General equilibrium of the economy through IS and LM function
The Keynes in his analysis of national income explains that national income is determined at the level where aggregate demand (i.e., aggregate expenditure) for consumption and investment goods (C +1) equals aggregate output. In other words, in Keynes’ simple model the level of national income is shown to be determined by the goods market equilibrium. In this simple analysis of equilibrium in the goods market Keynes considers investment to be determined by the rate of interest along with the marginal of capital and is shown to be independent of the level of national income.
The rate of interest, according to Keynes, is determined by money market equilibrium by the demand for and supply of money. In this Keynes’ model, changes in rate of interest either due to change in money supply or change in demand for money will affect the determination of national income and output in the goods market through causing changes in the level of investment.
In this way changes in money market equilibrium influence the determination of national income and output in the goods market. However, there is apparently one flaw in the Keynesian analysis which has been pointed out by some economists and has been a subject of a good deal of controversy.
It has been asserted that in the Keynesian model whereas the changes in rate of interest in the money market affect investment and therefore the level of income and output in the goods market, there is seemingly no inverse influence of changes in goods market i.e., (investment and income) on the money market equilibrium. It has been shown by J.R. Hicks and others that with greater insights into the Keynesian theory one finds that the changes in income caused by changes in investment or propensity to consume in the goods market also influence the determination of interest in the money market.
According to him, the level of income which depends on the investment and consumption demand determines the transactions demand for money which affects the rate of interest. Hicks, Hansen, Lerner and Johnson have put forward a complete and integrated model based on the Keynesian framework wherein the variables such as investment, national income, rate of interest, demand for and supply of money are interrelated and mutually interdependent and can be represented by the two curves called the IS and
LM curves. This extended Keynesian model is therefore known as IS-LM curve model. In this model they have shown how the level of national income and rate of interest are jointly determined by the simultaneous equilibrium in the two interdependent goods and money markets. Now, this IS-LM curve model has become a standard tool of macroeconomics and the effects of monetary and fiscal policies are discussed using this IS and LM curves model.
Goods Market Equilibrium: The Derivation of the is Curve:
The IS-LM curve model emphasises the interaction between the goods and money markets. The goods market is in equilibrium when aggregate demand is equal to income. The aggregate demand is determined by consumption demand and investment demand.
In the Keynesian model of goods market equilibrium we also now introduce the rate of interest as an important determinant of investment. With this introduction of interest as a determinant of investment, the latter now becomes an endogenous variable in the model.
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 c’ 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. In the derivation of the IS Curve we seek to find out the equilibrium level of national income as determined by the equilibrium in goods market by a level of investment determined by a given rate of interest. Thus IS curve relates different equilibrium levels of national income with various rates of interest. As explained above, with a fall in the rate of interest, the planned investment will increase which will cause an upward shift in aggregate demand function (C+7) 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.
How the IS curve is derived is In panel (a) of Fig. 13 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 Oro the planned investment is equal to 01. With Ol as the amount of planned investment, the aggregate demand curve is C+1 which, as will be seen in panel (b) of Fig. 13 equals aggregate output at OY! level of national income.
Therefore, in the panel (c) at the bottom of the Fig. 24.1, against rate of interest Or2, level of income equal to DYO has been plotted. Now, if the rate of interest falls to Dr2 the planned investment by businessmen increases from 010 to 010 [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 DY1 level of national income. Thus, in panel (e) at the bottom of Fig. 13 the level of national income DY 1 is plotted against the rate of interest, Or,.
With further lowering of the rate of interest to Or,, the planned investment increases to Ol, (see panel a). With this further rise in planned investment the aggregate demand curve in panel (b) shifts upward to the new position C+1, corresponding to which goods market is in equilibrium at OY, level of income. Therefore, in panel (c) the equilibrium income OY, is shown against the interest rate Or..
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. 13.1 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.
Money Market Equilibrium: Derivation of LM Curve:
Derivation of the LM Curve: The LM curve can be derived from the Keynesian theory from its analysis of money market equilibrium. According to Keynes, demand for money to hold depends upon transactions motive and speculative motive. 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. The demand for money depends on the level of income because they
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.
