5

The Keynesian Model of Income Determination in a Two Sector Economy

INTRODUCTION

This is the first of the series of four chapters, which focuses on the determination of the equilibrium level of income in the simple Keynesian model. This chapter is limited to only a two sector model, which includes only the households and the firms.

This model assumes that the aggregate supply curve is perfectly elastic (or parallel to the horizontal axis) up to the full employment level of output after which it becomes perfectly inelastic (or parallel to the vertical axis). Hence the price level, until the full employment level, will be determined solely by the height of the supply curve. Hence, the price variable gets less attention while the entire focus is on the determination of the equilibrium level of income, which is determined solely by the aggregate demand (or aggregate spending). Thus, the basic question relates to the determination of the aggregate demand.

AGGREGATE DEMAND IN A TWO SECTOR ECONOMY

The basic assumptions in this analysis are as follows.

1. The prices are constant or do not change.
2. Given the price level, the firms are willing to sell any amount of the output at that price level.
3. The short-run aggregate supply curve is perfectly elastic or flat.
4. Investment is assumed to be autonomous and thus independent of the income level.
5. There exist only two sectors in the economy, the households and the firms.

Aggregate demand is the total amount of goods demanded in an economy. The aggregate demand function can be expressed as

where, C =	aggregate demand for consumers goods
I =	aggregate demand for investment goods

As we have already assumed that investment is autonomous and independent of the income level, aggregate demand function will thus mainly depended on the consumption function. Thus, our focus will be mainly on the consumption function, which is one of the biggest sectors in any economy.

• As investment is autonomous, aggregate demand function will depend mainly on the consumption function.

CONSUMPTION

Consumption Spending

The consumption spending or the aggregate amount of goods bought in any time period will depend upon the real income of the households. Other factors are also important but the aggregate amount of goods bought is determined only by the real income of the households.

The Consumption Function

The consumption function is a relationship between income and consumption expenditure.

The two important aspects are:

1. Consumption expenditure varies directly with disposable income or we can say that it is a positive function of income.
2. Keynes had stated in his ‘fundamental psychological law’ that, in general, an individual increases his consumption expenditure when his income increases. However, the increase in consumption is less than the increase in income.

Non-linear Consumption Function

The most general non-linear form of the consumption function can be expressed as

where, C =	consumption expenditure
Y =	disposal income

 

The consumption function Eq. (2), which is a non-linear consumption function, has been depicted in Figure 5.1.

Figure 5.1 The Non-linear Consumption Function

Linear Consumption Function

The consumption function equation in a linear form can be expressed as

where, C =	consumption expenditure
Y =	disposal income

         C_a > 0

         0 < b < 1

In this equation,

1. C_a is the intercept of the consumption function on the y-axis. It shows the level of consumption at zero level of income. It is known as autonomous consumption.
2. The constant ‘b’ denotes the slope of the consumption function. It is known as the marginal propensity to consume, MPC. It indicates the increase in the consumption per unit of increase in the income.

Average Propensity to Consume (APC)

The APC is defined as the ratio of consumption to income for different levels of income. Thus,

Marginal Propensity to Consume (MPC)

The MPC is defined as the increase in the consumption per unit of increase in the income. Thus,

As b is less than 1 it implies that if income increases by a rupee, only a fraction, b, will be spent on consumption.

Figure 5.2 The Linear Consumption Function

Numerical Illustration 5.1

If the value of the marginal propensity to consume ‘b’ is 0.60, then for every rupee increase in income, what will be the increase in consumption?

Solution

For every rupee increase in income there will be an increase in consumption of 60 paisa.

Here, we will be restricting ourselves to the linear consumption function as in Figure 5.2.

• Consumption expenditure varies directly with disposable income.

SAVING AS A COUNTERPART OF THE CONSUMPTION FUNCTION

As there are only two uses of income—consumption and saving, income that is not spent on consumption is saved.

The Saving Function

The saving function is the counterpart of the consumption function. In its most general form, the saving function can be written as

We know that

or

Equation (6) is actually the budget constraint showing that, by definition, savings will equal income net of consumption.

