money (K), say one-fifth of R = 2,000 units

(iv) Then, the value of money (one rupee) = 2,000 units = (KR/M) = two units of goods, or prices level P = (M/KR) = 1/2 = 0.50 paise per unit. It is, therefore, clear that the value of money (its purchasing power) is found by dividing the total amount of goods, which the community wants to hold out of the total income (KR), by the amount of the supply of the money held by the public (M), and the price level (P) is found out by dividing the money supply (M) by the amount of goods which the community wants to hold (KR), as the price level is the opposite of the value of money.

Pigou expresses it in the form of an equation:

P = KR/M or (M/KR) where P stands for the value of money or its inverse the price level (M/KR), M represents the supply of Money, R the total national income and K represents that fraction of R for which people wish to keep cash.

Prof. D.H. Robertson’s equation is similar to that of Prof. Pigou’s with a little difference. Prof. Robertson’s equation is:

M = PKT or P = M/KT

where P is the price level, T is the total amount of goods and services (like R of Pigou), K represents the fraction of T for which people wish to keep cash. Prof. Robertson’s equation is considered better than that of Pigou as it is more comparable with that of Fisher. It is the best of all the Cambridge equations, as it is the easiest.

#### Superiority of Cash Balances Version:

Cash balances version of the quantity theory of money is superior to Fisher’s version of the quantity theory of money on the following grounds:

(i) The cash balances version lays stress on the subjective valuations and human motives which are the basis of all economic activities in sharp contrast to the highly mechanical nature of the concept of velocity in Fisher’s equation.

(ii) The Cambridge version of the theory brings to light a new element, namely, the level of income, changes therein and in its velocity. Instead of being concerned with the total transactions it is concerned with the level of income, which, in turn, determines the level of economic development, employment and price level. As a matter of fact, the problem of price level cannot be studied without a reference to changes in income and output. Moreover, it is not the velocity of money which matters but the velocity of circulation of money due to changes in income that matters.

(iii) The cash balances equation brings to light the demand for money to hold. This emphasis on the demand side is in sharp contrast with traditional emphasis on the supply side. Actually, the Cambridge equation was put forward to validate the classical quantity theory of money according to which the supply of money is the sole determinant of the price level.

(iv) The cash balances approach links itself with the general theory of value, since it explains the value to money in terms of the demand for and supply of money. The equation P = M/KT is a more useful device than the transaction equation P = MV/T , because it is easier to know how large cash- balances individuals hold than to know how much they spent on various types of transactions.

(v) The cash balances approach has given rise to the famous liquidity preference theory, which has become an integral part of the theory of income, output and employment.

(vi) Cash balances approach brings out the importance of k. An analysis of the factors responsible for fluctuations in k offered scope for the study of many important problems like uncertainty, expectations, rate of interest etc. which are not considered in the transactions approach. The symbol k reflects the desire for liquidity. A shift in k in the direction of an increased desire for liquidity shows a fall in demand for goods, i.e., a movement away from goods to money resulting in the revision of production plans, curtailment of output and fall of income.

Professor Robertson establishes the superiority of cash-balances approach in the words as:

“Broadly speaking, the sitting money exercise is more useful for enabling us to understand the underlying psychological forces determining the value of money; while the money on the wing exercise is more useful for equipping us to watch with understanding the actual processes by which in real life prices of goods and services change for reminding us that the quantity of money and the quantity of goods do not affect the price level by some kind of occult planetary influence, but by modifying the capacity or willingness of human beings to buy or refrain from buying, to sell or refrain from selling. But in any case we have not reached the end of our task’.”

#### Criticism of the Cash Balances Version:

Despite the superiority of the Cambridge version, it suffers from many shortcomings.

(i) Although this approach was evolved and popularized by Keynes, the theory does not to take into consideration various motives for holding money. Cambridge approach to the quantity theory ignored the speculative demand for money which turned out to be one of the most important determinants for holding money. Ignoring the speculative demand for money meant that the linkage between the theories of the rate of interest and the level of income through the demand for money was not complete.

(ii) Although Cambridge equation brought into the picture the level of income, yet it ignored other elements, like productivity, thrift, liquidity preference—all necessary in a comprehensive theory of the value of money.

(Hi) Cambridge approach like Fisher’s approach also assumes K and T as given, thus, it becomes subject to those criticisms, which were leveled against Fisher’s approach.

(iv) The Cambridge approach does not furnish an adequate monetary theory which could be utilized to explain and analyse the dynamic behaviour of prices in the economy, as it does not tell us by how much price and output shall change as a result of a given change in money supply in short period.

(v) The cash balances approach fails to assign an explicit role to the rate of interest thereby creating an impression that changes in the supply of money are directly related to the price level. A realistic theory of prices can hardly ignore the vital role of the rate of interest.

(vi) By assuming that an increased desire for holding cash balance leads, pari passu, to a fall in the price level to the same extent, the theory is assuming the elasticity of demand for money to be unity. Unitary elasticity of demand for money means that a 10 percent increase in the demand for cash balances (money) diminishes the price level by 10 per cent. This is true only when the stock of money and the volume of goods and services remain constant. The volume of goods and services which money buys is bound to change with variations in the money supply. Hence, the elasticity of demand for money cannot be assumed to its unity except in a stationary state.

(vii) The theory cannot explain the phenomenon of trade cycle, i.e., why prosperity follows depression and vice versa. Moreover, the theory deals with the purchasing power of money in terms of consumption goods only.