33 IS LM Model

Dr. Meenu Saihjpal

  1. Learning Outcome

 

After completing this module the students will be able to understand:

  • The concept of goods market
  • The concept of IS curve
  • The concept of money market
  • The concept of LM curve

2. Introduction

 

‘IS-LM curves’ are the standard tools of economic analysis which were developed subsequently to and in response to the then ‘General Theory’ put forward by Keynes in 1936. The chief architect of these curves is Prof. Hicks, who gave these curves in his book, ‘Mr. Keynes and Classics’ in 1937. Prof. Hansen popularized these curves, so these curves are also known as Hicks-Hansen Analysis. This model is also called as Neo-Classical Synthesis.

 

These curves were developed because of the shortcomings in the Keynesian theory. Therefore, to understand the determination of the IS-LM curves, it is essential to understand the Keynesian system and the shortcomings in the same. In the Keynesian system, in a two sector model, in the short run, the necessary condition for equilibrium is that aggregate demand (AD) must be equal to aggregate supply (AS) i.e.

 

In equilibrium, AD = AS

 

Aggregate demand is determined by consumption (C) and Investment (I) in a two sector model and aggregate supply is determined by consumption and savings (S). Therefore, in equilibrium

 

If AD = AS,

 

And if AD = C+I

 

And if, AS = C+S,

 

Then, in equilibrium,

 

C+I = C+S

 

Or, in equilibrium,

 

I = S.

 

Since, savings are a function of income and investment is a function of rate of interest, therefore, the graphic determination of the equilibrium must include the rate of interest as one of the variables however, in Keynesian system, the graphic determination of equilibrium simply assumes the rate of interest and no actual determination of the same takes place. This became a major criticism of this theory and subsequently, led to the development of IS curves.

 

Likewise, in the Keynesian money market, the condition for equilibrium is that there should be equality between demand for money (Dm) and supply of money (Sm). Demand for money is a function of income (Y) and rate of interest (r). The supply of money is determined exogenously. The graphic determination of the equilibrium in the money market is indeterminate as it does not include income as one of the variables. This shortcoming of the Keynesian system led to the development of the LM curves. So, basically from the Keynesian aggregate demand and aggregate supply curves (Keynesian cross) and from the Keynesian liquidity preference theory, we shall derive the IS and LM curves.

 

 

3 Assumptions: There are two basic assumptions. These are given below:

 

i) We assume a hypothetical economy which is divided into three markets. These are:

 

Goods market

 

Money market

 

Labour market

 

These markets are separate. Goods market determines the equilibrium of goods, money market determines the equilibrium of money and labour market determines the equilibrium of labour.

 

ii) Two sector model is assumed: two sector model implies that the economy under consideration is a closed economy, so there is no foreign sector. It also implies that there is no government sector also.

 

4 The Model : IS schedule implies investment (I) and saving (S) schedule. It represents equilibrium in the goods market or in the real market. IS schedule is the locus of the points of rate of interest and the levels of income. LM schedule implies demand for money (L) and supply of money (M) and it represents equilibrium in the money market.

 

