Keynesian Two-Sector Model of Income Determination | Macroeconomics

According to the Keynesian theory, level of employment is determined in a free market-based capitalist economy in the short run when the size of the labour force and capital stock remain constant and the state of technology (which shows how inputs can be converted into output) also remains unchanged.

In addition, Keynes assumed that the price level remains unchanged. Thus, under these restrictive assumptions, the level of income depends on the level of employment in a static framework. Since income is a function of employment, both are determined simultaneously.

So in the simple Keynesian model, like the level of employment, the level of income is determined by aggregate demand and aggregate supply. If employment increases, national income will also increase. In this chapter we analyse determination of national income in the context of a simple two-sector economy, with a fixed price level. We start with the key concept of the model, viz., aggregate demand.

Aggregate Demand and Aggregate Expenditure:

Aggregate demand refers to the total desired expenditure of households and firms at various level of national income per period. So we will use the terms ‘aggregate demand’ and ‘aggregate expenditure’ synonymously.

The Concept of Aggregate Demand (with a Constant Price Level):

In a two-sector closed economy without Government and foreign trade aggregate demand has two components:

(i) Household demand for consumption goods and

(ii) Business demand for capital goods or investment demand.

By aggregate demand Keynes means how much expenditure the households and businesses are making on consumption and investment, respectively per period.

So we can write:

Aggregate demand = Consumption demand + investment demand

or, AD = C + I … (1)

where AD stands for aggregate demand, C for household consumption and I for business investment. Accordingly we can rewrite equation (1) as

AE = C + I … (2)

where AE is aggregate expenditure. Now we discuss each component of aggregate demand one by one.

Consumption Demand (C):

In the short run, consumption demand depends on two main factors:

(i) The level of national income, and

(ii) The propensity to consume.

The propensity (tendency) to consume is likely to remain constant in the short run. So as income increases, consumption demand also increases.

This means that consumption demand depends on income or is a function of income. The functional relation between income and consumption is shown by the Keynesian consumption function. It can be either linear with a constant slope (the slope is MPC) or non-linear with a declining slope.

For analytical simplicity, we assume here a linear short-run consumption function which takes the following form:

C = a + bY … (3)

Here C is consumption, Y is income, b is MPC and a (the intercept of the consumption function) stands for autonomous consumption. Even if income is zero, consumption cannot be zero because of this autonomous component.

This represents subsistence consumption, i.e., the minimum amount an individual has to consume in order to survive even when his income is zero. The second component of equation (3) shows induced consumption. It depends on income (Y).

In Fig. 6.1 we present a simple Keynesian short- run consumption function. Here we measure dis­posable national income on the; horizontal axis and consumption expenditure on the vertical axis. Here we have drawn a 45° income line which acts as a guideline.

This line has an important property. If we drop a perpendicular from any point on the line, we see that national income = consumption expendi­ture. But this does not happen at all points. We see that the consumption line C = a + bY (which represents a linear consumption function) intersects the income line at point B. Point B is called the break-even point in the theory of consumption.

If income reaches a minimum level, Y_min. (shown on the horizontal axis), the entire income is consumed. However, if income is less than this, C exceeds Y. This means that saving is negative. Such negative saving is called dissaving. If, on the other hand, Y exceeds Y_min, Y > C, and S is positive.

So national income has to reach a minimum level for any saving to occur. The vertical distance between the income line and the consumption line shows the level of saving at each level of income. The reason is that like employment, and income, C and S are mirror image concepts.

We know that Y = C + S or S = Y – C (in the absence of G, T and M). So if Y remains constant and C increases or falls, 5 will increase or fall. After all 5 is a residue. It is that portion of Y which is not spent on currently produced goods and services.

We also see from Fig. 6.1 that the vertical distance (or the gap between Y and C) increases as Y increases. This means that as Y increases, C increases no doubt, but not proportionately or S increases more than proportionately. The reason is that at low levels of income people consume more and at high levels of income, they save more.

Movement Vs. Shift:

In the short run the consumption function does not change. There is just movement along the same consumption function. As Y increases, C also increases. But the consumption function does not shift to a new position.

The reason is that, apart from national income, consumption depends on various other factors such as the tastes and preferences of consumers, the pattern of income distribution in the economy, the size of the population, the age and sex composition of the people and so on.

