Equilibrium Value of National Income and Employment | Macroeconomics

In the Keynesian model, equilibrium levels of employment and national income are determined simultaneously through aggregate demand and aggregate supply (which together ensure macroeco­nomic equilibrium). In the Keynesian model employment is a function of output and output is equal to income.

The relation between income and employment is dictated by the aggregate production function Y = F(L) since capital stock (K) and the state of technology (T) remain constant. This means the larger the number of workers employed, the higher is the level of output and national income. This point is illustrated by the aggregate production function K = F (L) in Fig. 6.7(a). The curvature of the function indicates diminishing returns to labour.

In Fig. 6.7(b) we show how the equilibrium value of national income is determined. Suppose the economy is initially at full employment at point F which corresponds to aggregate output at Y_F, as shown in both panels of the diagram.

Now if due to sudden fall in MEC, investment demand falls by ΔI the combined C + I schedule will shift downward to C + I’ where I’ = I – ΔI (or I’ < I by ΔI). Now the aggregate demand curve intersects the aggregate supply curve OK at point E.

So a new macroeconomic equilibrium is established but at a lower level of output or national income (Y_E). This level of income in panel (a) corresponds to a lower level of employment L_E in panel (b). Thus E represents underemployment equilibrium or equilibrium at less-than-full employment.

An economy gets stuck in such a situation due to fall in investment demand. Thus deficiency of demand is the main cause of such involuntary unemployment in the Keynesian model of income determination. Such unemployment is called by modern economist’s cyclical unemployment.

Therefore equilibrium does not necessarily imply full employment as the classicists had thought. Equilibrium may occur even at less than full employment, as Keynes had postulated. Such involuntary unemployment cannot be automatically eliminated through the free play of the market forces.

Measures to Increase National Income and Employment:

Since national income, from the spending side, has four main components, there are four ways of increasing national income, viz., increasing C, I, G and NE:

1. Increasing C:

Consumption (C) can be increased by cutting taxes. A tax cut will lead to an increase in disposable income and an increase in C. As a result the short-run consumption function will shift upward causing the combined C + I schedule to shift upward parallely (assuming constant MPC) and the economy will be enabled to re-achieve full employment. This type of policy was adopted in the famous Kenedy budget of the USA in 1964 as also in the budget of 2003, presented by President George Bush (which announced a drastic tax cut).

2. Increasing I:

Investment can be increased in two ways. Firstly, the central bank can increase the supply of money. As a result Y will increase. This will induce business people to invest more. Secondly, the government can provide various types of incentives to investors in the form of tax cuts, investment tax credit and subsidies on investment. Tax cuts increase corporate profit, and make more funds available for investment. If I increase, the C + I schedule will shift upward. As a result employment and national income will increase.

3. Increasing G:

It was Keynes who first suggested the policy of increasing government spending in times of depression and unemployment. If the government spends more on public works or on slump clearance, government spending (G) will add to private spending C + I and thus increase aggregate demand.

This will lead to an increase in national income and employment and the economy will be enabled to re-achieve full employment. This type of policy was adopted by F. Roosevelt in 1934 and Bill Clinton in 1993-94. And both policies were highly successful in reducing unemployment considerably and raising national output and income.

4. Increasing NE:

Finally, if net exports (NE) are positive, i.e., exports are greater than imports, aggregate demand (C + I + G + X – M) will increase. This, in turn, will cause employment and national income to rise. By contrast, a deficit in a country’s balance of trade (i.e., an excess of imports over exports) will cause employment and national income to fall, in which case, the economy may get trapped in underem­ployment equilibrium of the Keynesian type.

We will discuss more about fiscal policy and balance of trade .We now pass on an alternative approach to income determination, viz., the saving-investment approach which is also known as the leakage-injection approach.

The S-I Approach to National Income Determination:

There is an alternative method of determining equilibrium value of national income, known as the S-I approach. It explains how national income is determined by desired (planned or intended) saving and desired investment. This method is illustrated in Table 6.2 and Fig. 6.8.

From Table 6.2 we see that investment (I) remains constant at 100 but S increases as Y increases. So long as I > S, Y will increase since the injection into the circular flow of income through investment will exceed the leakage from the flow through(s).

Table 6.3 presents a consumption function, from which saving plans can be obtained. Assuming that planned investment is autonomous and that all household plans are realised, an equilibrium level of income can be calculated.

