NATIONAL INCOME

Marginal Propensity to Consume (MPC)

The consumption function is based on the assumption that there is a constant relationship between consumption and income, as denoted by constant b which is marginal propensity to consume. The concept of MPC describes the relationship between change in consumption (∆C) and the change in income (∆Y). The value of the increment to consumer expenditure per unit of increment to income is termed the Marginal Propensity to Consume (MPC).                             Although the MPC is not necessarily constant for all changes in income (in fact, the MPC tends to decline at higher income levels), most analysis of consumption generally works with a constant MPC.

Average Propensity to Consume (APC)

Just as marginal propensity to consume, the average propensity to consume is a ratio of consumption defining income consumption relationship. The ratio of total consumption to total income is known as the average propensity to consume (APC).

                           

   APC = Total consumption/total income   = CC/YY    (2.6)

The table below shows the relationship between income consumption and saving.

Relationship between Income and Consumption

Income (Y)	Consumption (C )	APC ( C/Y)	MPC(∆C /∆Y)	MPS(∆S /∆Y) (1-MPC)
0	500	500/0 = ∞	-	-
1000	1250	1250/1000 = 1.25	750/1000 = 0.75	0.25
2000	2000	2000/2000 = 1.00	750/1000 = 0.75	0.25
3000	2750	2750/3000 = 0.92	750/1000 = 0.75	0.25
6000	5000	5000/6000 = 0.83	1500/2000 = 0.75	0.25
10,000	8000	8000/10,000 = 0.80	3000/4000 = 0.75	0.25

APC is calculated at various income levels. It is obvious that the proportion  of income spent on consumption decreases as income increases. What happens to the rest of the income that is not spent on consumption? If it is not spent, it must be saved because income is either spent or saved; there are no other used to which it can be put. Thus, just as consumption, saving is a function of income. S=f(Y).

The Saving Function

In figure 1.2.3, the consumption and saving functions are graphed. The saving function shows the level of saving (S) at each level of disposable income (Y). The intercept for the saving function, (—a) is the (negative) level of  saving at zero level of disposable income at consumption equal to ‘a’ . By definition, national income Y

= C + S which shows that disposable income is, by definition, consumption plus saving. Therefore, S = Y – C. Thus, when we represent the theory of the consumption-income relationship, it also implicitly establishes the saving-income relationship.

The Marginal Propensity to Save (MPS)

 The slope of the saving function is the marginal propensity to save. If a one-unit increase in disposable income leads to an increase of b units in consumption, the remainder (1 - b) is the increase in saving. This increment to saving per unit increase in disposable income (1 - b) is called the marginal propensity to save (MPS). In  other words, the marginal propensity to save is the increase in saving per unit increase in disposable income.

     Marginal Propensity to Consume (MPC) is always less than unity, but greater than zero, i.e., 0 < b < 1 Also, MPC + MPS = 1; we have MPS 0 < b < 1. Thus, saving is    an increasing function of the level of income because the marginal propensity to save (MPS) = 1- b is positive, i.e. saving increase as income increases.

Average Propensity to Save (APS)

     The ratio of total saving to total income is called average propensity to save (APS). Alternatively, it is that part of total income which is saved.

                

             APS = Total saving/ Total income  = SS/YY      (2.8)

                        In figure 2.3 showing the consumption and saving functions, the 45° line is drawn

to split the positive quadrant of the graph and shows the income-consumption relation with Y = C (AD = Y) at all levels of income. All points on the 45° line indicate that aggregate expenditure equal aggregate output; i.e. the value of the variables measured on the vertical axis (C+I) is equal to the value of  the variable measured  on the horizontal axis ( i.e. Y). Because aggregate expenditures equal total output  for all points along the 45-degree line, the line maps out all possible equilibrium income levels. As long as the economy is operating at less than its full-employment capacity, producers will produce any output along the 45-degree line that they believe purchasers will buy.

THE TWO-SECTOR MODEL  OF NATIONAL INCOME DETERMINATION

In this section, we shall describe the two-sector model of determination of equilibrium levels of output and income in its formal form using the aggregate demand function and the aggregate supply function. According to  Keynesian theory of income determination, the equilibrium level of national income is a situation in which aggregate demand (C+ I) is equal to aggregate supply (C +  S) i.e.,

                    C + I =  C + S

                             Or

         I  =  S                               (2.9)

In a two sector economy, the aggregate demand (C+ I) refers to the total spending

in the economy i.e. it is the sum of demand for the consumer goods (C) and investment goods (I) by households and firms respectively. In figure 1.2.4, the aggregate demand curve is linear and positively sloped indicating that as the level  of national income rises, the aggregate demand (or aggregate spending) in the economy also rises. The aggregate expenditure line is flatter than the  45-degree line because, as income rises, consumption also increases, but by less than the increase in income.