These factors, which cause shift of the consumption function, remain constant in the short run. This means that in the short run, consumption demand depends only on national income (or on disposable income).

Investment Demand:

No doubt, household consumption expenditure is the most important, component of aggregate demand. The second most important component of aggregate demand is investment. It plays a crucial role in the determination of the equilibrium level of national income.

It also causes short-run fluctuations in the level of income, or business cycles.

Investment demand depends on two main factors:

(1) The marginal efficiency of capital (MEC) and

(2) The rate of interest (r).

Since in the short run, the rate of interest normally remains constant, any fluctuations in the level of income occurs due to changes in MEC. MEC, in fact, refers to the rate of return the business people expect to earn from new investment, i.e., from the purchase or acquisition of new capital goods such as machines or equipment.

The MEC, in its turn, depends on two factors:

(1) The prospective rate of return from an asset over its economic life (which depends on the annual rate of depreciation) and

(2) The replacement costs of old capital goods (or purchase price of new capital goods).

In the short run, the replacement costs of old machines remain firmly constant. But profit expectations of business firms fluctuate every now and then. And this causes fluctuations in MEC, which, in turn, causes investment fluctuations.

Autonomous Vs. Induced Investment:

Investment is of two types:

(a) Autonomous (or independent of income) and

(b) Induced (or dependent on income).

Keynes assumed that all investment is autonomous and hence independent of national income or its rate of change.

In Keynes’s theory, investment depends on MEC and r. In Fig 6.2, we show the Keynesian investment demand schedule II which is horizontal. This means that investment remains constant at all levels of national income, i.e., whether national income is high or low. So its slope is zero. ‘

The Combined C + I Schedule:

Now by combining the Keynesian C and I functions, presented in Fig. 6.1 and Fig. 6.2, we present the combined C + I schedule in Fig. 6.3. This is known as the aggregate demand curve or, in modern terminology, the aggregate desired expenditure schedule (curve).

We proceed in four steps:

1. First we draw the 45° income line Y.

2. Then we draw the consumption line C.

3. In the next step we draw the investment line I.

4. Finally we superimpose the investment line on the consumption line to arrive at the combined C + I line.

Two points are to be noted here:

1. Since the investment line is horizontal, implying a fixed amount of investment at all levels of income, the consumption line and the C + I line are parallel to each other. In fact, the gap between the C line and the C + I line measures fixed autonomous investment.

2. The aggregate demand (expenditure) schedule, C + I, intersects the income line at point E at which Y = AE. To the left of point E, C + I > Y and to the right of point E, Y > C + I.

Aggregate Supply:

By aggregate supply Keynes means the total money value of (final) goods and services produced in an economy per year at constant prices.

Two components of aggregate supply are the following:

1. The output of all final consumer goods and services; and

2. The output of producer or capital (investment) goods.

Capital goods are the creators of other goods. For example, textile producing machines are used to produce textiles (or consumer goods). Machines are also used to produce other machines (or capital goods). For these reasons capital goods are also called producer goods.

National Product:

In fact, aggregate supply is another name of GNP. Both represent the total market value of all final goods and services produced in an economy per annum. In another sense, GNP is the same as national income.

The reason is that aggregate supply or money value of all final goods and services produced and sold is distributed among the various factors of production as rent, wages, interest and profits as rewards for their respective contributions to GNP.

The Short-Run Production Function:

Much like his predecessors (like classicists), Keynes derived his aggregate supply function from the short-run aggregate production function which is expressed as

Y = F (L, K̅, T̅) … (4)

where Y is GNP, L is labour input (which is the only variable factor), K̅ is the fixed stock of capital, and T̅ stands for unchanged technology.

Thus the aggregate production function may also be written as:

Y = F (L) … (5)

This means that in the short run more output can be produced only by employing more labourers (or using more labour inputs), so long as the economy has unutilised resources (mainly manpower) and of course, excess production capacity.

Since Keynes assumed that the size of the labour force remains constant in the short run, the level of employment (or the utilisation of the labour force) increases (falls) only if the demand for labour in­creases (falls). After all the Keynesian model is a demand-determined model.

