Chapter 3: The Theory of Demand for Money

Classical Theories of Money Demand

Developed by economists like Irving Fisher, Alfred Marshall, and A.C. Pigou.
Discusses how the nominal value of aggregate income is determined.
Explains how much money is held for a given amount of aggregate income.
Based on the concept of the velocity of money (the rate of turnover of money).

Velocity of Money

The average number of times a unit of currency is spent on goods and services in the economy.
Formula: $MV = PY$ , where:
- $V$ = velocity of money
- $M$ = money supply
- $P$ = average price level
- $Y$ = real level of income or volume of transaction
- $PY$ = nominal income
Velocity of money equation: $V = \frac{PY}{M}$
Classical economists believe velocity depends on institutional and technological factors, which are constant in the short run.
Therefore, in the short run, any change in money supply (M) will be reflected in the nominal income (PY).
Classicalists assume aggregate real income (Y) remains constant at the equilibrium level in the short-run because prices and wages are completely flexible.
Changes in money supply lead to changes in price only.
Example: If $V = 4$ and $Y = 100$ , then if $M = 25$ , $P = 1$ ( $M = \frac{PY}{V} = \frac{100 * 1}{4} = 25$ )
If M doubles to 50, P will double to 2 ( $M = \frac{PY}{V} = \frac{100 * 2}{4} = 50$ )
Quantity theory of money: Money is neutral with respect to the real sector, and price level changes result solely from changes in the quantity of money.
Formula for money holdings or money supply: $M = \frac{PY}{V}$
In equilibrium, $Ms = Md$ , so $M_d = \frac{1}{V}PY = KPY$ , where K is the money demand coefficient or the inverse of velocity
'K' indicates the fraction of nominal GDP that individuals and businesses prefer to hold as money.
A higher ‘𝐾’ suggests people hold a larger portion of their income as money (lower velocity of money).
A lower ‘𝐾’ implies people hold a smaller proportion of their income as money (higher velocity of money).
Classicalists' theory of money demand: Money demand is not a function of interest rate because people demand money only for transaction purposes.
Money demanded for transaction purposes depends on the volume of transactions.
The quantity of money demanded is a constant function of nominal income; people hold a fraction of their nominal income in the form of money.

The Cambridge Approach to Money Demand

The Cambridge school's approach resulted in a similar money demand equation: the quantity of money demanded is given by some proportion of the nominal income.
They didn't consider money demand to be solely affected by the volume of transactions or nominal income and velocity.
They allow flexibility in people’s decisions about money holding instead of being completely bound by institutional & technological factors.
As such, it did not rule out the effect of interest rate on the MD.
People demand money because it serves as a medium of exchange (transaction motive) and as a store of value.
The part of the demand for money for store of value depends on wealth and the relative expected return of money.
Nominal wealth is proportional to nominal income, suggesting that the part of money demanded as a store of value is also proportional to nominal income.
When people demand money as a store of value, they are also affected by the relative expected return of money in addition to their wealth (and hence income).
Bond is considered as an alternative to money as a store of value. If the return of the bond (interest) changes, the demand for money will fall since people will resort to bond.
If interest rate on bonds increases, less money will be demanded as a store of value and the whole quantity of demand for money will decrease, though quantity of money demanded for transaction purposes will not be affected by interest rates.
The quantity theory of money and the Cambridge economists developed a classical theory of money demand in which the demand for money is proportional to nominal income.
However, the two theories are different in that the first one emphasized technological and institutional factors and ruled out any possible effect of interest rates on the demand for money in the short-run, while the Cambridge economists emphasizes individual choice and allows interest rate to affect the demand for money by affecting people’s decision to hold money.

