6

Shifts in the Aggregate Demand and the Multiplier

INTRODUCTION

In Chapter 5, we had focused on the determination of equilibrium income and output in a simple two sector economy. In this chapter, we will anaylse the changes in the equilibrium income and output in a two sector model.

A change in the equilibrium income or output is the result of a shift in the aggregate demand (or aggregate spending) function or the C + I curve. The aggregate demand curve can either shift upwards or downwards. The amount of the change in the income will be a multiple of the amount of the shift in the aggregate demand curve. The multiplier is the amount by which there is a change in equilibrium income or output when autonomous aggregate expenditure (for example, autonomous investment) increases by one unit. It is this multiplier mechanism that has been discussed in the chapter. We also focus on the conditions necessary for the multiplier to work. The applicability of the multiplier to the less developed countries has also been examined in this chapter.

 

SHIFTS IN AGGREGATE DEMAND AND THE MULTIPLIER

In a two sector economy, the aggregate demand is a sum of consumption and investment expenditures. It is generally agreed that though both consumption and investment functions undergo a change from one period to another, the consumption function is relatively more stable than the investment function. Thus, the initial changes in income occur more due to the shifts in the investment function. This implies that in the Figure 6.1 it is not the consumption function or the saving function which shifts up and down, it is the investment function which shifts up and down and is responsible for the shift in the C + I curve. Hence, our analysis will be in terms of the shift in the investment function (though the same analysis will apply for a shift in the consumption function).

Figure 6.1 Effect of a Change in Investment on the Equilibrium Income or Output

where,	x-axis = income (or output)
	y-axis = aggregate demand, AD
	C = consumption function
	I = investment function
	ΔI = change in investment
	S = saving function
	Y = C + S is the guideline or the 45 degree line

 

In Figure 6.1(a) suppose that initially the C + I function intersects the guideline to determine the equilibrium at point E_l with the equilibrium level of income at Y₁. The same can be illustrated in Figure 6.1(b) where the saving function intersects the I function to determine the equilibrium at point E₁ with the equilibrium level of income at Y₁.

Assume that due to an improvement in the business expectations, there is a permanent increase in investment expenditures per time period by an amount equal to ΔI at all the levels of output. In Figure 6.1(a), this shift has been illustrated by a shift in the C + I curve to C + I + ΔI whereas in Figure 6.1(b), the same shift has been illustrated by a shift in the I curve to the I + ΔI curve. In both the figures, the new equilibrium will be at point E₂ with the equilibrium level of income at Y₂.

It is of extreme importance to note that an increase in the income from Y₁ to Y₂ (national income) can occur if and only if the economy is operating at less than full employment. Otherwise, there cannot be an increase in the income.

One would expect that the increase in income from Y₁ to Y₂, say ΔY would be by the same amount as the increase in the investment expenditures, that is ΔI or that ΔY = ΔI. However, one finds that the increase in income is much more than the increase in investment expenditure which was responsible for bringing about that increase in the income, or in other words ΔY > ΔI. In fact, ΔY = m ΔI where m is what is known as the investment multiplier and has a value greater than 1. Thus,

or

The multiplier can be defined as the amount by which there occurs a change in the equilibrium level of income due to a change in autonomous aggregate expenditure by one unit.

The Working of the Multiplier

Suppose the economy is initially in equilibrium. Let there be an increase in autonomous investment by Rs. 1 million (ΔI). If the economy is operating at less than full employment, this will be matched by an increase in production and output equal to Rs. 1 million to meet the increased demand. The increase in the production will lead to an equal increase in the income of Rs. 1 million (ΔI) in the form of wages, interest and profits. This is the first round of income generation due to the additional investment of Rs. 1 million.

Those who receive the additional income will consume only a part of it, depending on their marginal propensity to consume, and will save the rest of this income. Suppose the marginal propensity to consume, or b, is 0.8. Hence, they will spend Rs. 1 million × 0.8 = 0.80 million (or b × ΔI = b ΔI) on the consumer goods and services and save Rs. 0.20 million. Thus in the second round, there is an increase in consumption and expenditure by Rs. 0.80 million (or b ΔI). Again production and income will increase to match the increase in the expenditure.

