After studying this topic, you should be able to understand
This chapter is an extension of Chapter 16 which extends the IS–LM two sector model to a three sector model where there exists the government sector in addition to the households and the firms. The shifts in the IS curve due to the changes in fiscal policy and the shifts in the LM curve due to changes in monetary policy are also analysed.
The chapter goes on to discuss the effectiveness of monetary and fiscal policies in the different ranges of the LM curve. (Refer to Appendix B for the IS–LM framework for a four sector model)
The construction of a three sector model involves the inclusion of two new variables which pertain to the government sector, government expenditure and taxation. The analysis is based on certain assumptions:
The IS–LM model emerged as an aftermath of the Keynesian revolution. It showed how the economists from the period of the 1940s to the 1960s regarded the Keynesian economics and the classical economics. Later, many other macroeconomic models also came up like the Harrod–Domar growth model and the multiplier–accelerator business-cycle model. However, these failed to gain as much popularity as some of the other models like the IS–LM model.
As already observed, there are two approaches to determine the equilibrium level of income. In a three sector economy, they can be expressed as
(1) Aggregate Demand–Aggregate Supply Approach
Aggregate demand = Total value of output (or income)
or
Y = C + I + G
(2) Injections equal Leakages Approach
I + G = S + T
We have consumption function as C = C(Y); investment function as I = I(r); government expenditure G = ; saving function as S = S(Y); tax as T = + tY and equilibrium condition as Y = C(Y) + I(r) + .
The two equilibrium conditions can be used to develop a graphical approach to the derivation of the IS curve as in Figure 17.1.
In Figure 17.1 starting with a two sector model, Quadrant A shows the investment curve, I. Corresponding to the saving function S1 in Quadrant C, the two sector goods market equilibrium is represented by the curve IS1 in Quadrant D. The investment curve, I of Quadrant A and the savings curve, S1 of Quadrant C yields the curve ISl in Quadrant D. Quadrant D shows the goods market equilibrium in a three sector economy where the IS curve depicts the different combinations of the interest rates and the output levels at which planned investment equals saving or planned spending is equal to the income.
Next assume the government sector is introduced in the model or, in other words, we have a three sector model. In Quadrant A, government expenditures have been added to the investment curve to get the I + G curve. As government expenditures are independent of the interest rate, I + G curve lies to the right of the investment curve as shown in the figure.
Quadrant B gives the injections leakages equality in the form of a 45 degree line drawn through the origin. At all points along this 45 degree line, injections equal leakages or I + G = S + T.
Quadrant C shows the saving function S. When a tax is imposed, the saving curve will shift to the right by the amount of the tax to get the adjusted saving curve S2. When taxes are added to the adjusted saving function, we get the S2 + T curve in Quadrant C of Figure 17.1.
The investment curve I of Quadrant A and the saving curve S of Quadrant C yielded the curve IS1 in Quadrant D. The investment plus government expenditure curve (I + G) of Quadrant A and the saving plus tax curve (S2 + T) of Quadrant C yields the curve IS2 in Quadrant D.
In a three sector economy, the analysis of the money market will remain the same as in the two sector economy as government expenditure and taxes do not influence either the demand for money or the supply of money.
Figure 17.1 The Goods Market Equilibrium in a Three Sector Economy: The IS Curve
The goods market is in equilibrium when
Aggregate demand = Total value of output (or income)
or
Y = C + I + G
But,
C = Ca+b Yd,
G = ,
Yd = Y – T,
T = + tY
Thus,
Y = Ca + bYd + – hr +
Y = Ca + b(Y – T) + – hr +
Y = Ca + b[Y – ( + tY)] + – hr +
Y = Ca + bY – b – btY + – hr
Y – bY + btY = Ca – b + – hr +
Y(1 – b + bt) = Ca – b + – hr +
Equation (1) represents the IS curve in a three sector economy.
Numerical Illustration 1
Suppose the consumption and investment functions are as follows:
C = 10 + 0.5Y
I = 80 – 8r.
