# Derive the LM curve under the theory of liquidity preference. Does this depend on the real or nominal interest rate?

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Introduction

Derive the LM curve under the theory of liquidity preference. Does this depend on the real or nominal interest rate? What happens to the LM curve when there is: a. an increase in the price level b. an increase in the money supply c. an increase in disposable income The theory of liquidity preference, introduced in the General Theory, is Keynes' view on how the interest rate is determined in the short run. It is a demand and supply model of the economy's most liquid asset, money. However, money, in the model, is expressed in terms of the amount of goods and services it can purchase, real money balances. The supply of real money balances is an exogenous policy variable chosen by the Central Bank. It is therefore assumed to be fixed, and furthermore, it does not depend on the interest rate. Consequently, the supply curve for real money balances is vertical. The demand for real money balances however, does clearly depend on the interest rate which should be obvious from the shape of the demand curve for balances, a downward sloping demand curve. The theory of liquidity preference suggests that the interest rate is a determinant of how much money people want to hold. ...read more.

Middle

As we can then see from the diagram below (a), this causes an increase in the interest rate from r1 to r2. These changes are then summarized in the LM curve shown in diagram (b) below. The LM curve plots the relationship between income and the interest rate. The higher the level of income, (the higher the demand for transactions and therefore the higher the demand for money balances) the higher the equilibirum interest rate. (The higher the rate of interest that equilibriates the money market). Thus we have derived the LM curve under the theory of liquidity preference. a. An increase in the price level As noted earlier, the price level is an exogenous variable in the IS-LM model. However, it affects the supply of money balances. An increase in the price level has the affect of lowering purchasing power, and consequently, it reduces the amount of real money balances supplied. In the diagram below (a), this is depicted by a shift to the left of the supply curve for real money balances. Diagram (b) shows what happens to the LM curve: Income does not change in this situation. What does happen is that the increase in prices, leading to a fall in the supply of real balances, causes the interest rate to rise. ...read more.

Conclusion

It seems, prima facie, that the interest rate we are concerned with in deriving the LM relation is the nominal rate of interest. This is because, the money demand function depedns on the nominal rate of interest. As mentioned above, when we decide how much money to hold, we take into account the opportunity cost of holding money rather than financial investment. Money pays a zero nominal interest rate, whereas bonds (or savings accounts etc) pay a nominal interest rate of i. Hence, the opportunity cost of holding money is just the difference between the two interest rates, i - 0 = i, which is just the nominal interest rate. Therefore, money demand depends on the nominal interest rate. However, in the IS-LM, which is a short run model, where we assume are nominal rigidities, in this context, sticky prices. Therefore, in IS-LM there is no inflation since the price level is fixed. Recall that the equation for the real rate of interest is: r = i - *, and therefore, i = r + * However, in IS-LM (short-run) there is no * due to the sticky prices. Therefore, if *=0, then; i = r + 0 ==> i = r the nominal rate of interest is equivalent to the real rate of interest, and we can therefore say that the LM curve depends on the real rate of interest. ...read more.

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