IS - LM model

IS/ LM MODEL: GENERRAL EQUILIBRIUM OF PRODUCT AND MONEY MARKET

This chapter integrates money, interest and income into a general equilibrium model of product and money markets in the Hicks-Hansen diagrammatic framework. 

The IS = Investment/Saving which represents the product market equilibrium

LM = Money demand (L)/ Money supply (M) which represents the money market equilibrium

INTRODUCTION

In order to analyze the general equilibrium of product and money markets, it is instructive to study the derivation of the IS/LM functions and their slopes for the understanding of the effectiveness of monetary and fiscal policies.

The IS-LM curve model emphasizes the interaction between the goods and money markets. 

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The product market is in equilibrium when desired saving and investment are equal. Saving is a direct function of the level of income :

S = f(Y)…….(1)

Investment is a decreasing function of the interest rate :

I = f(r)……..(2)

From (1)and (2) = I=S

The product Market Equilibrium

IS schedule reflects the equilibrium of the product market. It shows the combinations of interest rate and income level where saving-investment equality takes place so that the product market of the economy is in equilibrium.

Keynes assumption that the rate of interest has little effect on Saving. 

The saving curve shows that saving increases as income increases. Saving is an increasing function of income.

S = f(Y) 

The derivation of IS curve

On the other hand , Investment depends on the rate of interest and the level of income.

As the rate of interest falls, the investment starts to decline and vice versa. The level of investment rises with the level of income.

 I = f(r)

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When the rate of interest falls the level of investment increases and vice versa. Thus, changes in the rate of interest affect aggregate demand or aggregate expenditure by causing changes in the investment demand. When the rate of interest falls, it lowers the cost of investment projects and thereby raises the profitability of investment.

The businessmen will there­fore undertake greater investment at a lower rate of interest. The increase in investment demand will bring about increase in aggregate demand which in turn will raise the equilibrium level of income.

A fall in the rate of interest, the planned investment will increase which will cause an upward shift in aggregate demand function  (C + I²) resulting in goods market equilibrium at a higher level of national income.

The lower the rate of interest, the higher will be the equilibrium level of national income. Thus, the IS curve is the locus of those combinations of rate of interest and the level of national income at which goods market is in equilibrium.

In panel (a) the relationship between rate of interest and planned investment is depicted by the investment demand curve II. It will be seen from panel (a) that at rate of interest Or0 the planned investment is equal to OI0. With OI0 as the amount of planned investment, the aggregate demand curve is C + I0 which, as will be seen in panel (b) equals aggregate output at OY1 level of national income.

Graph explanation

Therefore, in the panel (c) at the bottom against rate of interest Or2, level of income equal to OY0 has been plotted. Now, if the rate of interest falls to Or2 the planned investment by businessmen increases from OI0 to OI1 [see panel (a)]. With this increase in planned investment, the aggregate demand curve shifts upward to the new position C + 11 in panel (b), and the goods market is in equilibrium at OY1 level of national income. Thus, in panel (c) at the bottom the level of national income OY1 is plotted against the rate of interest, Or1.

With further lowering of the rate of interest to Or2, the planned investment increases to OI2 (see panel a). With this further rise in planned investment the aggregate demand curve in panel (b) shifts upward to the new position C + I2 corresponding to which goods market is in equilibrium at OY2 level of income. Therefore, in panel (c) the equilibrium income OY2 is shown against the interest rate Or2.

By joining points A, B, D representing various interest-income combinations at which goods market is in equilibrium we obtain the IS Curve. It will be observed from Fig. 24.1 that the IS Curve is downward sloping (i.e., has a negative slope) which implies that when rate of interest declines, the equilibrium level of national income increases (investment, income and saving increases).

The decline in the rate of interest brings about an increase in the planned investment expenditure. The increase in investment spending causes the aggregate demand curve to shift upward and therefore leads to the increase in the equilibrium level of national income. Thus, a lower rate of interest is associated with a higher level of national income and vice-versa. This makes the IS curve, which relates the level of income with the rate of interest, to slope downward.

Why does IS Curve Slope Downward? 

Steepness of the IS curve depends on (1) the elasticity of the investment demand curve, and (2) the size of the multiplier. The elasticity of investment demand signifies the degree of responsiveness of investment spending to the changes in the rate of interest.

Suppose the investment demand is highly elastic or responsive to the changes in the rate of interest, then a given fall in the rate of interest will cause a large increase in investment demand which in turn will produce a large upward shift in the aggregate demand curve.