Solution
Y = C + I
Y = 10 + 0.5Y + 80 – 8r
0.5Y = 90 – 8r
Y = 180 – 16r
Y = C + I + G
Y = 10 + 0.5 (Y – 30) + 80 – 8r + 20
0.5Y = 90 – 8r – 15 + 20
0.5Y = 95 – 8r
Y = 190 – 16r
The money–market equilibrium is similar to that of a two sector economy.
Thus,
md = ms
But,
md = mt + msp
where, | md = total demand for money |
mt = kY (transactions demand for money) | |
msp = g(r) (speculative demand for money) |
We assume that the speculative demand for money is a linear function (rather than a curve). Hence, we have msp = sp – g(r).
From the above, we have Supply of money ms = a
Demand for money md = kY + sp – g(r)
The money–market equilibrium condition can be written as
Thus,
Equation (2) represents the LM curve.
We have already observed in Chapter 16 that there is only one combination of income and the rate of interest at which both the goods and the money market are in equilibrium. This has been depicted in Figure 17.2. This combination exists at point E at which the IS and LM curves intersect to determine the equilibrium rate of interest at r* and the equilibrium level of income at Y*. It is important to note that at all other points, there exists disequilibrium in either the goods market or the money market.
All combinations of income and interest that lie above and towards the right of the IS curve, like point R, indicate a situation where Y > C + I + G or saving plus taxes is greater than planned investment plus government expenditures. There exists an excess supply of goods. Hence, the level of income will fall.
The initial IS–LM model (as compared to the new IS–LM model) plays an important role in policy decisions. However, it is being subject to criticism in that it is an obsolete instrument of monetary policy. It is unable to explain the existence of a high inflation rate and high unemployment rate simultaneously in the economy. However, attempts are being made to revive the initial IS–LM model through the expectation concepts.
Figure 17.2 Equilibrium in the Goods and the Money Market in a Three Sector Economy
All combinations of income and interest that lie below and towards the left of the IS curve, like point P, indicate a situation where Y < C + I + G or saving plus taxes is less than planned investment plus government expenditures. There exists an excess demand for goods. Thus, there will be an increase in the income level.
Similarly as far as the LM curve is concerned, at all combinations of income and interest that lie below and towards the right of the LM curve, like point R, the demand for money is greater than the supply of money or there is an excess demand for money. Hence, the rate of interest will rise.
At all combinations of income and interest that lie above and towards the left of the LM curve, the demand for money is less than the supply of money or there is an excess supply of money. Hence, the rate of interest will fall.
It is only at point E that there is equilibrium in both the goods and money markets which will remain unchanged until a shift in the IS or LM curve disturbs the equilibrium.
Numerical Illustration 2
Suppose the consumption and investment functions are as follows:
C = 60 + 0.60Yd(where Y = Yd – T)
I = 150 – 8r
Also, the government expenditure and taxes are
G = Rs. 50 crores
T = Rs. 50 crores
Assume that the supply of money is Rs. 120 crores. The demand for money function is md = 0.25 Y – 5r.
Find
Y = C + I
Y = 60 + 0.60(Y – 50) + 150 – 8r + 50
Y = 230 + 0.60Y – 8r
0.40Y = 230 – 8r
Y = 575 – 20r
md = 0.25Y – 5r
ms = 120
In equilibrium,
md = ms
Thus,
0.25Y – 5r = 120
0.25Y = 120 + 5r
Y = 480 + 20r
IS = LM
575 – 20r = 480 + 20r
40r = 95
r = 2.375%
Y = 575 – 20 × 2.375
Y = 527.5
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 527.5 and r = 2.375%.
Figure 17.3 Simultaneous Equilibrium for IS and LM Curves Exist When Y = 527.5 and r = 2.375%
In Chapter 16 we had observed that a shift in either the investment function or the consumption function leads to a shift in the IS curve. Similarly, the effects of a change in the fiscal policy can be analysed in terms of its influence on the IS curve and the resulting changes in income and the rate of interest. It is to be remembered that a fiscal policy relates to the government expenditures and its taxes.
In Figure 17.4, the initial equilibrium is at point E1 determined by the intersection of the IS1 and LM curves with the equilibrium income and the rate of interest at Y1 and r1 respectively.