By substituting Eq. (3), the consumption function, in Eq. (6), which is the budget constraint, we can arrive at the saving function as shown below:

where, s = 1 – b,

         s > 0

In this equation, the constant ‘s’ denotes the slope of the saving function. It is the marginal propensity to save. It indicates the increase in the savings per unit of increase in the income.

Average Propensity to Save (APS)

The APS is the saving counterpart to the APC. APS is defined as the ratio of saving to income for different levels of income. Thus,

Marginal Propensity to Save (MPS)

The MPS is defined as the increase in the saving per unit of increase in the income. Thus,

As the MPS or s is always positive, savings will be an increasing function of income. As b is less than 1 it implies that if income increases by a rupee, only a fraction, b will be spent on consumption.

Numerical Illustration 5.2

If the value of the marginal propensity to consume, b, is 0.60, then what is the marginal propensity to save?

Solution

The marginal propensity to save = 1 – 0.60 = 0.40. This implies that of every rupee of income. 40 paisa is saved.

The saving function Eq. (7) has been shown in Figure 5.3.

Relationship between APC and APS: From Eq. (5),

 

Y= C+ S

Dividing both sides of the equation by Y, we get

or

1 = APC + APS

Hence, the sum of APC and APS is always equal to one.

 

Figure 5.3 The Saving Function

Relationship between MPC and MPS: From Eq. (5),

 

Y = C + S

As a change in income, it can be split up into a change in consumption and a change in saving, we have

 

ΔY = ΔC + ΔS

Dividing both sides of the equation by Δ Y, we get

or

1 = MPC + MPS

Hence, the sum of MPC and MPS is always equal to one.

Numerical Illustration 5.3

If the consumption function is C = 40 + 0.75Y then what is the saving function?

Solution

Since	S = Y – C
	S = Y – (40 + 0.75Y)
	S = Y – 40 – 0.75 Y

Thus, the saving function S = – 40 + 0.25 Y.

The Aggregate Demand Function

After having determined the consumption and the saving functions, we can now determine the aggregate demand function in a two sector economy. We are assuming that investment is constant or I = . From the aggregate demand Eq. (1) and consumption function Eq. (3), we have

Substituting for C from Eq. (3) in Eq. (1), we get

Figure 5.4 depicts the derivation of the aggregate demand curve. While investment has been shown as a straight line parallel to the horizontal axis, I = , consumption has been shown as an upward sloping straight line, C = C_a + b Y. The aggregate demand function has been obtained by a vertical summation of the investment function and consumption function as AD = C_a + b Y + .

Figure 5.4 The Aggregate Demand Function

DETERMINATION OF EQUILIBRIUM INCOME OR OUTPUT IN A TWO SECTOR ECONOMY

In the most basic terms, an economy can be said to be in equilibrium when the production plans of the firms and the expenditure plans of the households are realized.

Some assumptions (already mentioned) necessary here are as follows:

1. There exist only two sectors in the economy, the households and the firms. There is no government sector and no foreign sector.
2. All the factors of production are owned by the households who sell the factor services to earn an income. With a part of this income, they purchase goods and services and save the rest.
3. As there is no government in the economy, there are no taxes and subsidies and no government expenditures.
4. As there is no foreign sector in the economy, there are no exports and imports and no external inflows and outflows.
5. As far as the firms are concerned, there are no undistributed profits.
6. All the prices are constant and do not change.

   Investment is assumed to be autonomous and thus independent of the income level.

7. The technology and the supply of capital are given.

According to the Keynesian theory, there are two approaches to the determination of income and output:

1. Aggregate Demand–Aggregate Supply Approach
2. Saving–Investment Approach

Equilibrium Income and Output: A Theoretical Explanation

Aggregate Demand–Aggregate Supply Approach

Equilibrium: The equilibrium national income is determined at that level where the aggregate demand is equal to the aggregate supply. Thus,

 

Aggregate demand = Aggregate supply

However, Keynes had argued that it is not necessary that aggregate demand will be always equal to aggregate supply. As far as aggregate supply is concerned, it can be assumed to be relatively stable as production depends on factors that do not change much in the short run. However, aggregate demand depends on the planned consumption expenditure of households and planned investment expenditure of firms. Aggregate demand is relatively unstable. This instability of aggregate demand can, to some extent, explain the changes in the real income.