When income is 500 the consumption spending is 450 and saving is 50. At this level of income autonomous planned investment is 50, thereby bringing total planned expenditure (consumption + investment) equal to the level of output (or income). With planned saving and investment being equal, the economy is in equilibrium— there are no forces at work changing the level of output or income.

However, at the higher level of income (600), planned saving exceeds planned investment, resulting in planned expenditure falling below planned income. As the rate of production exceeds the rate of sales by 20, the level of stock will rise, thereby resulting in a rise in unplanned investment. Any stock changes are regarded as changes in investment.

At this stage realised investment, made up of planned and unplanned investment, will still be equal to realised saving, but the discrepancy between the intentions of savers and investors will result in the level of income falling back until it reaches the equilibrium level of 500.

If income were 400 the consumption schedule would indicate that 3-70 would be consumed and 30 saved. With planned investment exceeding planned saving, planned expenditure would exceed planned income, resulting in a fall in the value of stocks (inventories). The fall in stocks can be regarded as unplanned disinvestment, giving a realised investment figure of 50 – 20 = 30 (which is the same as actual saving).

It may be noted that anything which exerts an expansionary pressure on Y is called a leakage and anything which exerts a contractionary pressure on it is called an injection. The reason is that if S increases, C will fall. Therefore, the combined C + I schedule will shift downward and Y will fall. As Keynes said in the early 1930s, “if you save 5 pence, you throw one worker out of job for the day”.

Thus, from Table 6.2 we see that so long as I > S.Y increases and when I = S, Y remains constant at 500. It neither increases, nor falls. It is in equilibrium. By comparison if S > I, Y will fall and will come back to 500, i.e., its equilibrium value.

The S-I approach is illustrated in two parts of Fig 6.8. In part (a) we present two approaches to income determination, viz., (a) the income-expenditure approach (according to which Y = C + I), and (b) the saving-investment approach (according to which S = I).

Although the two approaches are different, they are interrelated. In fact by using Fig 6.8, we have achieved synthesis between the two approaches. In other words, the S-I approach is a logical deduction from the income-expenditure approach. In panel (a), we derive the saving function 5 from the income line Y and consumption function.

In fact, the vertical distance between Y and C measures 5 at each level of income (since Y = C + S and S = Y – C). The saving schedule starts from point B’ which corresponds to the break-even point B. This shows that income has to reach a minimum level for any saving to occur.

The saving schedule which shows the positive relation between Y and S is upward sloping. It intersects the autonomous investment schedule I at point E’, at which S = I and national income attains its equilibrium value Y_E = 500.

Id panel (b), we illustrate the S-I approach separately. We see the same thing shown in Table 6.2 and panel (a) of Fig 6.8. We see that so long as I > S, Y increases and so long as S > I, Y falls. So it logically follows that when I = S, Y neither rises nor falls, i.e., it is in equilibrium. Now the question is how is this S-I equilibrium brought about.

S-I Equilibrium:

The classicists thought that S-I equilibrium is ensured by changes in the rate of interest. But Keynes presented a different view on this. According to him S-I equilibrium is ensured through income changes. If I > S, Y will increase. If Y increases, C and 5 will both increase (I remaining constant due to its autonomous character).

And the process of income generation will continue until and unless saving increases enough to match the fixed autonomous investment. The converse is also true. If S > I, more money will be withdrawn from the economy through saving (not spending on consumption goods) than injected in the form of investment expenditure.

The Algebra of the S-I Approach:

According to the AS-AD approach, national income is in equilibrium when the level of national income is equal to effective demand.

Thus we get:

Y = AD . . . (1)

From this equation, we arrive at the other condition of national income equilibrium, i.e., planned saving = planned investment

We know that in a simple two-sector Keynesian model Y = C + I.

So we can write:

AD = C + I

or, Y = C + I

We know that:

C = Y – S … (2)

Now the linear saving function corresponding to the linear consumption function C = a + bY is S = -a + (1 -b) Y where 1 – b = MPS

Since Y = C + S

ΔY = ΔC + ΔS or, ΔY/ΔY = ΔC/ΔC + ΔS/ΔY

or 1 = MPC + MPS or, 1 = b + (1 – b)

or MPC + MPS = 1 or, MPS = 1 – MPC = 1 – b

Now substituting Y – S in equation (2),

we get: 

Y = Y – S + I

or, Y – Y + S = I

or, S = I

Thus national income is in equilibrium when desired saving is equal to desired investment. Now we present the equilibrium condition of national income in terms of autonomous expenditure.