Derivation of IS schedule: The derivation of the IS schedule is explained in figure 4.1. In the part B of the figure, we are measuring investment on OX axis and savings on OY axis. The 450 line shows the points of equality between savings and investment. When the savings are OS0, then the level of investment in the economy is OI0. As the saving increases to OS1, the level of investment increases to OI1. Part A of the figure shows investment on OX axis and rate of interest on OY axis. If the market rate of interest is OR0 then the level of investment (OI0) can be plotted down in part A from the values of investment in the upper part, B. Likewise the values can also be plotted for OR1 level of rate of interest. It shows inverse relationship between investment and rate of interest. Part C shows the relationship between savings and income as savings are an increasing function of the income. At OS0 level of savings the corresponding level of income is OY0. As income increases the level of savings also increase. The values of income given in part C can be plotted down in part D of the figure. Part D measures income on OX axis and rate of interest on OY axis. By joining the OY0 level of income at OR0 level of rate of interest, we get point ‘a’ which is the first point of the IS curve. Likewise we can get point ‘b’ of the IS curve. By joining ‘a’ and ‘b’ points, we get the IS curve. This curve is sloping downwards from left to right. All points on the IS schedule show equilibrium in the goods market. All the points above or below the IS curve are the points of disequilibrium. In part D of the figure 4.1 any point above ‘a’ say c, show disequilibrium. At this point c, at the same rate of interest i.e.OR0, the level of income increases from OY0 to OY1. Since, the rate of interest is the same, therefore, the level of investment is also the same but since, the level of income increases, therefore, the level of savings also increase. So, at point ‘c’ the level of savings is more than the level of investment. Likewise any point below ‘a’ shows excess of investment over savings.

 

Properties of IS schedule: Given below are the different properties of IS schedule:

  1. IS schedule is the locus of different combinations of the rate of interest and the levels of income which ensures equilibrium in the goods market.
  2. The IS schedule is different from usual type of curves which represent a functional relationship between two variables. IS schedule simply show the combination of two variables and there is no functional relationship between the two.
  3. IS schedule is negatively sloped. The negative slope of the curve is implied in the definition of the curve and in the relationship between the underlying variables. When the rate of interest is decreased, level of investment increases. The increase in the level of investment raises the level of income in the economy through the principle of multiplier. Likewise, when the level of rate of interest is increased, investment decreases in the economy which in turn decreases the level of income. Thus, indirect but inverse relationship between rate of interest and the level of income is based upon the relationship between the underlying functions.
  4. Whenever the underlying functions will shift, IS schedule will also undergo a shift.
  • 5 The slope of the IS schedule depends upon the slope of the underlying functions i.e. the slope of the IS schedule depends upon:

 

a) Interest elasticity of the investment function

 

b) Marginal propensity to save

 

Derivation of LM schedule: LM schedule represents the equilibrium in the money market. In the Keynesian money market, equilibrium rate of interest is determined while assuming it at some level of income. However, in the LM model the equilibrium in the money market is determined along with the simultaneous determination of the rate of interest and income. For equilibrium in the money market, supply of money (Sm) must be equal to the demand for money (Dm). Supply of money is exogenously determined by the Central bank of the economy. Money is demanded for three main reasons: transaction, precautionary and speculative activities. Demand for money for transaction and precautionary purpose are dependent upon the level of income and the demand for money for speculative purpose is dependent upon rate of interest. The derivation of the LM curve is shown in figure 4.2.

Figure 4.2 has four parts-A, B, C and D. Part A measures speculative demand for money which is a function of rate of interest. On OY axis we are measuring rate of interest and on OX axis we are measuring speculative demand for money. There is inverse relationship between the two. When the rate of interest is high at OR0 level then the speculative demand for money is low at OSp0. As the rate of interest decreases to OR1 level, the demand for money for speculative purpose increases to OSp1. Part B explains total supply of money which is exogenously determined. The whole of the supply of money is divided between transaction and speculative demand for money and nothing is saved. Part C shows the demand for money for transaction purpose. According to Keynes, demand for money for transaction purpose is an increasing function of income which implies that whenever income of the consumer increases, the demand for transaction purpose also increases. As per Keynes, demand for money for transaction purpose (Trd) is a fixed proportion (K) of income (Y) i.e

 

Trd  = K (Y)

 

Here, we have assumed K to be 0.5 which implies that the households keep half of their income for carrying out day to day transactions. So, a line OZ is drawn at an angle of 450 as it divides the whole space into two equal zones i.e. vertical and horizontal distances from the line are the same. We start from part C. At a given level of income i.e. at OY0 income, the transaction demand for money is OTr0. When the transaction demand is OTr0 then part B shows that the speculative demand for money is OSp0. Since, the demand for money for speculative purpose has an inverse relationship with rate of interest, therefore, when the speculative demand is OSp0 then the rate of interest is high at OR0 in part A. Part D shows the LM curve which is drawn by extending the OR0 level of rate of interest from part A of the figure and OY0 level of income from part C of the figure. This gives us the first point of LM curve, point ‘a’. Likewise, we can get the second point, point b, to draw LM curve. By joining ‘a’ and ‘b’ points, we get the LM curve. Any point on this curve shows the equilibrium in money market. Any point above or below this curve shows disequilibrium in the money market.