Disequilibrium: In an economy as the production and expenditure decisions are taken by different groups of people, it is possible that aggregate demand may not be equal to aggregate supply.

Consider a situation where the firms underestimate the demand. Thus, a situation arises where the production is insufficient to meet the demand, or in other words, aggregate demand is greater than aggregate supply. There is a run down on inventories to meet the excess demand. The firms revise their production plans upwards till aggregate demand becomes equal to aggregate supply.

Now we consider another situation where the firms overestimate the demand. Thus, a situation arises where the production is in excess of demand, or in other words, aggregate demand is less than aggregate supply. There is an involuntary accumulation of inventories. The firms revise their production plans downwards till aggregate demand becomes equal to aggregate supply.

It is thus obvious that if any disequilibrium occurs, then the forces inbuilt in the system would operate in such a manner that the equilibrium is restored.

Saving-Investment Approach

Equilibrium: Before going into the depth of the saving–investment approach, it is necessary to understand the difference between ex ante and ex post saving and investment.

In the national income accounting, saving is said to be identically equal to investment. Thus,

1. National income is equal to the sum of income generated in the production of consumer goods and investment goods, or that Y = C + I.
2. National expenditure is equal to the sum of income spent on consumption and income that is saved or that Y = C + S.

But we know that national income = national expenditure,

or

C + I = C + S

Therefore,

I = S

Hence, as an identity, saving is always equal to investment.

However if we bring in the concepts of ex ante and ex post, it is not so simple. Ex ante (planned or desired) saving is not always equal to ex ante (planned or desired) investment. This is because while the households save, it is the firms who invest. There is no reason as to why the two will be the same. However, ex post (actual or realized) saving is always equal to ex post (actual or realized) investment. Thus while ex ante saving and investment may differ, ex post saving and investment are always equal.

The equilibrium national income is determined where not only the aggregate demand and the aggregate supply are equal but at that level where planned saving is also equal to planned investment. Thus,

 

Planned saving = Planned investment

This is possible because in a two sector economy while saving is the only leakage, investment is the only injection into the system.

Disequilibrium: Consider a situation where the firms underestimate the demand. Thus, planned saving will be less than planned investment. This implies that the consumption of goods is more than the current production. There will be a run down on inventories. Firms will expand production till the output increases to the level where planned investment is equal to planned saving.

Consider another situation where the firms overestimate the demand. Thus, planned saving will be more than planned investment. The consumption of goods is less than the current production. There will be an involuntary accumulation of inventories. Firms will cut back on production till the output decreases to the level where planned investment is equal to planned saving.

Equilibrium Income and Output: An Algebraic Explanation

Aggregate Demand–Aggregate Supply Approach

Aggregate demand = Total value of output (or income)

or

Y = C + I

But the consumption function is C = C_a + bY whereas investment has been assumed to be autonomous, or I = .

Thus,

Y = C_a + bY +

Hence, equilibrium income is

 

Y − bY = C_a +

or

Saving-Investment Approach

In equilibrium,

AD = AS

or

C + I = C + S

As C is common in both the sides, the equilibrium condition can be written as

 

I = S

But the saving function is S = – C_a + (1 – b) Y whereas investment has been assumed to be autonomous, or I = .

Thus,

= −C_a + (1−b) Y

or

This is the same equation as Eq. (9) above.

Hence, both the approaches yield the same equilibrium level of income.

Numerical Illustration 5.4

In a two sector economy when the level of the national income is Rs. 500 crores, savings are Rs. 50 crores and when the national income is Rs. 550 crores, savings are Rs. 70 crores, if planned investment is Rs. 70 crores what is the equilibrium level of the national income?

Solution

In an economy, equilibrium exists when planned saving equals planned investment. As planned investment is Rs. 70 crores, equilibrium will occur at an income level of Rs. 550 crores because at that income level alone planned investment equals planned saving of Rs. 70 crores. Thus, the equilibrium level of the national income is Rs. 550 crores.

Equilibrium Income and Output: A Graphical Explanation

Aggregate Demand–Aggregate Supply Approach

Equilibrium: The determination of the equilibrium income by the aggregate demand–aggregate supply approach in a two sector economy has been depicted in Figure 5.5(a).