This will lead to a third round of induced expenditures by the recipients of the income in the second round. There will be an increase in consumption and expenditure by Rs. 0.80 million × 0.8 = Rs. 0.64 million (or b ΔI × b = b²ΔI). Hence, an additional income of Rs. 0.64 million is generated in the third round.

It is important to note that the additional income generated in the second round, Rs. 0.80 million (b ΔI), is certainly less than the additional income generated in the first round, Rs. 1 million (ΔI). Similarly the additional income generated in the third round, Rs. 0.64 million (b²ΔI), is less than the additional income generated in the second round, 0.80 million (b ΔI). Thus, the induced expenditures in the second round are smaller than those in the first round whereas those in the third round are smaller than those in the second round. Thus the induced expenditures and, thus, the additional income generated in each round go on becoming smaller and smaller. The rounds of income generation will continue till the additional income generated falls to zero.

The total increase in the income in all the rounds can be summed up as

This is a geometric series and can be put in a simpler form as follows:

Multiplying both sides of Eq. (3) by b, we get

Subtracting Eqs. (4) from (3), we get

 

ΔY − bΔY = ΔI(1 + b + b² + b³ + … + bⁿ⁻¹) − ΔI(b + b² + b³ + b⁴ + … + bⁿ)

ΔY(1 − b) = ΔI(1 − bⁿ)

Thus,

If the multiplier process continues for a very long period, the value of n will become very large and bⁿ (b is a fraction with its value between zero and one) will approach zero. Hence,

Where m is the investment multiplier. Thus, we have

or

 

(as b is the marginal propensity to consume)

Table 6.1 depicts the working of the multiplier.

An Alternative Derivation of the Multiplier

The equilibrium level of income is

Let there be an increase in autonomous investment by ΔI. This will result in an induced increase in income, which will lead to an increase in consumption, or ΔC. Thus, now the equilibrium level of income will be

Subtracting Eq. (8) from Eq. (9), we get

But the consumption function is C = C_a+ bY.

 

Table 6.1 The Working of the Multiplier

Round	Increase in Aggregate Demand (or Aggregate Expenditure)	Total Increase in Income
1	ΔI	ΔI
2	bΔI	ΔI + bΔI = ΔI(1 + b)
3	b2ΔI	ΔI + bΔI + b2ΔI = ΔI(1 + b + b2)
4	…	…
…	…

Thus,

Substituting for ΔC from Eq. (11) in Eq. (10), we get

 

ΔY = bΔY + ΔI

or,

ΔY(1 − b) = ΔI

or,

or,

, where m is the investment multiplier.

It is obvious that the value of the multiplier depends on b, the marginal propensity to consume. The larger the marginal propensity to consume the larger will be the multiplier. When the marginal propensity to consume is 0.5, the multiplier is 2 and when the marginal propensity to consume increases to 0.9, the multiplier increases to 10.

• A shift in the investment function results in a change in the equilibrium income or output.
• The ratio of the change in income is a multiple of the change in the investment.
• ΔY = m Δl where m is the investment multiplier and has a value greater than 1.
• The larger the marginal propensity to consume the larger will be the multiplier.

USES AND LIMITATIONS OF THE MULTIPLIER

The importance of the multiplier is more obvious in a three sector and a four sector economy. However, it plays an important role even in a two sector economy in that it helps in evaluating the eff ects of an increase in the investment on the national income. Thus, it is able to determine the investment that would be required for a certain planned growth in the national income. Hence, the multiplier is of great importance in planning the economic growth of a nation.