An increase in government expenditure by ΔG shifts the IS curve to the right by an amount equal to the government expenditure multiplier times the change in government expenditure, 1/1 – b × ΔG. (We had discussed in Chapter 7 that the government expenditure multiplier is GM = ΔY/ΔG = 1/1 – b). Thus, the new IS curve is IS2 with the equilibrium at point E2. The equilibrium income and the rate of interest are Y2 and r2, respectively.
The above analysis shows that an increase in government expenditure brings about an increase in income from Y1 to Y2 and an increase in the rate of interest from r1 to r2.
One would expect that the increase in the government expenditure would result in an increase in the income level by an amount equal to the multiplier times the increase in the government expenditure or, in other words, by an amount equal to 1/1 – b × ΔG. In that case, equilibrium would be at point E′ on the IS2 curve and the increase in income would be from Y1 to Y′. Instead, the equilibrium is at E2 while the increase in income is from Y1 to Y2 only. This is due to the crowding out effect.
The level of government expenditure, G, is an important component of aggregate demand. As already discussed, Figure 17.4 analyses the effects of a shift in the IS curve due to an increase in aggregate demand. The initial equilibrium is at point E1. Given the rate of interest at r1, there is an increase in government expenditure and thus in the aggregate demand. To meet the increased demand, there will be an increase in the level of output. The IS curve will shift from IS1 to IS2 and equilibrium will move from point E1 to point E′ at the rate of interest, r1 There will be an increase in the equilibrium income from Y1 to Y′.
Crowding out is a situation which arises when an expansionary fiscal policy–for example, an increase in government expenditure–leads to an increase in the rate of interest, thus leading to a decrease in private investment.
Figure 17.4 Shift in the IS Curve Due to Changes in Fiscal Policy
At E′ though there exists goods market equilibrium, there is disequilibrium in the money market. This is because the increase in the income has generated an excess demand for money. Therefore, there will occur an increase in the rate of interest leading to a decrease in investment and hence in the aggregate demand. After all the adjustments for the increase in the government expenditures and the dampening effects of the higher rate of interest on investment are taken into consideration, both the goods and the money market are simultaneously in equilibrium only at point E2. It is only at this point that the planned spending equals income and the demand for money equals the supply of money. Thus, an increase in government expenditure (fiscal expansion) does lead to an increase in the income level, but it is to be noted that the increase in the rate of interest has a dampening effect on the expansion. In Figure 17.4, a comparison between the equilibrium at E2 and E′ in the goods market shows that the increase in the government expenditure leads to an increase in the income level from Y1 to Y2 (and not Y′).
Crowding out is a situation which arises when an expansionary fiscal policy–for example, an increase in government expenditure–leads to an increase in the rate of interest, thus leading to a decrease in private investment. Hence, the adjustments which occur in the rate of interest have a dampening effect on the increase in the output.
We consider two cases:
The impact of taxes is felt through a change in the consumption level. In Figures. 17.5 and 17.6, which show the impact of a tax, the economy’s initial equilibrium is at point E1 determined by the intersection of the IS1 and LM curves with the equilibrium income and the rate of interest at Y1 and r1, respectively.
Figure 17.5 depicts the impact of an increase in taxes. Suppose the government increases the tax by ΔT (there is no change in government expenditures), this will shift the IS curve to the left by an amount equal to the tax multiplier times the change in the tax, b/1 – b × ΔT. (We had observed in Chapter 7 that the tax multiplier is GT = ΔY/ΔT = b/1 – b). Thus, the new IS curve is IS2 with the equilibrium at point E2. The equilibrium income and the rate of interest are Y2 and r2, respectively. Thus, an increase in tax brings about a decrease in income from Y1 to Y2 and a decrease in the rate of interest from r1 to r2.