The Aggregate Supply Curve:

Since the aggregate price level is assumed to remain constant in the short run, the Keynesian aggre­gate supply curve relates the level of aggregate output to national income. In fact, while drawing this supply curve money wages and productivity of labour are also assumed to remain constant.

These assumptions to­gether imply that more output will be produced and supplied at the given price level if aggregate demand increases. Thus aggregate demand sets the tune and aggregate supply dances at it.

In Fig. 6.4 we draw the Keynesian short-run aggregate supply curve as a 45° line OK since aggregate supply or national product is always equal to national income. Due to constant marginal cost and average cost of production, the value of aggregate output increases at the constant rate along the 45° line.

The 45° line shows two things:

1. It shows that even at constant prices, varying amounts of output (of both consumer and capital goods) will be offered for sale in response to changes in aggregate demand. If aggregate demand rises, more output will be offered for sale until and unless the state of full employment of resources is reached. When full employment is reached, a society’s actual output will be equal to its potential output. At this stage, no further increase in production and in aggregate supply is possible.

2. Since national income is the same thing as national product, the 45° line represents national income in nominal (money) terms.

The Equilibrium Level of National Income:

In Fig. 6.5 we put forth both the aggregate demand and aggregate supply curves to show how the equilibrium level of national income is determined in the two-sector model of Keynes. Here we proceed in four steps. First we draw the aggregate supply curve schedule OK which is the 45° line. Then we draw the consumption schedule C.

Next we draw the investment schedule I. Finally we superimpose the investment schedule on the consumption schedule C to derive the aggregate demand schedule C + I. The C + I = AD = AE schedule intersects the aggregate supply curve at point E, which indicates macroeconomic equilibrium. Such equilibrium corresponds to the equilibrium level of national income Y_E.

The Logic of the Equilibrium:

It may be noted that national income cannot be in equilibrium if it is less than or greater than Y_E. The reason is that at any other level of income either AD will exceed AS (as at point D) or AS will exceed AD (as at point F) as shown in Fig. 6.5. Why does this discrepancy occur ? It occurs due to unplanned (undesired) changes in inventories. A simple example will make the point clear.

Table 6.1 presents data for a hypothetical economy. An equilibrium will be reached in this economy when output produced or income received (Y) is equal to its planned (desired) expenditure, i.e., C + I. When this happens desired saving is also equal to desired investment. Here we assume that MPC = 4/5 and a fixed level of autonomous investment of Rs. 100 crores takes place at all levels of income.

Total expenditure in this economy has two components: spending on consumer goods (C) and spending on investment (capital) goods (I). Thus total expenditure is C + I. From Table 6.1 we see that total desired (planned) expenditure is equal to income received at the level of Rs. 500 crores.

When national income reaches this level:

Y = C + I = Rs. 500 crores

and S = I = Rs. 100 crores

Three points are to be noted in this context:

1. When C + I > Y, I > S and Y increases (because the expansionary forces on national income are stronger than the contractionary forces).

2. When Y > C + I, S > I, and Y falls (because the contractionary pressure exerted on Y is stronger than the expansionary pressure).

3. When Y = C + I, S = I and Y neither increases nor decreases (because this is the equilibrium state).

If sales plan of business firms are fulfilled but not production plans, there will be excess demand and Y will increase. If production plans are fulfilled but not sales plans, there will be excess supply and Y will fall.

Thus we see that there is divergence between AS and AD since the two plans of business firms do not always coincide. As a result there are unplanned changes using inventories, which cause national income and output to rise or fall.

The Principle of Effective Demand:

From Fig. 6.5 we see that aggregate demand is equal to aggregate supply only at point E and not at any other level of national income. The aggregate demand corresponding to this equilibrium level of national income is called “effective demand.”

The reason is that it is that level of aggregate demand which determines national income by being equal to aggregate supply. This is known as the Keynesian principle of effective demand. In Fig. 6.5, effective demand is equal to EY_E which is in turn, equal to equilibrium output produced and supplied (0F_E). This means that income received is equal to both desired and actual expenditure, leaving neither a deficit (excess demand) nor a surplus (excess supply).

So there is no pressure on national income to rise or fall.