Figure 1.2.4

Determination of Equilibrium Income: Two Sector Model

     

You may bear in mind the basic point that according to Keynes, aggregate demand will not always be equal to aggregate supply. Aggregate demand depends on households plan to consume and to save. Aggregate supply depends on the producers’ plan to produce goods and services.  For  the aggregate demand and  the aggregate supply to be equal so that equilibrium is established, the households’ plan must coincide with producers’ plan. The expectations of businessmen are realized only when aggregate expenditure equals aggregate income. In  other words, aggregate supply represents aggregate value expected by business firms  and aggregate demand represents their realized value. At equilibrium, expected value equals realized value. However, Keynes held the view that that there is no reason to believe that:

                     i. consumers’ consumption plan always coincides with producers’ production plan, and

                   ii. that producers’ plan to invest matches always with households plan to save

Putting it differently, there is no reason for C + I and C + S to be always equal.

The figure 1.2.4 depicts the determination of equilibrium income. Income is measured along the horizontal axis and the components of aggregate demand, C and I, are measured along the vertical axis. The consumption function (I)  is shown   in panel B of the figure, the (C+ I) or aggregate expenditure schedule which is obtained by adding the autonomous expenditure component  namely  investment to consumption spending at each level of income. Since the autonomous expenditure component (I) does not depend directly on income, the (C+I) schedule lies above the consumption function by a constant amount. Equilibrium level of income is such that aggregate demand equals output (which in turn equals  income). Only at point E and at the corresponding equilibrium levels of income and output (Y0), does aggregate demand exactly equal output. At that level of output and income, planned spending precisely matches production.  Once  national income is determined, it will remain stable in the short run.

Our understanding of the equilibrium level of  income  would be better if we find  out why the other points on the graph are not points of equilibrium. For example, consider a level of income below Y0, for example Y1, generates consumption as shown along the consumption function. When this level of  consumption is added  to the autonomous investment expenditure (I), the aggregate demand exceeds income; i.e the (C +1) schedule is above the  45°  line.  Equivalently, at all those  levels I is greater than S, as can be seen in panel (B) of the figure 1.2.4. The aggregate expenditures exceed aggregate output. Excess demand makes businesses to sell more than what they currently produce. The unexpected sales would draw down inventories and result in less inventory investment than business firms planned. They will react by hiring more workers and expanding production. This will increase the nation’s aggregate income. It also follows that with demand outstripping production, desired investment will exceed actual investment.

Conversely, at levels of income above Y0, for example at Y2, output exceed demand (the 45° line is above the C +I schedule). The planned expenditures on goods and services are less than what business firms thought they would be; business firms would be unable to sell as much of their current output as they had expected. In  fact, they have unintentionally made larger inventory investments than they  planned and their actual inventories would increase. Therefore, there will be a tendency for output to fall. This process continues till output reaches Y0, at which current production exactly matches planned aggregate spending and unintended inventory shortfall or accumulation are therefore equal to zero. At this point, consumers’ plan matches with producers’ plan and savers’ plan matches with investors’ plan. Consequently, there is no tendency for output to change.

Since C + S = Y, the national income equilibrium can be written as

                        Y = C + I                          (2.10)

The saving schedule S slopes upward because saving varies positively with income.

In equilibrium, planned investment equals saving. Therefore, corresponding to this income, the saving schedule (S) intersects the horizontal investment schedule (I).  This intersection is shown in panel (B) of figure 1.2.4.

This condition applies only to an economy in which there is no government and no foreign trade. To understand this relationship, refer to panel (B) of figure 1.2.4 Without government and foreign trade, the vertical distance  between  the aggregate demand (C+I) and consumption line (C) in the figure is equal to planned investment spending, I. You may also find that the vertical distance between the consumption schedule and the 45° line also measures saving (S =  Y- C)  at each level of income. At  the equilibrium level of income (at point E in panel B), and only  at that level, the two vertical distances are equal. Thus, at the equilibrium level of income, saving equals (planned) investment. By contrast, above  the  equilibrium level of income, Y0 , saving (the distance between 45° line and the consumption schedule) exceeds planned investment, while below Y0 level of income, planned investment exceeds saving.

The equality between saving and investment can be seen directly from the identities in national income accounting. Since income is either spent or saved, Y = C + S. Without government and foreign trade, aggregate demand equals consumption plus investment, Y = C + I. Putting the two together, we have C + S = C + I, or S = I.

An important point to remember is that Keynesian equilibrium with equality of planned aggregate expenditures and output need not take place at full  employment. It is possible that the rate of unemployment is high. In the Keynesian model, neither wages nor interest rates will decline in the face of abnormally high unemployment and excess capacity. Therefore, output will remain at less than the full employment rate as long as there is insufficient spending in the economy. Keynes argued that this was precisely what was happening during the Great Depression.