Figure 17.5 Shift in the IS Curve Due to an Increase in Tax
Figure 17.6 Shift in the IS Curve Due to a Decrease in Tax
One would expect that an increase in the tax would result in a decrease in the income level by an amount equal to the tax multiplier times the increase in the tax, or in words b/1 – b × ΔT. In that case, the new equilibrium would be at point E′ on the IS2 curve and the decrease in income from Y1 to Y′. Instead, the equilibrium is at E2 while the decrease in income is from Y1 to Y2 only. The reason for this is that an increase in the tax results in a decrease in the consumption level which leads to a decrease in the production of the goods and services causing a decrease in the income levels. Hence, individuals demand less money leading to decrease in the interest rates. The decrease in the interest rates is responsible for an increase in investment, thus, offsetting the decrease in the consumption levels to some extent. The Keynesian model had ignored these effects and, thus, exaggerated the effects of an increase in the taxes.
Figure 17.6 depicts the impact of a decrease in taxes. Suppose that the government decreases the tax by ΔT (there is no change in government expenditures). This will lead to a shift in the IS curve to the right by an amount equal to the tax multiplier times the change in the tax, b/1 – b × ΔT. The new IS curve is IS with the equilibrium at point E2. The equilibrium income and the rate of interest are Y2 and r2, respectively. Thus, a decrease in tax brings about an increase in the income from Y1 to Y2 and an increase in the rate of interest from r1 to r2.
One would expect that a decrease in the taxes would result in an increase in the income level by an amount equal to the tax multiplier times the decrease in the taxes, or in words b/1 – b × ΔT. Then, the new equilibrium would be at point E′ on the IS2 curve and the increase in income from Y1 to Y′. Instead, the equilibrium point is E2 while the increase in income from Y1 to Y2 only. The reason for this is that a decrease in the taxes results in an increase in the consumption level which leads to an increase in the production of the goods and services causing an increase in the income levels. Hence, individuals demand more money leading to an increase in the interest rates. The increase in the interest rates is responsible for the firms reducing their investments. The Keynesian model had ignored these effects and understated the effects of a decrease in the taxes.
The monetary policy operates through the changes in the supply of money. A change in the money supply disturbs the money–market equilibrium causing a shift in the LM curve. The shift in the LM curve influences the income level and the rate of interest.
Let us examine the effects of an increase in the money supply. In Figure 17.7, the initial equilibrium is at point E1 determined by the intersection of the curves IS and LM1. The equilibrium income is Y1 while the equilibrium rate of interest is r1.
The mechanism by which the changes in the monetary policy affect the aggregate demand and, thus, the income level is called the monetary transmission process.
Suppose there is an increase in the money supply. Thus at the prevailing rate of interest r1, individuals are now holding excess money in their portfolio which they will try to deposit in the banks, buy bonds, etc. Hence, there will be a decrease in the interest rates. The equilibrium moves to point E′ at which there is equilibrium in the money market and the individuals are willing to hold a larger quantity of money due to a decrease in the interest rate. However, at point E′ there is disequilibrium in the goods market. The decrease in the interest rate will encourage investment leading to an increase in the income level. As a result, there occurs a movement up the LM2 until a new equilibrium is established at point E2, determined by the intersection of the curves IS and LM2. The equilibrium income increases to Y2 while the equilibrium rate of interest falls to r2.
The mechanism by which the changes in the monetary policy affect the aggregate demand and, thus, the income level is called the monetary transmission process.
Figure 17.7 The Effects of an Increase in the Money Supply
We have observed the impact of the monetary and fiscal policies in bringing about changes in the national income. However, we have yet to determine by how much the national income will change in response to the policies. This responsiveness depends on the elasticities of the IS and the LM curves.
The Elasticity of LM Curve: Given the supply of money in an economy, the LM curve has a positive slope as in Figure 17.8. For most analytical purposes, it can be divided into three ranges:
Figure 17.8 The LM Curve
The Elasticity of IS Curve: The IS curve has a positive slope. As far as the elasticity of the IS curve is concerned, it depends on the responsiveness of investment to changes in the interest rate and on the magnitude of the multiplier.
The effectiveness of a policy in achieving the economic objectives depends on the elasticity of the IS and LM curves. It is important to note that an expansionary fiscal policy, as it shifts the IS curve to the right, leads to an increase in both the income level and the interest rate. On the other hand, an expansionary monetary policy, as it shifts the LM curve to the right, leads to an increase the income level but a decrease in the interest rate.
