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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 in two forms – money and bonds. 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,

LT = 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 LT 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 chages in institutional and technological factors.

### Precautionary Motive

Keynes believed that individuals and besinessess hold money as a cushion against unexpected needs. Individuals hold money for unforeseen events like illness, accident, ect. while businessess hold money for unfavourable 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,

LP = 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 – money and 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 heve been earned by investing on bonds.

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:

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

Where,

LS = Speculative demand for money

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

r = Nominal interest rate

Equation (iii) shows the inserse relationship between interest rate and spculative demand for money.

## Liquidity Preference Function

Combining all of the three motives of money demand into a demand for real money balances led to what Keynes called the liquidity preference function:
Md/P=L(i,Y)

Equation states that the demand for real money balance is negatively related to nominal interest rate and positively correlated to real income.

James Tobin also expanded this theory pointing out those transactions and precautionary demands for money would also be negatively related to interest rate. An important implication of liquidity preference theory is that velocity of money is not constant and will fluctuate with changes in interest rates.

Lets write above equation as:
P/Md=1/(L(i,Y))
Multiplying both sides by Y and assuming money market equilibrium, Md = M, and rearranging the terms, we get
V= PY/Md=Y/(L(i,Y))

We know that the demand for money is negatively related correlated to interest rates; when i goes up, L(i, Y) declines, and therefore velocity rises. Because interest rates have substantial fluctuations, Keynesian theories of the demand for money indicate that velocity has substantial fluctuations as well. Thus Keynesian theories cast doubt on the classical quantity theory view that nominal income is determined primarily by movements in the quantity of money.

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