THE INVESTMENT MULTIPLIER

In our two-sector model, a change in aggregate demand may be caused by change in consumption expenditure or in business investment or in both. Since Consumption expenditure is a stable function of income, changes in income are primarily from changes in the autonomous components of aggregate demand, especially from changes in the unstable investment component. We shall now examine the effect of an increase in investment (upward shift in the investment schedule) causing an upward shift in the aggregate demand function.

Figure 1.2.5

Effect of Changes in Autonomous Investment

In the figure 1.2.5, an increase in autonomous investment by ∆ I shifts the aggregate demand schedule from C+I to C+I+ ∆I. Correspondingly, the equilibrium shifts from E to E1 and the equilibrium income increases more than proportionately from Yo      to Y1. Why and how does this happen? This occurs due to the operation of the investment multiplier.

The multiplier refers to the phenomenon whereby a change in an injection of expenditure will lead to a proportionately larger change (or multiple change) in the level of national income. Multiplier explains how many times the aggregate income increases as a result of an increase in investment. When the level of investment increases by an amount say ∆I, the equilibrium level of income will increase by some multiple amounts, ∆ Y. The ratio of ∆Y to ∆I is called the investment multiplier, k.

                         K = ∆Y/∆I                         (2.11)

The size of  the multiplier  effect is given by  ∆ Y = k ∆I.

For example, if a change in investment of ` 2000 million causes a change in national income of ` 6000 million, then the multiplier is 6000/2000 =3. Thus multiplier indicates the change in national income for each rupee change in the desired investment. The value 3 in the above example tells us that for every ` 1 increase in desired investment expenditure, there will be ` 3 increase in equilibrium national income. Multiplier, therefore, expresses the relationship between an  initial increment in investment and the resulting increase in aggregate income. Since the increase in national income (∆Y) is the result of increase in investment (∆I), the multiplier is called ‘investment multiplier.’

The process behind the multiplier can be compared to the ‘ripple effect’ of  water. Let us assume that the initial disturbance comes from a change in autonomous investment (∆I) of 500 units. The economy being in equilibrium, an upward shift in aggregate demand leads to an increase in national income which in a two sector economy will be, by definition, distributed as factor incomes. There will be an equal increase in disposable income. Firms experience increased demand and as a response, their output increases. Assuming that MPC is 0.80, consumption expenditure increases by 400, resulting in increase in production. The process does not stop here; it will generate a second-round of increase in income. The process further continues as an  autonomous rise in investment leads to induced increases  in consumer demand as income increases we  find  that the  marginal propensity  to  consume  (MPC)  is the

determinant of the value of the multiplier and that there exists a direct relationship between MPC and the value of multiplier.  Higher  the MPC, more  will be the value of the multiplier, and vice-versa. On the contrary, higher the MPS, lower will be the value of multiplier and vice-versa. The maximum value of multiplier is infinity when the value of MPC is 1 i.e the economy decides to consume the whole of its  additional income. We conclude that the value of the multiplier is the reciprocal of MPS.

For example, if the value of MPC is 0.75, then the value of the multiplier is multiplier as per (2. 11) is:

                1/0.25 =  4

The multiplier concept is central to  Keynes's theory because it  explains how shifts in investment caused by changes in business expectations set off a process that causes not only investment but also consumption to vary. The multiplier shows how shocks to one sector are transmitted throughout the economy.

Increase in income due to increase in initial investment, does not go on endlessly. The process of income propagation slows down and ultimately comes to a halt. Causes responsible for the decline in income are called leakages. Income that is not spent on currently produced consumption goods and services may be regarded as having leaked out of income stream. If the increased income goes out of the cycle  of consumption expenditure, there is a leakage from income stream which reduces the effect of multiplier. The more powerful these leakages are the smaller will  be  the value of multiplier. The leakages are caused due to:

a) progressive rates of taxation which result in no appreciable increase in consumption despite increase in income

b) high liquidity preference and idle saving or holding of cash balances and an equivalent fall in marginal propensity to consume

c) increased demand for consumer goods being met out of the existing stocks or through imports

d) additional income spent on purchasing existing wealth or purchase of government securities and shares from shareholders or bond holders

e) undistributed profits of corporations

f)  part of increment in income used for payment of debts

g) case of full employment additional investment will only lead to inflation, and

h) scarcity of goods and services despite having high MPC

The MPC on which the multiplier effect of increase in income depends, is high in under developed countries; ironically the value of multiplier is low. Due to structural inadequacies, increase in consumption expenditure is not generally accompanied   by increase in production. E.g. increased demand for industrial goods consequent  on increased income does not lead to increase in their real output;  rather prices tend to rise.

An important element of Keynesian models is that they relate to short-period equilibrium and contain no dynamic elements. There is nothing like Keynesian macro-economic dynamics. When a shock occurs, for example when there is a change in autonomous investment due to change in some variable, one equilibrium position can be compared with another as a matter of comparative statics. There is no link between one period and the next and no provision  is made for an analysis  of processes through time.