Part III - Derivation of the LM-Curve and Equilibrium

Synthesis of Monetary and Income Analysis - Part III

Derivation of the LM-Curve and equilibrium

The derivation is based on the following three propositions.

1. An increase in the level of income leads to an increase in the demand for money.
2. An increase in the demand for money leads to an increase in the rate of interest.
3. Therefore, an increase in the level of income leads to an increase in the rate of interest.

The left part of the diagram shows the Demand for and Supply of money.
Ms is the supply curve for money.
Md is the demand curve for money.
E is the point of equilibrium in the money market.
Oro is the equilibrium rate of interest.
The right part of the diagram shows the relationship between level of income and the rate of interest in the money market, and the derivation of the LM_Curve.
OYo is the level of income.
Oro is the rate of interest.

Now income increases from Yo to Y1. So the demand for money will go up, and the demand curve for money, Md, will shift to the right. M'd becomes the new demand curve for money. F becomes the new equilibrium point, and the rate of interest goes up to Or1.

Now if we join the points E', F' etc. in diagram (b), we get the LM-Curve. 'L' stands for the demand for money (speculative) or liquidity preference and 'M' stands for the supply of money. The LM-Curve shows the alternative combinations of the rate of interest and the level of income for which money market is in equilibrium. In other words, at any point on the LM-Curve demand for money or liquidity preference is equal to the supply of Money.

General Equilibrium of the Commodity market and the Money market

We have shown two different equilibrium relationships between the rate of interest and the level of income, in the form of the IS-Curve and the LM-Curve. The commodity market and the money market are closely related to one another. Decisions regarding consumption and investment determine people's behaviour regarding wealth-holding between money and bond, and thus their demand for money. The rate of interest and the level of income in both the commodity market and the money market are the same.

Therefore the general (overall) equilibrium of the economy is ensured when the rate of interest and income are such that these are compatible with equilibrium in both the markets. The IS-Curve shows the equilibrium in the commodity market, and the LM-Curve shows the equilibrium in the money market. In other words, what it implies is that the values in question must lie on both the LM and the IS Curves for an overall equilibrium condition to be true. This can occur only when both the curves intersect.

Here both the IS and LM Curves are plotted on the same axes. The equilibrium level of income is given at Ye, where OYe is the equilibrium level of income, and that of interest at re, where Ore is the equilibrium rate of interest. Only at point G both the markets are at equilibrium. The diagram shows the general equilibrium of the commodity market and the money market. This is called the Synthesis of Monetary Analysis and Income Analysis, or the Synthesis of Fiscal Policy and Monetary Policy.

Part III of IV | Part IV: Shifts of IS and LM Curves