Since it is aggregate demand which determines the equilibrium value of national income, we present the equilibrium condition of national income in terms of the Keynesian principle of effective demand as follows:

Y = AED … (6)

where AED = C + I.

So we can write:

Y = C + I

where all the terms have usual meaning.

Importance of the Concept:

Thus in the Keynesian model the level of employment and national income are determined simultaneously by aggregate effective demand. If aggregate effective demand rises, more output will be produced. So more workers will be employed and more income will be generated.

Thus it logically follows .that unemployment occurs due to deficiency of effective demand or purchasing power. And the solution to the problem lies in increasing effective demand. Therefore demand creates its own supply and not the other” way round as the classicists had thought.

Equilibrium at Less-than-Full Employment (or Underemployment Equilibrium):

The classical economists equated macroeconomic equilibrium with full employment. They believed in the Say’s law and wage-price flexibility which together ensured full employment in a self-adjusting free market-based capitalist economy. So the attainment of full employment was automatic in the classical model.

This view was challenged by Keynes. Keynes pointed out that national income may attain its equilibrium level (value) even at less-than-full employment. The reason is that there is always the possibility of involuntary unemployment in a capitalist economy due to deficiency of aggregate demand and downward rigidity of the nominal wage rate (which prevents smooth functioning of the labour market).

The concept of underemployment equilibrium is illustrated in Fig. 6.6. Here the economy reaches initial equilibrium at point E. The equilibrium value of national income corresponding to this macroeconomic equilibrium (at which AD = AS) is Y_E.

But this is not the full employment level of income. The economy is capable of producing more output and generating more employment and income in the process if aggregate demand increases. But, in this case, there is deficiency of aggregate demand due to inadequate investment demand.

If investment demand can be increased by ΔI, there will be a parallel upward shift of the aggregate demand schedule to C + I’ where I’ = I + ΔI, i.e., original investment plus the needed increase in investment.

The new aggregate demand schedule intersects the aggregate supply schedule at point F which is indeed the full employment point, at which actual output (income) is equal to potential output (income) of Y_F. Thus while at point E, the economy is in underemployment equilibrium, at point F it attains full employment.

Divergence between S and I:

However, there is no guarantee that desired saving will always be equal to desired investment. There are two reasons for this. Firstly, savers and investors are two different groups of people. Some people save, while others invest. For example, the major portion of saving originates from the household sector (families).

Of course companies also save by retaining a portion of their after-tax profits. Retained earnings provide internal funds for undertaking new investment activities. However, corporate saving is a very small proportion of total saving.

But investment activities are carried out only by business firms. Households are unlikely to know how much business firms are planning to invest. And businesses are unlikely to know how much households are planning to save.

Secondly the motives for saving and investment are different. Individuals save for certain personal motives such as children’s education and marriage as also for medical treatment. Some people save because they have a chance of being unemployed.

Others save certain amounts for maintaining their current living standards even after retirement, when their income suddenly falls. And some people save in order to buy durable goods such as cars, houses or even gold and jewellery.

Household saving decision is governed by two main factors — income (which affects the capacity to save) and the rate of interest (which affects the desire to save). By contrast business people invest in plant and machinery for making profits. And their decision to invest in fixed asset is mainly governed by the marginal efficiency of capital (or the yield) and the rate of interest.

For these two reasons, there can be divergence between the planned saving of the household sector and planned investment of the business sector. Although saving, like consumption is a stable function of income, investment is a volatile component of aggregate demand.

If, for some reason, there is a fall in the profit expectations of business firms, investment will fall. And this will lead to a fall in employment and equilibrium national income. This point will become clear when we study the saving- investment approach to national income determination.

Inflationary Gap:

It may also be noted that if aggregate demand exceeds the full employment level of output, there will be excess demand pressure in the economy. More output will be demanded by households and businesses than the economy is able to produce by utilising all its resources (including manpower) with its existing (unchanged) technology.

In such a situation only one outcome is possible —a rise in the prices of goods and services. This type of situation occurs if there is an improvement in profit prospects and businesses make more investment. In Fig. 6.6, if investment exceeds I’ = I + ΔI, then the economy will face the problem of demand-pull inflation which occurs due to a rise in aggregate demand at full employment.