In spite of its utility in economic planning, the multiplier has certain limitations which may prevent it from working. They are as follows:

1. Existence of leakages from the income stream: Keynes was of the view that the marginal propensity to consume remains constant over time. However, empirical evidence does not lend credence to this view. It has been observed that as income increases, often, consumption may not increase proportionately and hence the value of the multiplier may be reduced. Other than consumption, individuals may utilize their increased income for different purposes as the following:
   1. They may increase their holdings of money.
   2. They may use a part of the increased income to pay off their old debts.
   3. They may purchase old securities and property with the additional income.
   4. They may purchase imported goods and services, the income spent on which will certainly be a leakage out of the economy.
2. The availability of the consumer goods: For the multiplier principle to work, it is necessary that the consumer goods are available in the right quantities and at the right time. Often this may not be the case and hinder the multiplier from working properly.
3. There may exist time lags: The supply of goods may increase in response to demand but only with a time gap. Also, consumption may not increase immediately in response to an increase in income.
4. The full employment ceiling: When an economy is at the full employment level, any further increases in the income and output are not possible. Whatever is the marginal propensity to consume, the multiplier principle will not be able to work. In fact, any increase in the investment will trigger off inflationary expectations in the economy.

These limitations do not in any way undermine the importance of the multiplier. In fact, due to these limitations economists have time and again modified the multiplier which has further enhanced its utility in analysing the changes in income in response to an increase in the aggregate demand.

• The multiplier plays a very important role in planning the economic growth of a nation.
• The multiplier suffers from many limitations, which may prevent it from working.
• These limitations have been responsible for the modifications in the multiplier.

APPLICABILITY OF THE MULTIPLIER TO LESS DEVELOPED COUNTRIES

In the article ‘Investment, Income and the Multiplier in an Underdeveloped Economy’ in the Indian Economic Review, February 1953, Dr V. K. R. V. Rao raised doubts regarding the applicability of the multiplier principle to the less developed countries.

The less developed countries (LDCs) have a lower per capita income as compared to the other countries. It is also an established fact that at low levels of income, the marginal propensity to consume is always high. According to the Keynesian theory, the higher the b or the marginal propensity to consume the higher is the value of the multiplier [m = 1/(1 – b)]. Thus, it is to be expected that the multiplier should apply with a stronger effect in LDCs as compared to the developed countries of the world. This would imply that even a small increase in the investment in the LDCs would result in an increase in the income and output, which would be much larger than the increase in the income and output experienced in the developed countries. However, this does not seem to be the case. The reason for this, according to Dr V. K. R. V. Rao, is that the conditions necessary for the multiplier principle to work do not exist in the LDCs. They are satisfied only in the developed countries.

The conditions necessary for the multiplier principle to work are as follows:

1. There should exist only involuntary unemployment and no other form of unemployment: Such unemployment is characteristic of the developed countries where there exists wage employment in almost all the sectors of the economy. As compared to the developed countries, in the LDCs wage employment is a feature found only in the secondary sector which again is a very small sector as compared to the other sectors in the economy. Hence involuntary unemployment, which is associated with wage employment, is not so predominant in these countries.

   The type of unemployment most predominant in these countries is what is known as disguised unemployment. This is a type of unemployment, which is most prevalent in agriculture in a country like India where there exist plots of land on which the whole family may be employed. The additions to the total output and the income by the last few units of labour employed may actually be zero. Yet they continue to till the land simply because they are not aware that they are actually not contributing to the total output. Hence, their unemployment is a kind of concealed one of which even they themselves are not aware. The existence of this disguised unemployment prevents the working of the multiplier principle in the LDCs.

2. It must be mainly an industrial economy with an upward sloping supply curve for the consumer goods: In the developed economies, the supply curve is reasonably elastic in that an increase in demand results in an increase in the supply with not much of an inflationary increase in the prices. However, the situation is different in the LDCs where an increase in the demand is not followed by an increase in the supply. This is because due to the low incomes and poverty in the LDCs, any increase in income generates a demand largely for the agricultural goods. But agriculture is subject to the vagaries of nature. Hence, the multiplier may work in the first stage in that an increase in investment may result in a primary increase in the incomes but the increase in demand in response to an increase in these incomes may not result in an increase in the production, especially in the agricultural goods sector. The story is not any different for the non-agricultural goods sector which is characterized by outdated technology, lack of skilled workers and other problems. Thus, in the LDCs though there occurs an increase in the money incomes due to an increase in the investment, there is no perceptible increase in the output level. Thus, it is often argued that in the LDCs the multiplier principle functions only with respect to the money incomes and not with respect to the real incomes.
3. There should exist excess capacity in the consumer goods industries: In the Keynesian theory, which came at the time of the Great Depression, it was not unusual to assume the existence of idle capacity in the consumer goods industry. Thus, an increase in demand could be immediately satisfied by an increase in the production. However this is not the situation in the LDCs, especially in the agriculture sector. Hence, in these countries the multiplier does not work except in that it is responsible for contributing to the inflationary fires in the economy whenever there occurs an increase in demand in response to an increase in investment.
4. There should exist an elastic supply of capital: This is a necessary accompaniment to the labour if there has to occur an increase in the production in response to an increase in the demand. As the developed countries face no problem on this front, the multiplier functions quite efficiently in these countries. In the LDCs while there is not only a sufficient but in fact a surplus supply of labour as far as capital is concerned, there is a shortage of capital in these countries. Hence, again the multiplier principle does not work in the LDCs due to the acute shortage of capital that these countries face.