The negative slope of the IS curve reflects the increase in income and investment as the rate of interest falls. The slope of the IS curve depends on 2 factors :

The sensitivity (elasticity) of investment and saving to changes in the interest rate,

Size of the multiplier.  

Slope of the IS curve

If investment is very sensitive to the rate of investment, the IS curve is very flat. This is shown by the segment AB of the IS curve in a below graph. Where a small fall in the rate of interest from R1to R2 leads to a large increase in investment and consequently in saving via proportionately large rise in income from Y1 to Y2. The IS curve is interest elastic in the AB segment of the IS curve.   

On the other hand if investment is not very elastic or sensitive to the rate of interest, IS curve is relatively steep. When rate of interest falls more from R2 to R3, the increase in investment is small and so do saving and income increase by a relatively smaller amount Y2Y3. The BC segment of the IS curve is less interest elastic. Any further fall in the rate of interest from R3 will lead to no change in income because the IS curve is vertical in that range. It is interest inelastic.  

The shape of the IS curve also depends upon the size of the multiplier. If the size of the multiplier is large, the larger is the effect on income of a rise in investment and fall in saving. Thus income is more sensitive to changes in the interest rate and the IS curve is flatter. 

Multiplier means : Estimated number by which the amount of a capital investment (or a change in some other component of aggregate demand) is multiplied to give the total amount by which the national income is increased.

Graph

It is important to understand what determines the position of the IS curve and what causes shifts in it. It is the level of autonomous expenditure which determines the position of the IS curve and changes in the autonomous expenditure cause a shift in it. 

By autonomous expenditure we mean the expenditure, be it investment expenditure, the Government spending or consumption expenditure which does not depend on the level of income and the rate of interest.

Shift in IS Curve: 

The government expenditure is an important type of autonomous expenditure. The Government expenditure which is deter­mined by several factors as well as by the policies of the Government does not depend on the level of income and the rate of interest.

Similarly, some consumption expenditure has to be made if individuals have to survive even by borrowing from others or by spending their savings made in the past year. Such consumption expenditure is a sort of autonomous expenditure and changes in it do not depend on the changes in income and rate of interest. Further, autonomous changes in investment can also occur.

For instance, growing population requires more investment in house construction, school buildings, roads, etc., which does not depend on changes in level of income or rate of interest. Further, autonomous changes in investment spending can also take place when new innovations come about, that is, when there is progress in technology and new machines, equipment, tools etc., have to be built embodying the new technology.

Besides, Government expenditure is also of autonomous type as it does not depend on income and rate of interest in the economy. As is well- known government increases its expenditure for the purpose of promoting social welfare and accelerating economic growth. Increase in Government expenditure will cause a rightward shift in the IS curve.

With the increase in autonomous investment (or reduction in saving),the IS curve shifts from IS1 to IS2 and the new equilibrium established at point E2 which indicates a higher level of income Y2 at a constant rate of interest R2.  

In the opposite case when investment falls or saving increases, the IS function will shift to the left and the equilibrium will be established at a lower level of income at a constant rate of interest. 

Countinue

Graph

The LM curve can be derived from the Keynesian theory from its analysis of money market equilibrium. 

The money market is in equilibrium when the demand and supply of money are equal.

L = Demand for money

M = Money for supply

When L=M Money market is in equilibrium

According to Keynes, demand for money to hold depends upon transactions motive and speculative motive.

Money Market Equilibrium: Derivation of LM Curve: 

The demand for money L = Lt + Ls

Lt is the transaction demand for money

Ls is the speculative demand for money

Lt is a function of Y, Lt =f(Y) (directly related with income level)

It is the money held for transactions motive which is a function of income. The greater the level of income, the greater the amount of money held for transactions motive and there­fore higher the level of money demand curve.

Ls is a function of rate of interest 

Ls = f(r) which is inversely related to the rate of interest.

Thus in money market equilibrium 

M=Lt(Y) + Ls(r)

  LM curve shows all combination of interest rate and levels of income at which the demand for money and supply of money are equal. 

In other words, the LM schedule shows the combinations of interest rates and levels of income where the demand for money (L) and the supply of money (M) are equal such that the money market is in equilibrium.

For example

A family of liquidity preference curves L1Y1, L2Y2 and L3Y3 is drawn at income levels.