 

where, x-axis =	Disposable income
y-axis =	Aggregate demand or aggregate planned expenditure
C =	Aggregate consumption function, C = Ca + bY
Ca =	The intercept of the consumption function on the y axis showing consumption spending at zero income level.
b =	The MPC or the slope of the consumption function (it will remain constant as, in our analysis, the consumption function is a linear function)
AD =	Aggregate demand function (which is obtained by adding the consumption function and the investment function)
AS =	Aggregate supply function (also called the guideline or the 45 degree line)
Point E =	Point where the aggregate demand and aggregate supply curves intersect to determine the equilibrium income at Y*. It is also called the Keynesian cross.

Disequilibrium: Consider a situation where the firms produce an output equal to OY₁. At this level of output the aggregate demand Y₁A, consisting of consumption demand of Y₁C and investment demand of CA, is in excess of the aggregate supply of Y₁B. There is a run down on inventories to meet the excess demand. This excess demand will induce the firms to expand their output till equilibrium is reached at an income level of OY* where aggregate demand is equal to aggregate supply.

Suppose the firms produce an output equal to OY₂. At this level of output the aggregate demand Y₂G, consisting of consumption demand of Y₂ F and investment demand of FG, is insufficient to exhaust the aggregate supply of Y₂D. There is an involuntary accumulation of inventories. Thus, the firms will cut down on production till equilibrium is reached at an income level of OY* where aggregate demand is equal to aggregate supply.

Figure 5.5 Determination of Equilibrium Income or Output in a Two Sector Economy

This is a situation that arises where aggregate demand is smaller than aggregate supply.

Saving–Investment Approach

Equilibrium: The determination of the equilibrium income by the saving–investment approach in a two sector economy has been depicted in Figure 5.5(b).

 

where,	x-axis =	Disposable income
	y-axis =	Planned saving and planned investment
	S =	Aggregate saving function (it can be easily obtained from the consumption function)
	– Ca=	The intercept of the saving function on the y-axis
	s =	The MPS or the slope of the saving function (it will remain constant as the saving function, in our analysis, is a linear function)
	I =	Aggregate investment function (it is parallel to the x-axis because investment is independent of the income level)
	Point E′ =	Point where planned saving and planned investment functions intersect to determine the equilibrium income at Y*.

 

Disequilibrium: Consider a situation where the firms produce an output equal to OY₁. At this level of output, the planned saving S₁Y₁ is less than the planned investment I₁Y₁. Thus, the consumption of goods is larger than the current production. Thus, inventories will fall. Firms will be tempted to hire more workers and expand production till the output increases to Y* where planned investment is equal to planned saving.

Suppose the firms produce an output equal to OY₂. At this level of output, the planned saving S₂ Y₂ is greater than planned investment I₂ Y₂. There will be an involuntary accumulation of inventories. Firms will lay off workers and cut back on production till it decreases to Y* where planned investment is equal to planned saving.

The equilibrium level of income will be determined at the point where planned saving is equal to planned investment. At any other income level there will be disequilibrium, which will make the firms change their production and employment in such a manner that the system returns to the initial point of equilibrium. Thus it is clear that while actual saving is always equal to actual investment, planned saving is only equal to planned investment at the equilibrium point.

We find that the two approaches to the determination of the equilibrium income, the aggregate demand–aggregate supply approach and the saving–investment approach, both yield the same result.

• Although actual saving always equals actual investment, planned saving equals planned investment only at the equilibrium point.
• In an economy, disequilibrium exists when aggregate demand is not equal to aggregate supply or planned saving is not equal to planned investment.
• The two approaches to the determination of the equilibrium income, the aggregate demand–aggregate supply approach and the saving–investment approach, both yield the same equilibrium level of income.

INTRODUCTION

Here, we focussed on the determination of the equilibrium level of income in the simple Keynesian model in a two sector economy.