 

Properties of LM schedule

 

The properties of LM curve are given below:

  • LM curve shows equilibrium in the money market. It is the locus of the points of different combinations of rate of interest and the levels of income which ensures equilibrium in the money market.
  • LM curve is different from the usual curves. The usual curves give the functional relationship between two variables. For example; the demand for money curve shows the functional relationship between the demand for money and rate of interest. But the LM curve just gives us the combinations of the two variables (rate of interest and income) without establishing any functional relationship between the two.
  • LM schedule is positively sloped. Positive slope implies when one variable increases the other one must increase. When the income of the consumer increases, the transaction demand for money increases. Since both the transaction and speculative demand for money make the supply of money which is constant, therefore, this causes a decline in the speculative demand for money. When the speculative demand for money decreases then because of the inverse relationship between speculative demand and rate of interest, the market rate of interest increases. Thus, an increase in the income causes an increase in the rate of interest and vice-versa.
  • LM schedule is drawn with respect to a given money supply. Whenever there is any change in the money supply, the LM curve also undergoes a change. Supply of money shifts whenever there is an increase in nominal prices or price level decreases.
  • Slope of the LM schedule will depend upon the slope of the underlying functions i.e. demand for money for speculative purpose and demand for money for transaction purpose. Corresponding to the flatter part of the demand for money for speculative purpose curve, there is also a flatter part of LM schedule. After that the LM schedule is upward sloping. In figure 4.3, part ‘A’ shows the LM schedule and part ‘B’ shows the demand for money for speculative purpose curve. The flatter part of the demand for money for speculative purpose curve starts from ‘a’. This is because of the liquidity trap as discussed in the Keynesian theory. Corresponding to this flatter part, LM schedule also has a flatter part ‘bc’. After that the LM curve is upward sloping.

Simultaneous equilibrium in the goods market and money market

 

Through the IS curve we determine the equilibrium level of income which shows equilibrium in the goods market. Through the LM curve we determine the equilibrium level of rate of interest in the money market. For the simultaneous determination of the income and the rate of interest we superimpose both IS and LM curves. This also gives us the equilibrium in the goods and money market. This is explained in figure 4.4. On OX axis we are measuring income level and on OY axis we are measuring rate of interest. IS and LM curves are shown in the graph. Equilibrium is attained at a point where both the curves intersect each other. Point e shows equilibrium. At this point aggregate demand is equal to aggregate supply and supply of money is equal to demand for money. OY0 and OR0 are the equilibrium levels of income and rate of interest.

 

Properties of simultaneous equilibrium

 

Given below are some of the properties of the simultaneous equilibrium in the goods and money market:

  • It is unique equilibrium: once equilibrium is attained, it will be a unique equilibrium. Any other combinations either lead to disequilibrium in both or in at least one market. In figure 4.4 initially the simultaneous equilibrium is attained at point ‘e’. if the economy is moved to point ‘b’ on IS curve, the goods market is in equilibrium but the money market is in disequilibrium. Likewise, if the economy is moved to point ‘c’, where the money market is in equilibrium but the goods market is in disequilibrium. Thus, there is a unique equilibrium only at point e.
  • It is a stable equilibrium: the equilibrium attained through IS- LM curves is a stable equilibrium as once disturbed, it would be restored.