How the IS curve is derived is illustrated in. In panel (a) of 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 Oro the planned investment is equal to 01. With Ol as the amount of planned investment, the aggregate demand curve is C+1 which, as will be seen in panel (b) of Fig. 13 equals aggregate output at OY! level of national income.
Therefore, in the panel (c) at the bottom of the, against rate of interest Or 2, level of income equal to DYO has been plotted. Now, if the rate of interest falls to Dr2 the planned investment by businessmen increases from 010 to 010 [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 DY1 level of national income. Thus, in panel (e) at the bottom of Fig. 13 the level of national income DY 1 is plotted against the rate of interest, Or,.
With further lowering of the rate of interest to Or,, the planned investment increases to Ol, (see panel a). With this further rise in planned investment the aggregate demand curve in panel (b) shifts upward to the new position C+1, corresponding to which goods market is in equilibrium at OY, level of income. Therefore, in panel (c) the equilibrium income OY, is shown against the interest rate Or..
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. 13.1 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.
Money Market Equilibrium: Derivation of LM Curve:
Derivation of the LM Curve: The LM curve can be derived from the Keynesian theory from its analysis of money market equilibrium. According to Keynes, demand for money to hold depends upon transactions motive and speculative motive. 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. The demand for money depends on the level of income because they curves for money. As Income increases, money demand curve shifts outward and therefore the rate of interest which equates supply of the X-axis and plot the income level corresponding to the various interest money, with demand for money rises. In Fig. 14 (b) we measure income on
rates determined at those income levels through money market equilibrium by the equality of demand for and the supply of money in Slope of LM Curve:
It will be noticed from that the LM curve slopes upward to the right. This is because with higher levels of income, demand curve for money (Md) is higher and consequently the money- market equilibrium, that is, the equality of the given money supply with money demand curve occurs at a higher rate of interest. This implies that rate of interest varies directly with income.
It is important to know the factors on which the slope of the LM curve depends. 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. As the income increases, say from Y to Y, the demand curve for money shifts from Mdo to Md, that is, with an increase in income, demand for money would increase for being held for transactions motive, Md or LI=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 (M, L,) where r is the rate of interest, M, is the stock of money available for speculative motive and L 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,
Simultaneous Equilibrium of the Goods Market and Money Market: 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 Or, and the level of income determined is OY,. 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). 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 quantity of money.
We see, therefore, that 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, as we shall see below, 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.
Income Level:
speculative motive at a given level of income which will cause the interest rate to fall. As a result, the LM curve will shift to the right.
IM
Effect of Changes in Supply of Money on the Rate of Interest and Let us first consider what will happen if the supply of money is increased by the action of the Central Bank. Given the liquidity preference schedule, with the increase in the supply of money, more money will be available for With this rightward shi, in the LM curve, in the new equilibrium position, rate of interest will be lower and the level of income greater than before. where with a given supply of money, LM and IS curves intersect at point E.
With the increase in the supply of money, LM curve shifts to the right to the position LM’, and with IS schedule remaining unchanged, new equilibrium is at point G corresponding to which rate of interest is lower and level of income greater than at E. Now, suppose that instead of increasing the supply of money, Central Bank of the country takes steps to reduce the supply of money.
With the reduction in the supply of money, less money will be available for speculative motive at each level of income and, as a result, the LM curve will shift to the left of E, and the IS curve remaining un-changed, in the new equilibrium position the rate of interest will be higher and the level of income smaller than before.
Changes in the Desire to Save or Propensity to Consume:
Let us consider what happens to the rate of interest when desire to save or in other words, propensity to consume changes. When people’s desire to save falls, that is, when propensity to consume rises, the aggregate demand curve will shift upward and therefore, level of national income will rise at each rate of interest.
As a result, the IS curve will shift outward to the right. suppose with a certain given fall in the desire to save (or increase in the propensity to consume), the IS curve shifts rightward to the dotted position IS’. With LM curve remaining unchanged, the new equilibrium position will be established at H corresponding to which rate of interest as well as level of income will be greater than at E.
