What is the difference between fisher and Cambridge equation in economy?

Answer 1

Fisher's quantity theory of money establishes an exact relationship between money and transactions. But, other economists tried to link money to income via quantity theory of money by assuming that real income is a suitable scale variable for total volume of transactions. This assumption simply relates money to income without reliable economic evidences. Consider the following two equations. Equation (1) is the original Fisher's quantity theory and equation (2) is the other's interpretation of quantity theory.

MV = Pt = T (1)

MV = Py = Y (2)

where,

M: Stock of money.

V: Velocity or circulation of money.

P: Price level.

y: Real Income.

Y: Nominal income.

t: Volume of transaction.

T: Value of transaction.

In the equation (1), Fisher discusses around the quantity and value of goods and services sold, but by equation (2), other economists interpret that income is a suitable scale variable for transaction, and they link MV to income (produced value added) in the economy by simply replacing "y" by "t". In this section, now, we are going to determine the exact relationship between these two fundamental variables. On the other hand, it is tried to bridge between Fisher's original quantity theory (MV=Pt) and revisionists' interpretation of quantity theory (MV = Py) in a logical frame.
Simon Newcomb's and Irving Fisher's Quantity Theory relies entirely on the idea of a stable transactions demand for money. This requires that money is desired only for its medium of exchange function and this is institutionally imposed. An alteration on this point was brought in by several Cambridge economists in the earlier part of this century. In particular, A.C.Pigou (1917), Alfred Marshall (1923), D.H. Robertson (1922), John Maynard Keynes (1923), R.G. Hawtrey and Frederick Lavington (1921, 1922). These were the joint creators of what has since become known as the "Cambridge cash-balance" approach.

The proposition they advance is that money is desired as a store of value. The Cambridge story, then, is fundamentally different from the Fisher story. In Fisher, money is desired by agents in some fixed amount solely because it happens to be the medium of exchange. As Fisher noted, money yields no gains to the holder. However, in the Cambridge story, this is not the case. Money does increase utility in a way: namely, by enabling the divorce of sale and purchase as well as a hedge against uncertainty.

The first reason resembles that outlined by Adam Smith, W.S. Jevons (1875) and Carl Menger (1892) - where money is necessary to overcome transaction costs and coincidence of wants problems. As they note, in simultaneous, multilateral exchange with no transaction costs, the need for money by traders is not apparent. The advantage of money, in that it overcomes the need to obtain coincidence of wants; it implies that an agent can sell his good at one time for "money" and then extend his leisurely search for the best price, then trading his "money" for the goods he finally wishes to purchase.

The Cambridge lesson is that the sale and purchase of commodities are not simultaneous and thus there is a need for a "temporary abode" of purchasing power, i.e. some temporary store of wealth. In particular, A.C. Pigou (1917) also allowed for money demand to involve a precautionary motive - with money holdings acting as a hedge against uncertain situations.
As it is in its store-of-wealth and precautionary modes that money yields utility to the consumer, then it is demanded for itself in a way. How much of it is demanded depends partly on income and partly on other items, notably wealth and interest rates. The first part is obviously implied in transactions terms: the higher the volume of income, the greater the volume of purchases and sales, hence the greater the need for money as a temporary abode to overcome transactions costs. Thus, Cambridge theorists regarded real money demand as a function of real income, i.e. M/P = kY
where k is the famous "Cambridge constant". However, this is really misleading for the "constant" k is not constant at all. Rather, it relies on other components, such as interest (the opportunity cost of money) and wealth.

We can compare this to Fisher's system by simply recognizing that real income (Y) and transactions (T) are, in equilibrium, identical. Of course there are transactions in wealth (e.g. the sale of existing assets such as a house) which do not count as part of income or output proper since they are only transferrals of ownership. The way around this is, as Pigou (1927) notes, is to recognize that, properly valued, the sale value of a home is really the discounted value of rents (which are income).
the main points of the Cambridge approach were two: (1) neutrality remains but dichotomy is doubtful; (2) money yields services and is demanded by choice.