 

Shifts in the simultaneous equilibrium

 

Shifts in the simultaneous equilibrium will be caused by the shifts in either IS curve or LM curve or in both the curves. Therefore, the shifts in the simultaneous equilibrium are discussed under the following heads:

 

a) Shifts in simultaneous equilibrium due to shifts in IS curve, LM curve remaining the same:

 

IS schedule is drawn on the assumption of a given government expenditure. Whenever there is any change in the fiscal policy which is reflected in the government expenditure, IS curve will shift. When the government expenditure increases due to an upward change in the fiscal policy, the IS curve shifts outwards. This is explained in figure 4.5. In the figure, the initial IS curve is IS0 and the initial LM curve is LM0. The initial point of equilibrium is e0. The initial IS curve IS0 is at a given level of government expenditure say G0. When there is an increase in the government expenditure from G0 to G1, the IS curve shifts to the right from IS0 to IS1. This happens because with the increase in government expenditure, autonomous investment increases which causes a rightward shift in the investment curve.

 

With the rightward shift in the investment curve, the level of savings increases which through the multiplier effect increases the income in the economy from OY0 to OY1 and thus, new equilibrium is restored. In the same way, the downward shift in IS curve causes a downward shift in the equilibrium level when LM curve remains the same.

 

b) Shifts in simultaneous equilibrium due to shifts in LM curve, IS curve remaining the same:

 

When the IS curve remains constant and there is a shift in the LM curve, the equilibrium also shifts. This occurs because of the changes in the money supply. When the money supply increases the LM curve shifts outwards to the right and thus, if IS curve is the same then the equilibrium point will shift to the right. This is explained through the figure 4.6. LM0 and IS0 are the initial curves and e0 is the initial equilibrium point. When the money supply increases the LM curve shifts from LM0 to LM1 and IS curve remaining the same at IS0, the equilibrium point shifts to the right from e0 to e1. This causes a downward shift in the equilibrium rate of interest and an increase in the level of income. In the same way, the downwards shift in the LM curve causes a upward shift in the equilibrium point when IS curve remains the same.

 

  1. c) Shifts in simultaneous equilibrium due to simultaneous shifts in IS and LM curves:

 

Figure 4.7 shows the simultaneous shifts in the IS and LM curves. IS0 and LM0 are the initial curves and e0 is the initial equilibrium point. Initially, when the government expenditure increases, the IS curve shifts to the right from IS0 to IS1 (LM curve has not yet shifted) in figure 4.7. Through the multiplier effect, rate of interest also increases. Since, rate of interest is inversely related with the level of investment, therefore, the level of private investment will decrease.

 

This adverse impact of the changes in government expenditure on the private investment is called as ‘crowding out’ effect. If now, the LM curve shifts outwards from LM0 to LM1 due to increase in money supply, then the new equilibrium will be at e2 which will be attained at the earlier level of rate of interest i.e. OR0. Thus, at e2 level, the resultant increase in income Y0Y2 is greater than the increase in income when only the IS curve shifts (YOY1).

 

Thus, when money supply and government expenditure increase only then the economy can realize the maximum increase in income. Hence, this simultaneous shift shows the significance of both the monetary and fiscal policies. This is also to be kept in mind that to get the maximum increase in income the shift in IS and LM curves should be equal.

 

5 Conclusions

 

Thus, in this chapter we have learnt how the weaknesses of the Keynesian system were overcome. The IS and LM model helps us in the simultaneous determination of the equilibrium in the goods market and in the money market. Such a model helps in the simultaneous determination of the rate of interest and the level of income while ensuring equilibrium in both the markets also. However, doubts have been raised about its validity.

 

Learn More

 

1. Dwivedi, D.N., Macroeconomics Theory and Policy, Tata McGraw Hill Education Private Limited, New Delhi, 2011.

2. Froyen,R. T., Macroeconomics- Theories and Policies, Pearson India, 2006.

3. Shapiro, E., Macroeconomic Analysis, Galgotia Publications,  2006.