The Keynesian theory of money demand is also called liquidity preference theory. This article tries to explain about Keynesian theory of money demand and elaborate how it differs from classical theory of money demand.

## Assumption of Two Assets World

Keynes assumed the two assets world, where people can hold their entire portfolios either in money or in bonds. They cannot hold portfolio of both of them. Bond is a risky and income earning assets whereas money is risk-free assets with virtually no earning.

Even if the balance on bank checking accounts would provide some minimal interest earnings, and holding monetary assets could have cost associated with it the forgone interest income, Keynes did not take it into analysis considering it as an insignificant matter.

## Keynesian Foundation for Money Demand

Unlike the classical theory of money demand, which posits transactions motive as the only motive for money demand, Keynes postulates three motives for money demand. They are transactions motive, precautionary motive, and speculative motive. These three motives are the reasons for money demand, and they serve as the foundation in Keynesian theory of money demand.

### Transactions Motive

In line with the quantity theory of money, people demand money because it is the medium of exchange and use to carry out everyday transactions. The transaction demand for money arises from the needs of personal and business exchanges. The transaction demand for money is proportional to income (as assumed by quantity theory of money). The relationship between transaction demand for money and income level can be mathematically expressed as

$$L_T = kY \qquad … (i)$$

Where,

L_{T} = Transaction demand for money

k = Fraction of income set aside for transaction purpose

Y = Income level

The equation (i) shows the proportionate and positive relationship between L_{T} and Y. Unlike the value of k in classical theory of money demand, value of k in Keynesian theory of money demand may change due to the changes in institutional and technological factors.

This motives of money demand primarily considers the function of money as medium of exchange. So, the money demand is for medium of exchange.

### Precautionary Motive

Keynes believed that individuals and businesses hold money as a cushion against unexpected needs. Individuals hold money for unforeseen events like illness, accident, etc. while businesses hold money for unfavorable conditions, or to benefits from contingent gains. Precautionary money balance, people want to hold, will also be directly proportional to the income level.

This relationship between precautionary money balance and income level can be expressed as precautionary money balance function as follows:

$$L_P = kY \qquad … (ii) $$

Where,

L_{P} = Precautionary demand for money

k = Proportion of income for precautionary purpose

Y = Income level

The equation (ii) also show the proportionate and direct relationship between precautionary demand for money and income level.

### Speculative Motive

Keynes’s belief is that people can hold wealth only in two forms of assets – either all in money or all in bonds. One of the important function of money is the store of wealth; and people’s choice to hold money as a store of wealth is the speculative motive of money demand.

In Keynes’s analysis, definition of money includes currency and bank deposits on checking accounts. Currency earns no interest while bank deposits on checking accounts earns typically little interest. That’s why, Keynes assumes money earns no interest, and its opportunity cost is the nominal interest rate that would have been earned by investing on bonds. Hence, speculative motive of money demand is the function of nominal interest rate or market interest rate.

When the nominal interest rate on bond raises, opportunity cost of holding money also raises. This makes the holding of money costly in comparison to bonds. Consequently, the quantity of money demanded falls. Similarly, when interest rate on bond falls, opportunity cost of holding money and, thus, quantity of money demanded raises.

This implies that there is inverse relationship between interest rate and quantity of money demanded. This inverse relationship between interest rate and money demand can be shown mathematically as follows:

$$L_S = f(\frac{1}{i}) \qquad … (iii) $$

Where,

L_{S} = Speculative demand for money

f() = Functional relationship between interest rate and speculative demand for money

i = Nominal interest rate, or current market interest rate

Equation (iii) shows the inverse relationship between interest rate and speculative demand for money.

## Keynesian Money Demand Function

Keynesian money demand function is the relationship between money demand and factors affecting it. To Keynes, transaction and precautionary motives for money demand are highly income elastic, but interest inelastic; speculative motive for money demand is interest elastic at the high interest rate. Therefore, these three motives of money demand serves as the collective determinants of liquidity preference function or Keynesian money demand function.

In addition, money demand is actually the demand for real cash balance primarily because of two reasons: First, people hold cash balance for transaction and precautionary motives to serve the function of money as medium of exchange. Second, when the price raises, people holds more of cash to maintain the same level of purchase. Therefore, we can assume that demand for money is dependable on real income rather than nominal income.

Similarly, the real demand for money arising from speculative motive is dependable on nominal interest rate. This is because the opportunity cost of holding money is expressed in terms of nominal interest that a bond can earn.

Therefore, there are two basic determinants – nominal interest rate and real income – of real money demand function in Keynesian analysis. Mathematically, the real money demand function can be presented as:

$$L = f(i, y) \qquad … (iv)$$

where L is real money demand, i is nominal interest rate, and y is real income. The real demand for money is negatively related to nominal interest rate and positively related to real income.

## Keynesian Liquidity Trap

What is liquidity trap?

The liquidity trap in Keynesian theory of money demand is a situation wherein the money demand function becomes perfectly elastic at the very low interest rate. That means, people holds their all assets real cash balance when interest is very low. In other terms, liquidity trap is a paradoxical condition where people save too much when interest is too low. As a consequence, the real money demand function becomes flat at low interest rate and money supply is ineffective to change the interest rate.

The negative relationship between real money demand and nominal interest rate can graphically be illustrated as:

As you can see in the figure, when the interest rate raises from i1 to i2, demand for money decreases from L1 to L2. In contrast, demand for money will raise up for any decrease in interest rate to a certain level, say i0. The downward slopping red line, L, is the real money demand function which is flat for any interest rate below i0. So, the CL portion of L is the liquidity trap, wherein people hold their assets all in money, and monetary policy becomes ineffective to alter the interest rate.

## Keynesian Money Demand Function in Money Market Equilibrium

When money market is in equilibrium, total demand for money (liquidity preference) is equal to total money supply. In equation (iv), L is real money demand, therefore the equilibrium condition in real terms will be $$L =\frac{M}{P} \qquad … (v) $$

where P is price level, M is total nominal money supply and M/P is total real money supply, which is assumed to be fixed by central monetary authority.

Now, let’s combine equation (iv) and (v) to get,

$$\frac{M}{P} = f(i, y) $$

Rearranging the the equation, we get:

$$\frac{P}{M} = \frac{1}{f(i, y)} $$

Again, let’s multiply on both side by real income, y, to get the value of velocity of money as explained in the calssical theory of money demand.

$$V = \frac{Py}{M} = \frac{y}{f(i, y)} \qquad … (vi)$$

We know that the demand for money and nominal interest rate are negatively related. Therefore, in equation (vi), raising i means declining f(i, y), and declining f(i, y) means raising velocity of money, V. That means velocity of money is not constant in Keynesian theory of money demand as opposed to classical theory of money demand.

## Implication of Keynesian Theory of Money Demand

As the interest rate is highly volatile, it leads to the volatile velocity of money. This is an important implication of Keynesian theory of liquidity preference. Hence, Keynesian theory of liquidity preference contradicts the proposition of classical theory of money demand, which assumes the constant velocity of money. Further, Keynesian theory of income, thus, casts doubt on classical theory of income that nominal income is solely determined by the supply of money.

When the interest rate is too low, or economy is in liquidity trap, monetary policy should not target money supply to achieve its goal.

## Criticism of Keynesian Theory of Money Demand

The assumption of two world assets, in which entire portfolio is kept either in cash or in bond is unrealistic. Because, individuals maintain their portfolio with the mixture of cash, bond, and others assets.

James Tobin proposed a theory of money demand pointing out that even the transactions and precautionary demands for money would also be interest rate elastic and negatively related to interest rate.