**Let us make an in-depth study of Money Supply on the LM-Curve. **

The interest sensitivity of the money supply can now be shown in terms of the IS-LM curve model.

Fig. 20.5 shows the supply and demand curves for money balances M.

With an initial income level Y_{0}, the demand-for-money curve is M(Y_{0}).

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With an initial money supply M_{0} we hold P constant throughout this analysis. So we do not draw a distinction between nominal balance and real balance. The interest rate is r_{0}. Now suppose income rises, due to a rightward shift of the IS curve. Then the demand curve in Fig 20.5 shifts up to M(Y_{1}), and with a money supply fixed at M_{0}, the interest rate will rise to i_{1}.

But if the money supply is responsive to interest rate changes, the money supply function through the initial equilibrium point i_{0}, M_{0} (Y_{0}) will be the positively sloped supply function M(i – i_{d}) in Fig. 20.5. In this case, the increased demand for money leads to an increase in supply equal to M_{1} – M_{0} as the interest rate rises to i_{2} instead of i_{1}.

Thus, the interest elasticity of the money supply reduces the increase in i (from i_{1} – i_{0} to i_{2} – i_{0}) needed to maintain money market equilibrium with a given increase in Y, from Y_{0} to Y_{1}, in Fig. 20.5.

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Thus with an interest-sensitive money supply, the slope of the LM curve is flatter than otherwise. This is shown in LM diagram of Fig. 20.6. At the initial interest rate i_{0}, the real money supply is equal to M(i_{0}) in the southwest quadrant. If the interest rate rises to i_{1}, with the money supply fixed at M(i_{0}), the level of income must rise to Y_{1} to maintain money market equilibrium.

The interest rate increase reduces the speculative and transactions demand for money. Now it is not necessary for money supply to support an increase in Y within the constraint of a given M.

**If the money supply is not fixed, but is a function of the interest rate i: **

M = M(i); M’ > 0,

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then an increase in the interest rate from i_{0} to i_{1} shifts the money supply out from M(i_{0}) to M(i_{1}) in Fig. 20.6. This increase in money supply will support an increase in income to Y_{2} as opposed to Y_{1}. Thus, the LM curve with an interest-sensitive money supply looks like L_{1}M_{1} in Fig. 20.6 — flatter than L_{0}M_{0} — which assumes a fixed real money supply.

We can now derive the modified expression for the slope of the LM curve with an interest- sensitive money supply by using the equilibrium condition in the money market. The demand for money can be expressed as either