So the saving function is: 

S = – a + (1 – b) Y

and I = I

In equilibrium I = S

or I = – a + (1 – b) Y

or (1 – b) Y = I + a

or, Y = 1/1 – b (I + a) = 1/1 – b (A)

where A = I + a.

Here, as we know 1/1 – b is the autonomous expenditure multiplier and b is MPC and (1 – b) is MPS. Thus the equilibrium value of national income is found by multiplying the autonomous expenditure multiplier by autonomous expenditure.

Numerical Problems:

Problem 4:

Find the equilibrium level of income when S = – 50 + 0.20Y and I

Solution:

National income reaches equilibrium when:

S = I

Given S = – 50 + 0.20Y and

I = Rs 100 crores

we arrive at the following by substituting the values of S and I in equation (1)

– 50 + 0.20Y = 100

or, 0.20Y = 100 + 50 = 150

or, Y = 150/0.20 = Rs 150 × 5 = Rs 750 crores.

We can check the result by using the other formula:

Y = 1/1 – b (I + a)

Here b = 1 – 0.20 = 0.80, a = 50 and I = 100

Y = 1/1 – 0.08 (100 + 50)

= 1/0.20 (150) = Rs 750 crores.

The Relation between S and I:

According to classical economists saving is equal to investment only when the money market is in equilibrium. The money market has no relation to real economy due to the classical dichotomy which implies neutrality of money.

This equilibrium is brought about by changes in the interest rates. Keynes, however, did not agree and argued that saving and investment are not always equal. Keynes challenged the view which generated a serious controversy which was resolved by modern economists.

According to modern economists, there are two senses in which the terms ‘saving’ and ‘investment’ are used. In one sense S and I are always equal whether they correspond to the equilibrium level of Y or not. In another sense, S and I are equal only when national income attains its equilibrium value.

Recall that saving is that part of income which is not spent on consumption goods and can be positive, zero or negative. Investment is expenditure on capital goods. It is a flow concept which is positive. It refers to the change in the stock of capital of an economy per year: I_t = K_t – K_{t – 1} or I_t = ΔK. Therefore I_t > 0 if ΔK > 0 or K_t > K_{t – 1}. Investment may be gross or net. Gross investment less depreciation is net investment.

Nowadays saving and investment are made by two classes of people. However, we can think of a wheat farmer who saves and invests at the same time. He sets aside a portion of output to be used as seed next year. In this sense, wheat is both a consumption good and a capital good (a form of circulating capital).

Let us take another example. Suppose the farmer’s annual income is Rs 15,000 and he spends Rs 10,000 on consumer goods and spends another Rs 2,000 on the construction of a tubewell for his field and Rs 3,000 for buying a husking machine. His saving will be Rs 15,000 – Rs 10,000 = Rs 5,000.

His expenditure of Rs 5,000 on the tubewell and machine will be his saving on one hand and investment on the other assuming that he does not deposit any part of his saving in banks to earn interest and he does not borrow fund to buy the machine or construct the tubewell either. However, this is true of an individual but not for the economy as a whole. For the economy as a whole, saving may differ from investment.

Modern economists point out that since savers and investors are two different groups of people and the motives for S and I are diverse, there can be divergence between S and I.

According to Keynes, actual saving is always equal to actual investment during a year. Actual saving is called ex-post (realised) saving and actual investment is called ex-post (realised) investment. The actual figures of S and I are presented in the national income accounts of a country.

However, according to modern economists the concepts of S and I are to be used in another sense. Such S and I are known as desired S and desired I. Desired S is also known as ex-ante or planned or intended saving. Similarly, desired I is also known as ex-ante or planned or intended investment.

A. Saving-Investment Equality:

According to Keynes, saving and investment are equal in the ex-post (actual) sense.

This can be proved as follows:

Since a country’s national income is earned by producing and selling two types of goods:

(i) consumer goods,

(ii) capital goods, national income is the total market value of both types of goods.

So we can write:

National income = C + I

or, Y = C + I . . . (1)

where Y is national income, C is consumption demand and I is investment demand.