• Dr V. K. R. V. Rao had raised doubts regarding the applicability of the multiplier principle to the less developed countries.
• It seems that the conditions, which are necessary for the multiplier principle to work, are not satisfied in the less developed countries.

THE MULTIPLIER AND THE PARADOX OF THRIFT

It was widely believed, especially by the classical economists, that saving or thrift was a ‘virtue’ for not only an individual but also for an economy. An individual has to refrain from consumption if he wishes to save. By saving, he is able to amass huge amounts of wealth. Similarly, it was believed that an economy could become rich if every individual in the economy became thrifty.

Keynes, in his General Theory, criticized these beliefs. He argued that what applies to an individual was not necessarily true for the economy. Contrary to the popular beliefs at that time Keynes argued that if the whole economy becomes thrifty, or in other words starts saving more, there will be a decrease in the total consumption in the economy. Hence there will be a decrease in the aggregate demand, and thus the income and output will decrease. As saving is a function of income, a decrease in income will ultimately lead to a decrease in the savings. This is what Keynes called the paradox of thrift. It is a contradiction in that what is good for an individual is not good for an economy.

Figure 6.2 Paradox of Thrift

where,	I	= Investment demand schedule where I is assumed to be constant at
	S1	= Saving schedule where saving is positively related to income.
	E1	= The equilibrium point at which the saving schedule, S1 and investment schedule, I intersect.
	OY1	= Equilibrium income when equilibrium is at point E1.
	S2	= Saving schedule when the economy becomes more thrifty.
	E2	= The equilibrium point at which the saving schedule, S2 and investment schedule, I intersect.
	OY2	= Equilibrium income when equilibrium is at point E2.

 

Figure 6.2 depicts the paradox of thrift. If everyone in the economy becomes thriftier, the saving schedule will shift upwards from S₁ to S₂. The equilibrium point will move from E₁ to E₂ whereas the equilibrium income decreases from Y₁ to Y₂. This lends credence to the paradox of thrift that an increase in the thrift by one individual may be good in that it may help in increasing his fortunes in the long run but if the whole economy becomes thrifty, the economy’s equilibrium income and output may in fact actually decrease, rather than increase!

Some economists describe this process, where through the paradox of thrift there is ultimately a decrease in the economy’s savings, as a reverse multiplier. The increase in savings, by a reduction in consumption expenditures, will lead to a decrease in the aggregate demand. Thus, there will be a decrease in production leading to a decrease in the income which will further lead to a decrease in savings (which are a function of the income level). The economy will finally reach a new equilibrium at which saving is equal to investment. It is imperative to remember that the paradox of thrift will operate only if the increase in the economy’s saving is not accompanied by an increase in the investment. If there is an increase in investment, then there will occur an increase in the income through the multiplier which will lead to additional savings and investment in the economy, rather than a decrease.

• The classical economists believed that saving or thrift was a ‘virtue’ for both individual and economy.
• Keynes was of the view that an increase in the thrift by one individual may be good but if the whole economy becomes thrifty, then the economy’s equilibrium income may decrease.