AGGREGATE DEMAND IN A TWO SECTOR ECONOMY

1. Aggregate demand is the total amount of goods demanded in an economy. The aggregate demand function can be expressed as AD = C + I.
2. The consumption spending or the aggregate amount of goods bought in any time period will depend upon the real income of the households.
3. The consumption function is a relationship between income and consumption expenditure.
4. The most general non-linear form of the consumption function can be expressed as C = C(Y).
5. The consumption function equation in a linear form can be expressed as C = C_a + bY.
6. C_a also known as autonomous consumption; it is the intercept of the consumption function on the y axis whereas the constant b is known as the MPC and it denotes the slope of the consumption function.
7. The APC is defined as the ratio of consumption to income.
8. The MPC is defined as the increase in the consumption per unit of increase in the income.

SAVING AS A COUNTERPART OF THE CONSUMPTION FUNCTION

1. Income that is not spent on consumption is saved.
2. The saving function is the counterpart of the consumption function and can be written as S = – C_a + sY where the constant s is the MPS and denotes the slope of the saving function.
3. The APS is the saving counterpart of the APC and is defined as the ratio of saving to income.
4. The MPS is defined as the increase in the saving per unit of increase in the income. As the MPS or s is always positive, savings will be an increasing function of income.
5. The sum of APC and APS is always equal to one.
6. The sum of MPC and MPS is always equal to one.

THE AGGREGATE DEMAND FUNCTION

1. To determine the aggregate demand function in a two sector economy, we assume that investment is constant and that C = C_a + bY.
2. Thus, the aggregate demand function can be written as AD = C_a + bY + .

DETERMINATION OF EQUILIBRIUM INCOME OR OUTPUT IN A TWO SECTOR ECONOMY

1. In the most basic terms, an economy can be said to be in equilibrium when the production plans of the firms and the expenditure plans of the households are realized.
2. According to the Keynesian theory, there are two approaches to the determination of income and output: Aggregate demand–Aggregate supply approach and Saving–Investment approach.

Equilibrium Income and Output

AGGREGATE DEMAND–AGGREGATE SUPPLY APPROACH

1. The equilibrium national income is determined at that level where the aggregate demand = aggregate supply.
2. Keynes had argued that it is not necessary that aggregate demand will be always equal to aggregate supply.
3. Disequilibrium occurs if aggregate demand is not equal to aggregate supply. However, if any disequilibrium occurs then the forces inbuilt in the system would operate in such a manner that equilibrium is restored.

SAVING – INVESTMENT APPROACH

1. Though ex ante saving and investment may differ, ex post saving and investment are always equal.
2. The equilibrium national income is determined where not only the aggregate demand and the aggregate supply are equal but at that level where planned saving is also equal to planned investment.
3. Disequilibrium occurs when planned saving is not equal to planned investment. However, firms expand production or cut back on production till planned investment is equal to planned saving.
4. The two approaches to the determination of the equilibrium income, the aggregate demand-aggregate supply approach and the saving–investment approach, both yield the same result.

TRUE OR FALSE QUESTIONS

1. As investment is autonomous, aggregate demand function will depend mainly on the consumption function.
2. The MPC is defined as the ratio of consumption to income for different levels of income.
3. The APS is defined as the increase in the saving per unit of increase in the income.
4. Though planned saving always equals planned investment, actual saving equals actual investment only at the equilibrium point.
5. In an economy, disequilibrium exists when aggregate demand is not equal to aggregate supply.

VERY SHORT-ANSWER QUESTIONS

1. What is aggregate demand in the Keynesian model in a two sector economy?
2. Write a short note on the
   1. Average propensity to consume
   2. Marginal propensity to consume
3. Write a short note on the
   1. Average propensity to save
   2. Marginal propensity to save
4. Discuss the relationship between
   1. APC and APS
   2. MPC and MPS
5. Write a short note on the aggregate demand function.

SHORT-ANSWER QUESTIONS

1. Write a short note on the consumption function.
2. Write a short note on the saving function.
3. ‘As an identity, saving is always equal to investment.’ Comment.
4. ‘If any disequilibrium occurs, then the forces inbuilt in the system would operate in such a manner that equilibrium is restored.’ Comment by using the aggregate demand–aggregate supply approach to the Keynesian theory.
5. With the help of the saving–investment approach, depict equilibrium and disequilibrium in a two sector Keynesian model.