Keynes's Liquidity Preference Theory

Keynes developed a theory of demand that emphasized the importance of interest rates like the Cambridge economists.
His approach is more detailed, identifying different motives for demanding money and showing the effect of interest rate on the demand for money more explicitly.
As to Keynes, there are three motives for demanding money:
- Transaction motive
- Precautionary motive
- Speculative motive

Transaction Motive

Demanding money for the purpose of transaction.
People demand money to fulfill their current consumption demand of goods and services i.e., they demand money as a medium of exchange.
This part of the demand for money is determined by the amount of current consumption which as to Keynes is proportional to income; it is purely a function of income & interest rate does not affect it.

Precautionary Motive

Money is demanded as a cushion against unexpected transactions in the future.
People could not predict their future volume of transactions and hence their future demand for money and they hold some amount of money as a precaution for future unexpected demand for money and this what Keynes called the precautionary motive.
For example, future health expense and price change expectation.
As income increases, people will hold more money for both purposes - current transaction and future expected transactions.

Speculative Motive

Keynes agreed with the Cambridge economists that money is also demanded as a store of value (wealth).
This motive is affected by wealth, which is believed to be closely related to income.
Interest rate is an important determinant of this part of money demand.
People hold their wealth in different assets, and money is one alternative.
People can hold their wealth either in the form of money or bond & since money does not earn interest people will choose to hold bond if they expect a positive return from holding bond.
The speculative motive is inversely affected by interest rate, i.e., as interest rate from bonds increases the return from bonds will increase and people will shift from money to bonds (they will hold less money and more bond).
Though Keynes considered only bond as an alternative asset to money in terms of storing wealth, there many alternative assets of storing wealth including different physical assets and financial assets other than bond.
Keynes argued that people worry about real money balances since what matters in terms of their motives is how much they can buy using their money holding.
He therefore chose to put his demand function for money in real terms.
The first two motives are not affected by interest rate, according to Keynes, while the third motive is inversely affected by interest rate.
The strength of the effect of interest rate on demand for money will depend on the importance of the speculative motive in deriving the total demand for money.
Keynes’ demand function for money can be put mathematically: $\frac{M_d}{P} = f(i^-, y^+)$
- Where:
  - $i$ = interest rate
  - $y$ = real income
  - $M_d$ = demand for nominal money balances
  - $P$ = price level
  - $\frac{M_d}{P}$ = demand for real money balances
The function shows that the real demand for money is a function of both interest rate and real income.
Real money demand is inversely affected by interest rate and positively affected by real income or transaction.
The fact that money demand is affected by interest rate implies that velocity of money is no more constant and it is rather volatile.
This is so because money holding changes even without change in nominal income, if interest rate changes. This can be showed mathematically by first deriving the formula for velocity of money from the real demand for money given above.
By taking the reciprocal of both sides we will get the following: $\frac{P}{M_d} = \frac{1}{f(i^-, y^+)}$
And multiplying both sides by ‟y‟ will give us the following: $\frac{Py}{M_d} = \frac{y}{f(i^-, y^+)}$
But, money demand (Md) and money supply (M) are equal in equilibrium and hence we can substitute one by the other, thus: $\frac{Py}{M_s} = \frac{y}{f(i^-, y^+)} = V$
This shows that velocity of money is not constant even in the short run and this is reflected on the real demand for money equation which is part of the above velocity function.
Velocity of money is inversely affected by the real demand for money which in turn is inversely affected by interest rate.
Thus, we can conclude that the velocity of money under the Keynesian framework is positively affected by interest rate, i.e., as interest rate increases the velocity of money will rise.
This can also be shown by taking the first order derivative of the velocity function with respect to interest rate (the quotient rule).
The intuition behind is that, as interest rate increases people will hold less money since money will become less attractive as a store of wealth and hence people will resort to other asset like bond.
And, as the money hold by the public falls, taking the real transaction level constant (PY), the velocity of money has to increase i.e., money should circulate faster than before in order for the money hold by people to be enough for all the transactions.
In other words, If people hold less money (M) due to higher interest rates, but the level of transactions in the economy (PY) remains constant, 𝑉 must increase to balance the equation.
This means money must circulate faster to support the same volume of transactions.
Here, the velocity of money doubles, meaning each dollar circulates twice as fast as before to support the same level of economic activity.
When people hold less money due to higher interest rates, they rely on circulating the existing money faster (increased 𝑉 ) to meet their transactional needs.
This adjustment ensures that the economy continues functioning efficiently despite lower money balances.