Fiscal Policy relates to the utilization of government expenditure and taxation to achieve some well-defined objectives relating to growth, employment and many others. The fiscal policy has an immediate impact on the goods market and, thus, leads to shift in the IS curve.
In Figure 17.9, we examine the effectiveness of the fiscal policy in the three different ranges of the LM curve:
Figure 17.9 Effectiveness of Fiscal Policy
An increase in government expenditure and the interest rate and an unchanged income level imply that there occurs an offsetting decrease or crowding out of private investment which equals the increase in the government expenditure. Hence, there is full crowding out. Hence, fiscal policy is completely ineffective in the classical range.
In this range, the expansionary effect of the fiscal policy does succeed in raising the income level. However, the increase in the income is not as much as in the Keynesian range. This is due to the increase in the interest rate because of which investment decreases and, thus, the expansionary effect of the fiscal policy gets negated to some extent. Thus, fiscal policy is less effective in the intermediate range as compared to the Keynesian range.
Monetary policy relates to changes in the supply of money by the central bank to achieve the objectives relating to growth, employment and others. Monetary policy has an immediate impact on the money market and leads to a shift in the LM curve.
In Figure 17.10, we examine the effectiveness of the monetary policy in the three different ranges of the LM curve with the help of two types of IS curves, one elastic and the other inelastic.
Figure 17.10 Effectiveness of Monetary Policy
Monetary policy is ineffective in the liquidity trap whatever the elasticity of the IS curve.
In the classical range, the speculative demand for money is zero due to the high interest rates. Money is demanded only for transaction purposes. In such a situation, a monetary expansion will push down the rate of interest and, thus, encourage investment leading to an increase in the income level. Monetary policy is totally effective in the classical range in bringing about an increase in the income level.
As far as the intermediate range is concerned, monetary policy is effective but not as much as in the classical range because the increase in the money supply is absorbed partly as transactions money balances and partly as speculative money balances.
In the intermediate range, a monetary expansion will push down the rate of interest to some extent and, thus, encourage investment but the increase in the investment in not as much as in the classical range. Hence though there is an increase in the income level, it is not as much as the increase in the classical range.
Monetary policy is less effective in the intermediate range as compared to the classical range. Thus we find that the fiscal policy is completely effective in the Keynesian range, less effective in the intermediate range and completely ineffective in the classical range. On the other hand, monetary policy is completely ineffective in the Keynesian range, less effective in the intermediate range and completely effective in the classical range.
There are two approaches to determine the equilibrium level of income. In a three sector economy, they can be expressed as Aggregate demand–Aggregate supply approach and Injections equal Leakages approach.
In a three sector economy, the analysis of the money market will remain the same as in the two sector economy.
The equation of the IS curve in a three sector economy can be written as
The equation of the LM curve in a three sector economy can be written as
The IS curve has a positive slope. The elasticity of the IS curve depends on the responsiveness of investment to changes in the interest rate and on the magnitude of the multiplier.
The effectiveness of a policy in achieving the economic objectives depends on the elasticity of the IS and LM curves.
Numerical Problem 1
Suppose the consumption and investment functions are as follows:
C = 50 + 0.80 (Y – 0.25Y)
I = 200 – 5r
Also,
G = 100
Find
Suppose the consumption and investment functions and the government expenditure are as follows:
C = 50 + 0.75(Y – 80)
I = 150 – 10r
G = Rs. 120 crores
Also assume that the supply of money is Rs. 196 crores. The demand for money function is md = 0.4 Y – 6r.