LONG-ANSWER QUESTIONS

1. Discuss the aggregate demand–aggregate supply approach to the determination of the equilibrium income and output in the Keynesian theory.
2. Discuss the saving–investment approach to the determination of the equilibrium income and output in the Keynesian theory.
3. Give the algebraic explanation to the determination of equilibrium income and output in the Keynesian theory.
4. Show the determination of equilibrium income and output in the Keynesian theory with the help of a graphical approach.
5. Discuss: (a) consumption function and (b) saving as a counterpart of the consumption function.

SOLVED NUMERICAL PROBLEMS

Numerical 1

In an economy, the basic equations are as follows: the consumption function is C = 120 + 0.80 Y and investment is = 250.

1. Find the equilibrium level of income
2. Find the equilibrium level of consumption
3. Find the equilibrium level of saving
4. Show that at the equilibrium level, aggregate demand equals aggregate supply and saving leakages equals investment injections.

Numerical 2

Suppose the consumption function is C = C_a + bY and investment is I = , then

1. Find an equation for the equilibrium level of output.
2. Find the equilibrium level of output when C_a = 150, b = 0.80 and = 250.

Numerical 3

The fundamental equations in an economy are given as: consumption function C = 200 + 0.75 Y, investment = 200.

1. Find the equilibrium level of income.
2. Find the equilibrium level of consumption.

Numerical 4

The fundamental equations in an economy are given as: consumption C = 150 + 0.80Y and investment = 200.

1. Derive the saving function.
2. Find the equilibrium level of output by equating the saving leakages to the investment injections.

Numerical 5

If in an economy C = 450 + 0.80Y and investment is I = 540, then

1. Determine the equilibrium level of income and consumption.
2. Derive the saving function and determine the savings at the equilibrium level.
3. Determine the equilibrium level of income by equating planned saving and planned investment.

UNSOLVED NUMERICAL PROBLEMS (WITH ANSWERS)

1. Suppose the consumption function is C = 50 + 0.60Y and the investment is = 80, then
   1. Find the equilibrium level of income.
   2. Find the equilibrium level of consumption.
   3. Find the equilibrium level of saving.
   4. Show that at the equilibrium level, aggregate demand equals aggregate supply and saving leakages equals investment injections.
2. In a two sector economy, the consumption function is C = 60 + 0.75Y and investment is = 60. Find the equilibrium level of income by equating the
   1. Output and Spending
   2. Saving and Investment
3. Suppose the consumption function is C = 50 + 0.8Y and the investment is = 70, then
   1. Find the equilibrium level of income.
   2. Find the equilibrium level of consumption.
   3. Find the equilibrium level of saving.
   4. Show that at the equilibrium level, aggregate demand equals aggregate supply and saving leakages equals investment injections.
4. If the consumption function is C = 70 + 0.8Y and investment is = 70, find
   1. The equilibrium level of income
   2. The equilibrium level of consumption
   3. The equilibrium level of saving
5. In an economy, planned consumption is C = 50 + 0.60Y and planned investment is = 70.
   1. Find the equilibrium level of income.
   2. Find the equilibrium level of consumption.
   3. Find the equilibrium level of saving.
   4. Show that at the equilibrium level, aggregate demand equals aggregate supply and saving leakages equal investment injections.

TRUE OR FALSE QUESTIONS

1. True. As we have assumed that investment is autonomous and independent of the income level, aggregate demand function will depend mainly on the consumption function.
2. False. The APC is defined as the ratio of consumption to income for different levels of income.
3. False. The MPS is defined as the increase in the saving per unit of increase in the income.
4. False. While actual saving always equals actual investment, planned saving equals planned investment only at the equilibrium point.
5. True. In an economy, disequilibrium exists when aggregate demand is not equal to aggregate supply or planned saving is not equal to planned investment.

SOLVED NUMERICAL PROBLEMS

Solution 1

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

   Thus,

   Y = 120 + 0.80Y + 250

   Y − 0.80Y = 120 + 250

   0.20Y = 370

   

   Y = 1850

   The equilibrium level of income is 1850.

2. The consumption function is C = 120 + 0.80Y.

   When Y = 1850,	C = 120 + 0.80 (1850)
   	C = 120 + 1480
   	C = 1600

   The equilibrium level of consumption is 1600.

