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Different Variants of Cash Balance Equation (Note-Compiled from Internet for Teaching Purpose )

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Different Variants of Cash Balance Equation (Note-Compiled from Internet for Teaching Purpose ) Different Variants of Cash Balance Equation (Note-Compiled from internet for teaching purpose ) There are various forms of cash balance equation. Important ones are described as follows: Marshall’s Equation: Dr. Marshall has explained the value of money through the M = kY below mentioned equation: (Here, M : quantity of money, Y: monetary income, K: that part of the income which people want to keep as cash) Because monetary income (Y) is the product of gross production (O) and price level (P), i.e., Y = PXO. Hence, the above equation may be written as follows: M = POk or P =M/Ok Pigou’s Equation: Pigou’s equation is as follows: P = kR M (Here, M: total quantity of money, R: gross actual income, k: That part of actual income which people want to keep as cash.) Value of money is inverse of the general price level. In Fig. 12.2, demand and supply of money is shown on axis OX and value of money is shown on axis OY. DD is the demand curve of money. Q1M1; Q2M2; Q3M3 are supply curves of money. At a specified point oftime, supply of money is constant; hence it is represented through a straight line. When supply of money increases from OM1 to OM2, then, value of money decreases from OP1 to OP2. Reduction in value of money is in proportion to increase in supply of money. In the same way, when supply of money increases from OM2 to OM3, value of money decreases from OP2 to OP3. Still in reference to change in value of money, Pigou has given more importance to K as compared to M. i.e., in comparison to supply of money, demand for money is considered to be a more important determinant of value of money. D.H. Robertson gave an equation similar to that of Pigou but with a slight difference. He stated: P = M/KT (Here, P: Price level, M: Quantity of Money; T: quantity of goods and services bought at a specified point of time; k: that part of T which people want to keep as cash) Robertson’s equation is considered to be better than Pigou’s equation because it is easy. The similarities between the Fisherian and the Cambridge approaches are discussed below: 1. Similar Equations: Robertson’s cash-balance equation, P = M/KT is quite similar to that given by Fisher; P = MV/T. Both the equations use the same symbols with same meanings. The only difference lies in V and K which are, in fact, reciprocal to each other; V refers to rate of spending and K refers to the extent of holding or not spending. It means when people want to hold more money (higher the K), they want to spend less or the velocity of circulation of money will be less (lower the V). Thus, by substituting 1/V for K and 1/K for V, the two equations can be reconciled. 2. Same Conclusions: Both the approaches lead to the same conclusions, i.e., the price level or the value of money depends upon the money supply. In other words, there is direct proportionate relationship between the money supply and the price level and inverse proportionate relationship between money supply and the value of money. If the money supply is doubled, the price level is also doubled and the value of money is halved. 3. Same Phenomenon of Money: MV of Fisher’s equation, M of Robertson’s and Pigou’s equation, all refer to the same thing, i.e., the total supply of money. 4. V and K-Two Sides of the Same Phenomenon: Fisherian and Cambridge approaches are not fundamentally different from each other because they represent two sides of the same phenomenon. The Fisherian approach emphasises money as a stock, while the Cambridge approach stresses money as flow. Dissimilarities between the Two Approaches: In spite of similar conclusions and implications of the two approaches, they have some notable differences. Important dissimilarities between the two approaches are discussed below: 1. Relative Stress of Supply and Demand for Money: Fisher’s approach stresses the supply of money, whereas, the Cambridge approach lays more emphasis on the demand for money to hold cash. 2. Definition of Money: The two approaches use different definitions of money. The Fisherian approach emphasises the medium of exchange function of money, whereas the Cambridge approach stresses the store of value function of money. 3. Flow and Stock Concepts: The Fisherian approach regards money as a flow concept; money is considered in terms of flow of money expenditures. The Cambridge version regards money as a stock concept; money supply refers to a given stock at a particular point of time. 4. Transaction and Income Velocities: Fisherian approach emphasises the importance of the transaction velocity of circulation (i.e., V). The Cambridge Version, on the contrary, lays stress on the income velocity of the part of income which is held in the cash balance (i.e., K). 5. Nature of P: In both approaches, the price level (P) is not used identically. In Fisher’s version, P is the average price level of all goods. On the contrary, in Cambridge version. P refers to the price of consumer goods. 6. Factors Affecting V and K: Fisher is concerned about the institutional and technological factors governing how fast individuals can spend their money (i.e., V). The Cambridge School, on the other hand, is concerned about the economic factors determining what portion of their wealth the public desires to hold in the form of money (i.e., K). 7. Relationship between M and P: The Fisherian approach maintains that any change in the money supply produces proportional changes in the price level. This is because Fisher believes that both velocity and real income are in the long run independent of each other and of supply of money. In the Cambridge approach, the price level may change by more or less than the money supply; it depends upon what happens to the stock of non-monetary assets and their expected yields on which the Cambridge economists believed the desired cash balances depend. 8. Different Approaches to Monetary Theory: Both Fisher and Cambridge School led to the development of two different approaches to the monetary theory. Fisher’s approach has given rise to an inventory theory of money holding largely for transactions purposes. On the other hand, the Cambridge approach has been developed into portfolio, or capital theoretic approach to monetary demand. The Cambridge version is superior to the Fisherian version on the following grounds: 1. Realistic Theory: The Fisherian approach is mechanical in the sense that it maintains a mechanical, i.e., direct and proportional relationship between the supply of money and the price level. The Cambridge approach, on the contrary, provides a realistic analysis. By emphasising K, it introduced the role of human motives in the determination of the price level. 2. Broader Theory: The Cambridge approach is broader and comprehensive because it takes into account income level as well as changes in it as important determinant of the price level. The Fisherian approach ignored income level and makes the price level dependent upon the quantity of money and the total number of transactions. 3. More Useful: According to Kurihara, the Cambridge equation, P = M/KT, is analytically more useful than the Fisherian equation, P = MV/T, in explaining money value. It is easier to know the amount of cash balances of an individual than to know his expenditure on various types of transactions. 4. Causal Process: According to Fisher, changes in the price level are caused by the changes in the quantity of money. But according to the Cambridge economists, the price level may change even without a change in the quantity of money, if K changes. Given the quantity of money, a desire to keep less money balances will raise the price level and vice versa. 5. Explanation of Cyclical Fluctuations: The variable K in the Cambridge equation is more significant in explaining the trade cycles than the variable V in Fisher’s equation. During inflation, people decrease their cash balances (K) and as a result, the value of money falls and the price level rises. On the contrary, during depression, the desire to hold money (K) rises and, as a consequence, the value of money rises and the price level falls. .
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