Numerical Problem 3
Assume that the consumption and investment functions are as follows:
C = 50 + 0.6Yd
I = (I = 200 – 5r)
Also
G = 130
0 = 0
Find
Numerical Problem 4
In a three sector model, suppose the fundamental equations are:
C = Rs. 1000 + 0.80(Y – 0.25)
I = Rs. 1500 – 60r
G = Rs. 1000
L = 0.20Y – 20r
M = Rs. 1500
Find
Numerical Problem 5
Find the simultaneous equilibrium for the IS curve and LM curves when
C = 200 + 0.80Yd
I = 250 – 7.2r
G = 90
T = 0.20Y
ms = 180
md = 0.2Y – 2r
C = 500 + 0.80(Yd)
I = 1500
G = 1000
T = 1000
L = 0.20Y – 100r
M = 2100
Yd = Y – T
Find
C = 180 + 0.80(Y – 100)
I = 280 – 5r
G = Rs. 100 crores
Assume that the supply of money is Rs. 400 crores. The demand for money function is md = 0.20 Y.
C = 100 + 0.6Yd
I = 220 – 10r
G = 100
T = 100
The supply of money is Rs. 110. The demand for money function is md = 0.2 Y – 5r.
C = 100 + 0.70Yd
I = 200 – 6.6r
G = 140
T = 0.20Y
ms = 80
md = 0.2Y – 2r
Solution 1
Y = C + I
Y = 50 + 0.80(Y – 0.25 Y) + 200 – 5r + 100
Y = 0.80 (0.75Y) + 350 –5r
Y – 0.6Y = 350 – 5r
0.4Y = 350 – 5r
Y = 875 – 12.5r
Y = C + I
Y = 50 + 0.80(Y – 0.25Y) + 200 – 5r + 140
Y = 0.80 (0.75Y) + 390 – 5r
Y – 0.6Y = 390 – 5r
0.4Y = 390 – 5r
Y = 975 – 12.5r
Solution 2
Y = 50 + 0.75(Y – 80) + 150 – 10r + 120
Y = 50 + 0.75Y – 60 + 150 – 10r + 120
Y – 0.75Y = 50 – 60 + 150 – 10r + 120
0.25Y = 260 – 10r
Y = 1040 – 40r
ms = 196
In equilibrium, md = ms
Thus,
0.4Y – 6r = 196
0.4Y = 196 + 6r
Y = 490 + 15r
IS = LM
1040 – 40r = 490 + 15r
40r + 15r = 1040 – 490
55r = 550
r = 10%
Y = 1040 – 40 × 10
Y = 640
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 640 and r = 10%.
IS equation
Y = C + I + G
Y = 50 + 0.75(Y – 80) + 150 – 10r + 175
Y = 50 + 0.75Y – 60 + 150 – 10r + 175
Y – 0.75Y = 50 – 60 + 150 – 10r + 175
Figure 17.11 The IS Curves Plotted
Y = 1260 – 40r
LM equation will remain unchanged at
Y = 490 + 15r
Simultaneous equilibrium for the IS curve and LM curve
IS = LM
1260 – 40r = 490 + 15r
15r + 40r = 1260 – 490
55r = 770
r = 14%
Y = 1260 – 40 × 14
Y = 700
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 700 and r = 14%.
Solution 3
Y = 50 + 0.6Yd + 200 – 5r + 130
Y = 50 + 0.6(Y – 0) + 200 – 5r + 130
Y = 50 + 0.6Y + 200 – 5r + 130
Y – 0.6Y = 380 – 5r
0.4Y = 380 – 5r
Y = 950 – 12.5r
Y = C + I + G
Y = 50 + 0.6(Y – 0) + 200 – 5r + 180
Y = 50 + 0.6 (Y – 0) + 200 – 5r + 180
Y = 50 + 0.6Y + 200 – 5r + 180
Y – 0.6Y = 430 – 5r
0.4Y = 430 – 5r
Y = 1075 – 12.5r
Y = C + I + G
Y = 50 + 0.6(Y – 50) + 200 – 5r + 130
Y = 50 + 0.6(Y – 50) + 200 – 5r + 130
Y = 50 + 0.6Y – 30 + 200 – 5r + 130
Y – 0.6Y = 350 – 5r
0.4Y = 350 – 5r
Y = 875 – 12.5r
Y = C + I + G
Y = 50 + 0.6(Y – 50) + 200 – 5r + 180
Y = 50 + 0.6(Y – 50) + 200 – 5r + 180
Y = 50 + 0.6Y – 30 + 200 – 5r + 180
Y – 0.6Y = 400 – 5r
0.4Y = 400 – 5r
Y = 1000 – 12.5r
(a) The IS curve when government expenditure increases by Rs. 50 crores, Y = 1075 – 12.5r is given by the curve IS2. This indicates a horizontal shift of Rs. 125 crores.