INTRODUCTION

1. In this chapter, we anaylsed the changes in the equilibrium income and output in a two sector model.
2. A change in the equilibrium income or output is the result of a shift in the aggregate demand (or aggregate spending) function or the C + I curve.
3. The multiplier is the amount by which there is a change in equilibrium income or output when autonomous investment increases by one unit.

SHIFTS IN AGGREGATE DEMAND AND THE MULTIPLIER

1. In a two sector economy, the initial changes in income occur more due to the shifts in the investment function.
2. It is to be noted that the increase in income is much more than the increase in investment expenditure, or in other words ΔY > ΔI.
3. In fact ΔY = m ΔI where m is what is known as the investment multiplier and has a value greater than 1.

THE WORKING OF THE MULTIPLIER

1. Suppose the economy is initially in equilibrium.
2. Let there be an increase in autonomous investment by Rs. 1 million (ΔI).
3. If the economy is operating at less than full employment, this will be matched by an increase in production and output equal to Rs. 1 million, which will lead to an equal increase in income of Rs. 1 million (ΔI) in the form of wages, interest and profits. This is the first round of income generation due to the additional investment of Rs. 1 million. Similarly, there will occur other rounds of income generation.
4. The induced expenditures and thus the additional income generated in each round goes on becoming smaller and smaller.
5. We have

   where m is the investment multiplier and b is the marginal propensity to consume.

6. The value of the multiplier depends on b, the marginal propensity to consume. The larger the marginal propensity to consume the larger will be the multiplier.

USES AND LIMITATIONS OF THE MULTIPLIER

1. The multiplier plays an important role even in a two sector economy in that it is able to determine the investment, which would be required for a certain planned growth in the national income.
2. The multiplier suffers from many limitations, which may prevent it from working.

APPLICABILITY OF THE MULTIPLIER TO LDCS

1. Dr V. K. R. V. Rao has raised doubts regarding the applicability of the multiplier principle to the underdeveloped countries.
2. The conditions necessary for the multiplier principle to work do not exist in the LDCs.

THE MULTIPLIER AND THE PARADOX OF THRIFT

1. It was widely believed, especially by the classical economists, that saving or thrift was a ‘virtue’ for not only an individual but also for an economy.
2. Keynes argued that what applies to an individual was not necessarily true for the economy. This is what Keynes called the paradox of thrift.
3. An increase in the thrift by one individual may be good in that it may help in increasing his fortunes in the long run but if the whole economy becomes thrifty, the economy’s equilibrium income may in fact actually decrease.

TRUE OR FALSE QUESTIONS

1. A change in the equilibrium income is the result of a shift in the aggregate supply function.
2. The multiplier is the amount by which there is a change in autonomous investment when income or output when increases by one unit.
3. In a two sector economy, the aggregate demand is a sum of consumption and investment expenditures.
4. Keynes had pointed out that if the whole economy starts saving more, there will be an increase in the total consumption in the economy.
5. The larger the marginal propensity to consume the larger will be the multiplier.

VERY SHORT-ANSWER QUESTIONS

1. What is the multiplier?
2. Why do the initial changes in income occur due to the shifts in the investment function?
3. Why is the existence of excess capacity in the consumer goods industries necessary for the multiplier principle to work?
4. What is disguised unemployment?
5. Mention some of the limitations, which may prevent the multiplier from working?

SHORT-ANSWER QUESTIONS

1. How is the multiplier useful for an economy?
2. What were the classical views regarding thrift?
3. What was Keynes’ belief as far as the thrift is concerned?
4. In the context of the paradox of thrift, discuss the reverse multiplier.
5. Describe the Paradox of Thrift graphically.

LONG-ANSWER QUESTIONS

1. Analyse the effects of a change in investment on the equilibrium income or output.
2. Discuss the working of the multiplier.
3. Mention some of the limitations of the multiplier, which prevent it from working efficiently.
4. What is the multiplier? Show the simple mathematical derivation of the multiplier.
5. What is the Paradox of Thrift? Discuss.

SOLVED NUMERICAL PROBLEMS

Numerical Problem 1

In an economy, the basic equations are as follows: the consumption function is C = 150 + 0.80Y and investment is = 180 crores. Find

1. the equilibrium level of income.
2. the equilibrium level of income when planned investment increases from 180 to 200 crores, a total increase of 20 crores
3. the multiplier effect of the 20 crore increase in planned investment.