Equation (1) represents national income from the output or income side. From the expenditure side, national income is largely spent on consumption goods and partly saved. So we can write

National income = Consumption + saving

or, Y = C + S … (2)

By combining the above two equations, we see that:  

Consumption + saving = C + I … (3)

Now if we cancel C from both sides, we get the following equation:

Saving = Investment

or, S = I

In Keynes’s view, investment is that part of national output (income) which arises from the production of goods (I = Y – C). Similarly saving is that part of national income which is not spent on consumption (S = Y – C). Hence, actual or ex-post S is always equal to actual I. This identity follows from the standard national income accounting system of a country.

As we have noted for an individual saving may differ from investment. But for the community as a whole saving is equal to investment. But this is not true as far as ex-ante S and I are concerned. This point may now be explained further.

Following Keynes, modern economists have pointed out that ex-ante (anticipated or desired) S is not always equal to ex-ante I. This point is explained by referring to inventories (i.e., goods produced in the current year but not sold in the same year). And unplanned (undesired) changes in inventories play an important role in the Keynesian theory of income determination based on the S-I approach. This point may now be explained.

Let us suppose, at a certain arbitrarily chosen level of income ex-ante S exceeds ex-ante I. This means that aggregate expenditure (C + I) will not be sufficient to absorb all the goods and services produced at that level of income. So business firms will find that their unplanned (undesired) investments are increasing. The problem arises due to deficiency of aggregate demand.

Since prices remain fixed in the Keynesian model, the unplanned income in stocks will be cleared. In such a situation actual (ex-post) investment equals planned investment plus unplanned increase in inventories and actual investment will, of course, be equal to actual saving. Now since businesses do not want to hold these extra undesired inventories, a cut back on production in the next period is inevitable.

By contrast, if at another arbitrarily chosen level of income, planned investment exceeds planned saving, aggregate expenditure (C + I) will exceed planned output of goods and services. Since sales exceed this output, there will be a unplanned fall in inventories. Consequently actual investment (which equals planned investment minus unplanned running down of inventories) will be equal to actual saving in the same period.

This, in its turn, will stimulate production in the next period. As a result national income and employment will rise. Thus, in the ex-post or realised sense, S and I are always equal. This is known as S-I equality or S-I identity, which is different from S-I equilibrium, a concept to which we turn now.

S-I Equilibrium:

We have noted that planned S may differ from planned I for two reasons:

(i) Savers and investors are two different groups of people and

(ii) The motives for saving and investment are different

However, the divergence between the two cannot last for long.

They are brought into equality by changes in national income. Let us see how this happens. If in a particular year planned I exceeds planned S, the level of national income rises. As y increases both C and S will increase. And the process of increase in Y continues until and unless planned S is brought into balance with planned I.

By contrast, if planned S exceeds planned I, the income contractionary process will start. As Y falls, both C and S fall. And the process of income contraction will continue until and unless desired S is brought into balance with desired I.

Now we present the views of two great economists in this context:

View 1:

According to Paul Samuelson in Keynes’ theory of income determination, investment calls the tune and saving dances at it.

View 2:

According to R. G. Lipsey, there is no reason why saving will always be equal to some randomly chosen level of investment. However, if there is any divergence between the two, it will get corrected sooner or later through income changes and the process of income change will continue until and unless the level of saving is equated to a fixed level of investment.

The equality of planned S with planned I is known as S-I equilibrium because such equality is achieved only when Y is in equilibrium and not at other values of Y.

Thus while actual S is always equal to actual I, desired S has only a tendency to match desired I. This matching occurs only when Y is in equilibrium.

The balance between desired S and desired I is illustrated in Fig. 6.9.

Desired S = desired I at point E, which corresponds to the equilibrium value of national income (Y_E). If actual income is Y₁ I > S and Y will increase and ultimately reach Y_E. Since I remains the same but S increases with an increase in Y, S will be equal to I. The converse is also true. If actual income is Y₂, S > I and Y will fall and ultimately return to Y_E. Since I remains constant and S falls with a fall in Y, S-I equilibrium will be reached at point E.

Thus while actual (ex-post) S is always equal to actual (ex-post) I, planned (ex-ante) S will be equal to planned (ex-ante) I only when national income is in equilibrium. This means that S-I equality is not the same thing as S-I equilibrium.