In such a situation, national income will increase beyond 0Y_F only in nominal (money) terms and not in real terms. Thus full employment is taken as the economy’s inflation threshold. The end of full employment is the beginning of inflation. True inflation starts only when output expansion comes to an end as soon as all the resources are fully employed and the economy’s actual output exceeds the full employment output.

Keynes pointed out that for such inflation to occur there must be an inflationary gap in the economy. This concept may now be explained.

Classical economists believed that the root cause of inflation was continuous rise in the money supply. But modern discussion of inflation goes in terms of what Keynes called ‘inflationary gap’. It is a situation in which aggregate demand in the economy is greater than the aggregate supply of resources coming forward to the market. The consequences are persistently rising prices (and disequilibrium in the balance of payments).

Suppose the total value of output in a country in a particular period is Rs. 900 crores. The government now takes away Rs. 150 crores in taxes to meet its own expenditure. So the private sector is left with Rs. 750 crores for its own expenditure — consumption and investment.

From the national income analysis we know that the value of money income of the country is always equal to the net value of output. Here also the total money income of the people (Rs.750 crores) is equal to the net value of output (Rs. 900 crores – Rs. 150 crores = Rs. 750 crores) at current prices. As long as expenditure is equal to income there is no pressure on prices and no inflation. Prices remain virtually stable.

Suppose now the government injects Rs. 200 crores of money in the economy (either by borrowing from banks or by printing new money) to finance its own expenditure. This expenditure is made on factors of production. They earn incomes of an equivalent amount.

So money income of the people rises to Rs. 950 crores (Rs. 750 crores + Rs. 200 crores). The government may now tax a part of the income (say, Rs. 50 crores). A part of the increased (disposable) income will be saved and a part spent. Suppose people save Rs. 50 crores and spend Rs. 100 crores.

So the net money income available for expenditure is (Rs. 950 – Rs. 100) = Rs. 850 crores. So there is an increase over the previously available income amounting to (Rs: 850 crores – Rs. 750 crores =) Rs. 100 crores. The excess represents the inflationary gap, which will put an upward pressure on prices. If there is no corresponding increase in output, the price rise will continue until the value of output and the level of income become equal.

Income Determination through Simple Algebra:

The process of determination of equilibrium level of national income will become clear if we use simple algebra. We know that national income (Y) is equal to consumption demand (C) plus investment demand (I). So we can write:

Y = C + I . . . (1)

We also know that the simple Keynesian short-run consumption function is the following:

C = a + bY … (2)

In equation (2), a is autonomous consumption which remains fixed at all levels of income. So we put a bar on it to indicate its fixed value. Here b is the constant slope of the consumption function and represents the marginal propensity to consume (MPC). It is expressed as b = ΔC/ΔY. Thus total consumption demand has two components — autonomous consumption spending (a) and induced consumption spending (bY).

Keynes also assumed that all investment is autonomous and hence independent of income. It may be denoted by the symbol I_a.

Thus we get the following three structural equations’ for our simple two-sector economy:

Y = C + I … (1) definitual identity

C = a̅ +bY … (2) consumption function

I = I̅_a … (3) autonomous investment

Now if we substitute the values of C and I in equation (1), we have:

Y = a̅ + bY + I̅_a

or, Y – bY = a̅ + I̅_a

or, Y (1 – b) = a̅ + I̅_a

or, Y = 1/1 – b(a̅ + I̅_a)

or, Y = 1/1 – b (A̅) … (4)

where A̅ = a̅ + I̅_a, i.e., total autonomous expenditure (= autonomous of consumption spending + autonomous investment expenditure).

Equation (4) shows the equilibrium value of national income when aggregate demand equals aggregate supply. Total autonomous expenditure A̅ or aggregate demand equals the income generated through the production of goods and services.

Equation (4) also shows that the equilibrium value of national income (Y) can be found out by multiplying autonomous expenditure A by the autonomous expenditure multiplier 1/1 – b. [Since b is MPC and 1 – b is the marginal propensity to save (MPS), the autonomous expenditure multiplier, is the reciprocal of the MPS].

It may finally be noted that if either autonomous investment I_a increases or the MPC increases, national income will rise. Students can check this result by using hypothetical data on A and b.

The following numerical examples will clearly illustrate how the equilibrium level of national income is determined.