Friedman’s Modern Quantity Theory of Money

Developed by Milton Friedman in 1956, in his famous article, “The Quantity theory of money: A Restatement”.
His analysis is closer to Keynes’ & Cambridge economists than to Fisher’s Qty. theory of money.
Though, Friedman, like his predecessors, pursued the question of why people choose to hold money, he did not however, deal with the specific motives for holding money, as Keynes did.
Friedman claimed that the demand for money is affected by the resources available to the individual (wealth) and the expected returns on other assets (which can serve as substitute for money) relative to the expected return on money.
Friedman identified bonds, equities (stocks) and real goods as substitutes for money and hence their relative return will affect the demand for money.
Like Keynes, he recognized that people want to hold a certain amount of real money balance, i.e., he put his demand function for money in real terms & included wealth & the relative returns of bond, stock and real goods as factors.
His demand function is given below: $\frac{Md}{P} = f(Yp^+, rb - rm^-, re - rm^-, \pi^e - r_m^-)$
- Where:
 - $\frac{M_d}{P}$ = demand for real money balances.
 - $Y_p$ = Friedman's measure of wealth, known as permanent income (technically, the present discounted value of all expected future income, but more easily described as expected average long-run income).
 - $r_m$ = Expected return on money
 - $r_b$ = Expected return on bonds
 - $r_e$ = Expected return on equity (common stocks)
 - $\pi^e$ = Expected inflation rate
Because the demand for an asset is positively related to wealth, money demand is positively related to Friedman's wealth concept, permanent income.
Unlike our usual concept of income, permanent income (which can be thought of as expected average long-run income) has much smaller short run fluctuations because many movements of income are transitory (short-lived).
For example, in a business cycle expansion, income increases rapidly, but because some of this increase is temporary, average long-run income does not change very much.
Hence in a boom, permanent income rises much less than income.
During a recession, much of the income decline is transitory, and average long-run income (hence permanent income) falls less than income.
One implication of Friedman's use of the concept of permanent income as a determinant of the demand for money is that the demand for money will not fluctuate much with business cycle movements.
An individual can hold wealth in several forms besides money; Friedman categorized them in to three types of assets: bonds, equity (common stocks) and goods.
The incentives for holding these assets rather than money are represented by the expected return on each of these assets relative to the expected return on money.
The minus sign beneath each indicates that as each term rises, the demand for money will fall.
The expected return on money, 𝑟𝑚, appears in all three terms and is influenced by two factors:
1. The services provided by banks on deposits included in the money supply, such as provision of receipts in the form of canceled checks or the automatic paying of bills. When these services are increased, the expected return for holding money rises.
2. The interest payments on money balances. Now accounts and other deposits that are included in the money supply currently pay interest. As these interest payments rise, the expected return on money rises.
The terms 𝒓𝒃− 𝒓𝒎, and 𝒓𝒆− 𝒓𝒎, represent the expected return on bonds and equity relative to money; as they rise, the relative expected return on money falls, and the demand for money falls.
The final term, 𝝅𝒆 − 𝒓𝒎, , represents the expected return on goods relative to money. The expected return from holding goods is the expected rate of capital gains that occurs when their prices rise and hence is equal to the expected inflation rate.
If the expected inflation rate is 10 percent, for example, then goods' prices are expected to rise at a 10 percent rate, and their expected return is 10 percent. When 𝝅𝒆 − 𝒓𝒎, rises, the expected return on goods relative to money rises, and the demand for money falls.