Numerical Problem 2

Suppose in an economy the marginal propensity to consume is 0.75 and the level of autonomous investment decreases by 20 crores. Find

1. the change in the equilibrium level of income.
2. the change in consumption expenditures.

Numerical Problem 3

Calculate the value of the investment multiplier when the marginal propensity to consume is (i) 0.85, (ii) 0.70, (iii) 0.60 (iv) 0.40.

Find the effect of a decrease in the equilibrium income when autonomous investment decreases by 30 crores when the marginal propensity to consume is (i) 0.85, (ii) 0.70, (iii) 0.60 (iv) 0.40.

Numerical Problem 4

In an economy, the marginal propensity to consume is 0.50. The level of autonomous investment decreases by 30 crores. Find

1. the change in the equilibrium level of income.
2. the change in autonomous demand.
3. the induced change in the consumption expenditures.

Numerical Problem 5

Assume that in a two sector economy, the income is Rs. 500 billion while the marginal propensity to consume is 40%. Suppose the government wants to increase the income to Rs. 800 billion, by an amount of Rs. 300 billion. By how much should the autonomous investment be increased?

UNSOLVED NUMERICAL PROBLEMS (WITH ANSWERS)

1. In an economy, the basic equations are as follows: the consumption function is C = 80 + 0.75Y and investment is = 100 crores. Find
   1. the equilibrium level of income.
   2. the equilibrium level of income when planned investment increases from Rs. 100 to 120 crores, a total increase of 20 crores.
   3. the multiplier effect of the 20 crore increase in planned investment.
2. Suppose in an economy, the marginal propensity to consume is 0.80. The autonomous investment rises by 40 crores. Find
   1. the change in the equilibrium level of income
   2. the change in consumption expenditures.
3. In a two sector economy, the income is Rs 200 billion whereas the marginal propensity to consume is 60%. Suppose the government wants to increase the income by 100%. By how much should the autonomous investment be increased?
4. In an economy, the marginal propensity to consume is 0.75. The level of autonomous investment decreases by Rs. 40 crores. Find
   1. the change in the equilibrium level of income.
   2. the change in autonomous demand
   3. the induced change in the consumption expenditures.
5. Suppose the marginal propensity to consume is (i) 0.40, (ii) 0.50, (iii) 0.80, (iv) 1.0 and (v) 0,
   1. Calculate the marginal propensity to save.
   2. Calculate the value of the multiplier.
   3. Using the values of the marginal propensity to consume, find the effect of an increase in the equilibrium income when autonomous investment increases by 40 crores.

TRUE OR FALSE QUESTIONS

1. False. A change in the equilibrium income or output is the result of a shift in the aggregate demand or aggregate spending function or the C + I curve.
2. False. The multiplier is the amount by which there is a change in equilibrium income or output when autonomous investment increases by one unit.
3. True. Consumption constitutes the demand of the household sector whereas investment is that of the firms.
4. False. Keynes had argued that if the whole economy becomes thrifty or in other words starts saving more, there will be a decrease in the total consumption in the economy.
5. True. As the value of the multiplier depends on b, the marginal propensity to consume or m = 1/1 – b, the larger the marginal propensity to consume the larger will be the multiplier.

SOLVED NUMERICAL PROBLEMS

Solution 1

1. The equilibrium condition is given as Y = C + I

   Thus,

   Y = 150 + 0.80Y + 200

   Y − 0.80Y = 150 + 180

   0.20Y = 330

   Y = 330/0.20

   Y = 1650

   The equilibrium level of income is 1650 crores.

2. The equilibrium condition is given as Y = C + I

   Thus, now

   Y = 150 + 0.80Y + 200

   Y − 0.80Y = 150 + 180

   0.20Y = 350

   Y = 330/0.20

   Y = 1750

   The equilibrium level of income is 1750 crores.