100 million, 200m and 300 m. These curves together with the perfectly inelastic money supply curve MQ give us the LM curve. The LM curve consists of a series of points, each point representing an interest-income level at which the demand for money (L) equals the supply of money (M). If the income level is Y1 the demand for money L1Y1 equals the money supply (MQ) at interest rate R1.

At the Y2 income level Y2L2 at the rate of interest R2 and so on. The liquidity preferences the level of income and rate of interest provide data for the LM curve.

The LM curve slopes upward from left to right because given supply of money, increase in the level of income, increase the demand for money which leads to higher rate of interest.

There are two factors on which the slope of the LM curve depends. First, the responsiveness of demand for money (i.e., liquidity preference) to the changes in income.

Slope of the LM curve

As the income increases, say from Y0 to Y1 the demand curve for money shifts from Md0 to Md1 that is, with an increase in income, demand for money would increase for being held for transactions motive, Md or L1 =f(Y).

This extra demand for money would disturb the money market equilibrium and for the equilibrium to be restored the rate of interest will rise to the level where the given money supply curve intersects the new demand curve corresponding to the higher income level.

It is worth noting that in the new equilibrium position, with the given stock of money supply, money held under the transactions motive will increase whereas the money held for speculative motive will decline.

The greater the extent to which demand for money for transactions motive increases with the increase in income, the greater the decline in the supply of money available for speculative motive and, given the demand for money for speculative motive, the higher the rise in tie rate of interest and consequently the steeper the LM curve, r = f (M2 L2) where r is the rate of interest, M2 is the stock of money available for speculative motive and L2 is the money demand or liquidity preference for speculative motive.

The second factor which determines the slope of the LM curve is the elasticity or responsiveness of demand for money (i.e., liquidity preference for speculative motive) to the changes in rate of interest. The lower the elasticity of liquidity preference for speculative motive with respect to the changes in the rate of interest, the steeper will be the LM curve. On the other hand, if the elasticity of liquidity preference (money demand-function) to the changes in the rate of interest is high, the LM curve will be flatter or less steep.

If the central bank follows an expansionary monetary policy, it will buy securities in the open market. As a result the money supply with the public increases for both transaction motive and speculative motive. This shifts the LM curve to the right side

Shifts in the LM Curve: 

1.The LM curve is a schedule that describes the combinations of rate of interest and level of income at which money market is in equilibrium.

2. The LM curve slopes upward to the right.

3. The LM curve is flatter if the interest elasticity of demand for money is high. On the contrary, the LM curve is steep if the interest elasticity demand for money is low.

The LM Curve: The Essential Features: 

4. The LM curve shifts to the right when the stock of money supply is increased and it shifts to the left if the stock of money supply is reduced.

5. The LM curve shifts to the left if there is an increase in the money demand function which raises the quantity of money demanded at the given interest rate and income level. On the other hand, the LM curve shifts to the right if there is a decrease in the money demand function which lowers the amount of money demanded at given levels of interest rate and income.

The IS and the LM curves relate the two variables: 

(a) Income and

(b) The rate of interest.

Income and the rate of interest are therefore determined together at the point of intersection of these two curves,

The equilibrium rate of interest thus determined is Or2 and the level of income determined is OY2. At this point income and the rate of interest stand in relation to each other such that (1) the goods market is in equilibrium, that is, the aggregate demand equals the level of aggregate output, and (2) the demand for money is in equilibrium with the supply of money (i.e., the desired amount of money is equal to the actual supply of money). 

Equilibrium of the Goods Market and Money Market: 

It should be noted that LM curve has been drawn by keeping the supply of money fixed.

Thus, the IS-LM curve model is based on: 

(1) The investment-demand function,

(2) The consumption function,

(3) The money demand function, and

(4) The supply of money.

According to the IS-LM curve model both the real factors, namely, saving and investment, productivity of capital and propensity to consume and save, and the monetary factors, that is, the demand for money (liquidity preference) and supply of money play a part in the joint determination of the rate of interest and the level of income. Any change in these factors will cause a shift in IS or LM curve and will therefore change the equilibrium levels of the rate of interest and income.

The IS-LM curve model explained above has succeeded in integrating the theory of money with the theory of income determination. And by doing so, it has succeeded in synthesising the monetary and fiscal policies. Further, with the IS-LM curve analysis, we are better able to explain the effect of changes in certain important economic variables such as desire to save, the supply of money, investment, demand for money on the rate of interest and level of income.

prpared by NSHIMIRYAYO ANGE +250788719816