Thus, a fall in the desire to save has led to the increase in both rate of interest and level of income. On the other hand, if the desire to save rises, that is, if the propensity to consume falls, aggregate demand curve will shift downward which will cause the level of national income to fall for each rate of interest and as a result the IS curve will shift to the left.
With this, and LM curve remaining unchanged, the new equilibrium position will be reached to the left of E, say at point L corresponding to which both rate of interest and level of national income will be smaller than at E.
Changes in Autonomous Investment and Government Expenditure Changes in autonomous investment and Government expenditure will also shift the IS curve, If either there is increase in autonomous private investment or Government steps up its expenditure, aggregate demand for goods will increase and this will bring about increase in national income through the multiplier process.
This will shift IS schedule to the right and given the LM curve, the rate of interest as well as the level of income will rise. On the contrary, if somehow private investment expenditure falls or the Government reduces its expenditure, the IS curve will shift to the left and given the LM curve, both the rate of interest and the level of income will fall.
Changes in Demand for Money or Liquidity Preference:
Changes in liquidity preference will bring about changes in the LM curve. If the liquidity preference or demand for money of the people rises, the LM curve will shift to the left. This is because, greater demand for money, given the supply of money, will raise the rate of interest corresponding to each level of national income. With the leftward shift in the LM curve, given the IS curve, the equilibrium rate of interest will rise and the level of national income will fall.
On the contrary, if the demand for money or liquidity preference of the people falls, the LM curve will shift to the right. This is because, given the supply of money, the rightward shift in the money demand curve means that corresponding to each level of income there will be lower rate of interest. With rightward shift in the LM curve, given the IS curve, the equilibrium level of rate of interest will fall and the equilibrium level of national income will increase.
We thus see that changes in propensity to consume (or desire to save). autonomous investment or Government expenditure, the supply of money and the demand for money will cause shifts in either IS or LM curve and will thereby bring about changes in the rate of interest as well as in national income.
The integration of goods market and money market in the IS-LM curve model clearly shows that Government can influence the economic activity or the level of national income through monetary and fiscal measures.
Through adopting an appropriate monetary policy (t.e., changing the supply of money) the Government can shift the LM curve and through pursuing an appropriate fiscal policy (expenditure and taxation policy) the Government can shift the IS curve. Thus both monetary and fiscal policies can play a useful role in regulating the level of economic activity in the country.
Critique of the IS-LM Curve Model
The IS-LM curve model makes a significant advance in explaining the simultaneous determination of the rate of interest and the level of national income. It represents a more general, inclusive and realistic approach to the determination of interest rate and level of income.
Further, the IS-LM model succeeds in integrating and synthesising fiscal with monetary policies and theory of income determination with the theory of money. But the IS-LM curve model is not without limitations.
Firstly, it is based on the assumption that the rate of interest is quite flexible, that is, free to vary and not rigidly fixed by the Central Bank of a country. If the rate of interest is quite inflexible, then the appropriate adjustment explained above will not take place.
Secondly, the model is also based upon the assumption that investment is interest-elastic, that is, investment varies with the rate of interest. If investment is interest-inelastic, then the IS-LM curve model breaks down since the required adjustments do not occur.
Thirdly, Don Patinkin and Milton Friedman have criticized the IS-LM curve model as being too, artificial and over simplified. In their view, division of the economy into two sectors- monetary and realis artificial and unrealistic. According to them, monetary and real sectors are quite interwoven and act and react on each other. Further, Patinkin has pointed out that the IS-LM curve model has ignored the possibility of changes in the price level of commodities. According to him, the various economic variables such as supply of money, propensity to consume or save, investment and the demand for money not only influence the rate of interest and the level of national income but also the prices of commodities and services.
Patinkin has suggested a more integrated and general equilibrium approach which involves the simultaneous determination of not only the rate of interest and the level of income but also of the prices of commodities and services.