3. The equilibrium level of income increases from 1650 crores to 1750 crores when planned investment increases from 180 to 200 crores. There is an increase in income by 100 crores. Hence, the multiplier effect is 5 (m = 1/1 – b = 1/1 – 0.80 = 5).

Solution 2

We know that

But m is the investment multiplier

Also,

Thus, .

Hence, the decrease in autonomous investment causes a decrease in the equilibrium level of income by 80 crores. This effect occurs due to the reverse multiplier.

1. Y = C + I

   Therefore, ΔY = Δ C + Δ S

                       − 80 = Δ C − 20

   (As autonomous investment decreases by 20 crores, the saving will also decrease by 20 crores)

    

   Δ C = − 80 + 20 = − 60 crores

   Δ C = − 60 crores

   The consumption expenditure decreases by 60 crores.

Solution 3

1. The value of m, the investment multiplier is
   

   Hence,

   1. 
   2. 
   3. 
   4. 
2. We know that
   

   Thus,

   Δ Y = ΔI m

   The decrease in the equilibrium income when autonomous investment decreases by 30 crores is

   1. ΔY = ΔIm = 30 × 6.67 = 200
   2. ΔY = ΔIm = 30 × 3.33 = 100
   3. ΔY = ΔIm = 30 × 2.5 = 75
   4. ΔY = ΔIm = 30 × 1.67 = 50

Solution 4

1. We know that
   

   But m is the investment multiplier.

   Also,

   

   Thus,

   

   Hence, the decrease in autonomous investment causes a decrease in the equilibrium level of income by 60 crores.

2. The decrease in investment by 30 crores is the change in the level of autonomous demand.
3. Y = C + I

   Therefore,

   ΔY = ΔC + ΔS

   − 60 = ΔC − 30

   (As autonomous investment decreases by 30 crores, the saving will also decrease by 30 crores)

    

   Δ C = − 60 + 30 = − 30 crores

   Δ C = − 30 crores

   The consumption expenditure falls by 30 crores.

Solution 5

The income level = Rs. 500 billion

 

The planned income level = Rs. 800 billion

Change in income = ΔY = 800 – 500 = Rs. 300 billion

But

Thus,

ΔI = Rs. 180 billion

Thus, autonomous investment should be increased by Rs. 180 billion for the income to increase to Rs. 800 billion, an increase in income by Rs. 300 billion.

UNSOLVED NUMERICAL PROBLEMS

1. (a) Y = 720

   The equilibrium level of income is 720 crores.

   (b) Y = 800

   The equilibrium level of income, when planned investment increases from 100 to 120 crores, is 800 crores.

   (c) The multiplier effect is 4.

   m = 4

2. (a) Δ Y = 200

   The increase in autonomous investment causes an increase in the equilibrium level of income by 200 crores.

   (b) Δ C = 160 crores

   The consumption expenditure increases by 160 crores.

3. ΔI = Rs. 80 billion

   Autonomous investment should be increased by Rs. 80 billion for a 100 per cent increase in the income level.

4. (a) Δ Y = –160

   The decrease in autonomous investment causes a decrease in the equilibrium level of income by 160 crores. This effect occurs due to the reverse multiplier.

   (b) The decrease in investment by 40 crores is the change in the level of autonomous demand.

   (c) Δ C = –120 crores

   The consumption expenditure falls by 120 crores.

5. (a) (i) mps = 1 – mpc = 1 – 0.40 = 0.60

   (ii) mps = 1 – mpc = 1 – 0.50 = 0.50

   (iii) mps =1 – mpc = 1 – 0.80 = 0.20

   (iv) mps = 1 – mpc = 1 – 1.0 = 0

   (v) mps =1 – mpc = 1 – 0 = 1

   (b) (i) m = 1.67

   (ii) m = 2

   (iii) Nm = 5

   (iv) m = ∞

   (v) m = 1

   (c) (i) ΔY = ΔIm = 40 × 1.67 = 67

   (ii) ΔY = ΔIm = 40 × 2 = 80

   (iii) ΔY = ΔIm = 40 × 5 = 200

   (iv) ΔY = ΔIm = 40 × ∞ = ∞

   (v) ΔY = ΔIm = 40 × 1 = 40