(b) The IS curve when taxes increase by Rs. 50 crores, Y = 875 – 12.5r is given by the curve IS3. This indicates a horizontal shift towards the left of Rs. 75 crores from the IS1 curve.
(c) The IS curve when government expenditure increases by Rs. 50 crores and taxes increase by Rs. 50 crores, Y = 1000 – 12.5r, given by the curve IS4. This indicates a horizontal shift towards the right of Rs. 50 crores. This is because ΔG = ΔT = 50 crores.
Solution 4
Y = C + I + G
Y = 1000 + 0.80(Y – 0.25Y) + 1500 – 60r + 1000
Y = 1000 + 0.80(0.75Y) + 1500 – 60r + Rs. 1000
Y = Rs. 3500 + 0.6Y – 60r
Y = Rs. 8750 – 150r
M = L
Y = 7500 + 100r
IS = LM
Subtracting Eq. (2) from (1), we get
0 = 1250 – 250r
r = 5%
Y = Rs. 8000
Solution 5
Equation of the IS curve
Y = C + I + G
Y = 200 + 0.80Yd + 250 – 7.2r + 90
Y = 200 + 0.80(Y – T) + 250 – 7.2r + 90
Y = 200 + 0.80(Y – 0.20Y) + 250 – 7.2r + 90
Y = 200 + 0.80Y – 0.16Y + 340 – 7.2r
Y – 0.80Y + 0.16Y = 540 – 7.2r
0.36Y = 540 – 7.2r
Y = 1500 – 20r
Equation of the LM curve
ms = 180
md = 0.2Y – 2r
In equilibrium, md = ms.
Thus,
0.2Y – 2r = 180
0.2Y = 180 + 2r
Y = 900 + 10r
Simultaneous equilibrium for the IS curve and LM curves
IS = LM
1500 – 20r = 900 + 10r
20r + 10r = 1500 – 900
30r = 600
r = 20%
Y = 1100
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 1100 and r = 20%.
(a) Equation of the goods market equilibrium or the IS curve
Y = 11000
(b) Equation of the money-market equilibrium or the LM curve
Y = 10500 + 500r
(c) The equilibrium income and the interest rate:
Y = 11000
r = 1%
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 11000 and r = 1%.
(a) Equation of the IS curve
Y = 2400 – 25r
(b) Equation of the LM curve
Y = 2000
(c) Simultaneous equilibrium for the IS curve and LM curves
r = 16%
Y = 2000
(d) Simultaneous equilibrium for the IS curve and LM curves exists when Y = 2000 and r = 16%.
I = 200
(a) Equation of the IS curve when government expenditure increases by Rs. 20 crores
Y = 2500 – 25r
(b) Equation of the LM curve
Y = 2000
Hence, the equation of the LM curve remains unchanged as there is no change in the demand and supply of money.
(c) The equilibrium income level and the rate of interest
r = 20%
Y = 2000
(d) Simultaneous equilibrium for the IS curve and LM curves exists when Y = 2000 and r = 20%.
I = 180
(a) Equation of the IS curve
Y = 900 – 25r
(b) Equation of the LM curve
Y = 550 + 25r
Simultaneous equilibrium for the IS curve and LM curves.
r = 7 %
Y = 725
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 725 and r = 7%.
(c) Equilibrium of the economy if G increases from 100 to 200
Equation of the IS curve
Y = 1150 – 25r
Equation of the LM curve
Y = 550 + 25r
Simultaneous equilibrium for the IS curve and LM curves.
r = 12%
Y = 850
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 850 and r = 12%.
Y = 1000 – 15r
Equation of the LM curve
Y = 400 + 25r
Simultaneous equilibrium for the IS curve and LM curves.
r = 15%
Y = 775
Simultaneous equilibrium for the IS curve and LM curves exists when Y = 775 and r = 15%.