Quantity theory of money: Fisher's cash-transactions and the Cambridge cash-balance approach

1. The idea

The quantity theory is the oldest explanation of the value of money. In its crude form: other things being equal, the price level varies directly and proportionately with the quantity of money, and the value of money varies inversely. If money doubles, prices double and the value of money halves. The idea goes back to Jean Bodin and David Hume and was restated with precision by Irving Fisher in The Purchasing Power of Money (1911).

2. Fisher’s cash-transactions approach

Fisher started from the identity that in any period the total money spent on purchases equals the total value of things sold. His equation of exchange is:

MV + M′V′ = PT, so P = (MV + M′V′) / T

• M: quantity of legal tender money (currency);
• V: velocity of circulation of currency, the average number of times a unit of money changes hands in the period;
• M′: bank (credit) money, that is, demand deposits;
• V′: velocity of bank money;
• P: the general price level;
• T: the total volume of transactions (goods and services exchanged for money).

The left side is the supply of money (money spent); the right side is the demand for money (the money value of transactions). Money is demanded only as a medium of exchange.

Assumptions

1. V and V′ are constant in the short run, being fixed by habits, the banking system and the speed of transport, which change slowly.
2. T is constant, because the economy is at full employment (the classical assumption).
3. M′ bears a fixed ratio to M: bank credit expands in proportion to cash.
4. P is passive: it is the effect, not a cause, of changes in M.
5. The theory applies in the long run.

Illustration. Let M = Rs. 1,000, V = 4, M′ = Rs. 500, V′ = 2 and T = 2,500 units. P = (4,000 + 1,000) / 2,500 = Rs. 2. If M and M′ double to Rs. 2,000 and Rs. 1,000, P = (8,000 + 2,000) / 2,500 = Rs. 4. Prices double; the value of money halves from 1/2 to 1/4.

Diagrammatically, a curve showing P against M is a straight line through the origin (prices proportional to money); the curve of the value of money (1/P) against M is a rectangular hyperbola.

Criticisms

• Truism. The equation is an identity, true by definition; it does not by itself explain causation.
• Unrealistic assumptions. V and T are not constant; full employment is the exception (Keynes). Below full employment more money raises output, not only prices.
• Static. It cannot explain the trade cycle or why prices fall in a depression even when money is plentiful.
• Ignores the rate of interest and the store-of-value function: money affects prices through interest, investment and income.
• Mixes stocks and flows: M is a stock at a point of time, while T is a flow over a period.
• T is too wide: it includes intermediate and financial transactions; the price level P is not well defined.
• Neglects the demand for money: the cash-balance approach repairs this.

Its merit: it explains, broadly, why large increases in money (hyperinflations, wartime note issue) lead to large price rises, and it is the basis of the monetarist revival by Milton Friedman.

3. The Cambridge cash-balance approach

The Cambridge economists (Marshall, Pigou, Robertson, Keynes in his early work) asked a different question: how much money do people wish to hold? The value of money is then fixed by the supply of money and the demand to hold it as cash balances. People hold a proportion (k) of their income or wealth in money for convenience and security.

• Marshall: M = kPY, where Y is real income and k the proportion of income held as money. So P = M / kY.
• Pigou (“The Value of Money”, 1917): P = kR / M, where R is total real resources (wheat) and P here is the value of money (purchasing power), not the price level. Extended for bank money: P = kR / M × [c + h(1 − c)], c being the proportion held as cash and h the bank reserve ratio.
• Robertson: M = PkT, or P = M / kT, where k is the proportion of transactions for which money is held. Close to Fisher; k is the reciprocal of V.
• Keynes (A Tract on Monetary Reform, 1923): n = p(k + rk′), where n is currency, p the price of a consumption unit, k the consumption units held in cash, k′ those held in bank deposits and r the bank reserve ratio.

Illustration. Real income Y = 1,000 units, k = 1/4, M = Rs. 500. P = 500 / (0.25 × 1,000) = Rs. 2. If people decide to hold more money (k = 1/2) with M unchanged, they spend less and P falls to 500 / 500 = Re. 1. So prices change even when the money supply does not: the demand side matters.

Merits

• It brings in the demand for money and human motives (convenience, security), a link to Keynes’ later liquidity preference.
• It relates money to income, which is more meaningful than the vague T.
• k is a psychological variable that can explain the trade cycle (a rise in k depresses prices).
• M and k both relate to a point of time, so there is no stock-flow confusion.

Criticisms

• It still assumes k and Y constant, so it reaches the same proportional result.
• It ignores the rate of interest and the speculative motive (Keynes).
• Pigou’s “wheat” standard for real resources is narrow.
• It explains the price level of consumption goods rather than all goods.

4. Comparison of the two approaches

Both reach the conclusion that prices vary with the quantity of money, and both assume full employment. Keynes’ General Theory (1936) replaced them with an income-expenditure theory: money affects the rate of interest, the rate of interest affects investment, and investment determines income and employment. Prices rise in proportion to money only after full employment (true inflation).

How this is examined

August 2024 set “Critically examine the cash transaction approach to the quantity theory of money” for 10 marks; the cash-balance approach and the comparison of the two are the natural alternatives and short notes. In the essay, write the equation in a box, explain the symbols, give the numerical illustration, state the assumptions as a numbered list and end with Keynes’ criticism. For the comparison, the table above is enough for six marks.