3. The saving equation is S = Y – C.

   When Y =	1850 and C = 1600, we have
   S =	1850 – 1600
   S =	250

   The equilibrium level of saving is 250.

4. Aggregate demand equals aggregate supply

    

   C + I = C + S

   1600 + 250 = 1600 + 250

   or

   1850 = 1850

   Saving equals investment.

   S = I

   250 = 250

Solution 2

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

    

   Thus,

   Y = C_a + bY +

   Y – bY = C_a +

   Y (1 – b) = C_a +

   

   The equation for the equilibrium level of output is

2. Substituting for the values in , we get
   

   Y = 2000

   Thus, the equilibrium level of output is 2000.

Solution 3

1. In a two sector economy the equilibrium level of income is

   In the above equation, C_a = 200, = 200, b = 0.75.

   By substituting the above values, we get

   

   Y = 1600

   Thus, the equilibrium level of income is 1600.

2. In a two sector economy, the consumption function is

    

   C = C_a + b Y

   In the above equation, C_a = 200, = 200, b = 0 .75.

   By substituting the above values, we get

    

   C = 200 + 0.75Y

   C = 200 + 0.75 (1600)

   C = 1400

   Thus, the equilibrium level of consumption is 400.

Solution 4

1. The saving function is given by S = Y – C

    

   S = Y – (150 + 0.80 Y)

   S = – 150 + 0.20 Y

   Thus, the saving function is given by S = – 150 + 0.20Y

2. The equilibrium level of output can be determined by equating the saving leakages to the investment injections.

   Thus,

   −150 + 0.20Y = 200

   or

   −150 + 0.20Y = 200

   0.20Y = 350

   

   Y = 1750

   Thus, the equilibrium level of output is 1750.

Solution 5

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

   Thus,

   Y = 450 + 0.80Y + 540

   Y − 0.80Y = 450 + 540

   0.20Y = 990

   

   Y = 4950

   Thus, the equilibrium level of income is 4950.

   The consumption function is C = 450 + 0.80 Y.

   When	Y = 4950,	C = 450 + 0.80 (4950)
   		C = 450 + 3960
   		C = 4410

   Thus, the equilibrium level of consumption is 4410.

2. The saving function is given by S = Y − C.

                                                                    S = Y − (450 + 0.80Y)

                                                                    S = 0.20Y − 450

                                                                    S = − 450 + 0.20Y

   Thus, the saving function is given by S = – 450 + 0.20Y.

   At the equilibrium level, S = −450 + 0.20 (4950)

                                                      S = −450 + 990

                                                      S = 540

3. The planned saving is given by S = –450 + 0.20Y.

   In equilibrium, planned saving equals planned investment.

   Thus, −450 + 0.20Y = 540

                                0.20Y = 540 + 450

                                          

                                          Y = 4950

    

   Thus, the equilibrium level of income is 4950.

UNSOLVED NUMERICAL PROBLEMS

1. (a) Y = 325 (The equilibrium level of income is 325.)
(b) C = 245 (The equilibrium level of consumption is 245.)
(c) S = 80 (The equilibrium level of saving is 80.)
(d) Aggregate demand equals aggregate supply or 325 = 325.
       Saving leakages equals investment injections or 80 = 80.

2. (a) Y = 480 (The equilibrium level of income is 480.)
(b) S = I (The equilibrium level of income is 480.)

3. (a) Y = 600 (The equilibrium level of income is 600.)
(b) C = 530 (The equilibrium level of consumption is 530.)
(c) S = 70 (The equilibrium level of saving is 70.)
(d) C + I = C + S (600 = 600)
       S = I (70 = 70)

4. (a) Y = 700 (The equilibrium level of income is 700.)
(b) C = 630 (The equilibrium level of consumption is 630.)
(c) S = 70 (The equilibrium level of saving is 70.)

5. (a) Y = 300 (The equilibrium level of income is 600.)
(b) C = 230 (The equilibrium level of consumption is 230.)
(c) S = 70 (The equilibrium level of saving is 70.)
(d) C + I = C + S (300 = 300)
       Saving equals investment, S = I (300 = 300).