Multiplier and Accelerator in Economics: Working, Equational Model and Limitations

In this article we will discuss about Multiplier and Accelerator in Economics:- 1. Concept of Multiplier 2. Relation between MPC and Multiplier 3. Working 4. Reverse Working 5. Assumptions 6. Leakages 7. Criticisms 8. Importance 9. Principle of Acceleration 10. Equational Model 11. Working 12. Importance.

Concept of Multiplier:

The concept of multiplier is an integral part of Keynes’ theory of employment. It is an important tool of income propagation and business cycle analysis. Keynes believed that an initial increment in investment increases the final income by many times. To this relationship between an initial increase in investment and the final increase in total income, Keynes gave the name of ‘investment multiplier,’ which is also known as ‘income multiplier’ or simply ‘multiplier’.

According to Keynes, “Investment multiplier tells us that when there is an increment of aggregate investment; income will increase by an amount which is K times the increment of investment.” Similarly, according to Kurihara, “The multiplier is the ratio of change in income to the change in investment.” In the words of Dillard, “Investment multiplier is the ratio of an increase of income to given increase in investment”

In short, the multiplier tells us how many times the income increases as a result of an initial increase in investment. Given the marginal propensity to consume (MPC), the multiplier establishes a quantitative relationship between aggregate income (or employment) and the investment. The multiplier is expressed as-

where K denotes the multiplier, ∆Y the change in income and ∆I the change in investment.

The basic idea behind the theory of multiplier is that of the induced consumption as a result of increased investment. Whenever an investment is made, the effect is to increase income not only by the amount of original investment but by a multiple of it.

The initial effect of an increase in investment expenditure is the increase in income by the same amount. But as income increases, consumption also increases. Consumption expenditure, in turn, becomes additional income of those employed in the consumer goods industries. Thus, there is a further increase in income due to induced consumption and so on.

To sum up, the investment does not increase income in the industries where investment is originally made, but also in other industries whose products are demanded by the men employed in the investment industries.

Relation between MPC and Multiplier:

The size of marginal propensity to consume (MPC) is a key to the size of the multiplier. The value of multiplier is in fact determined by the MPC.

The formula of the multiplier which highlights the close relationship between the MPC and the size of the multiplier can be derived in the following manner:

It is clear from Table-1 that greater the MPC, higher the size of the multiplier and lesser the MPC, lower the size of the multiplier. Since, according to the psychological law of consumption, the value of the MPC lies between zero and one, i.e., 0 < MPC < 1, it follow that the size of the multiplier can never be unity or infinity, but remains between these two limits.

Working of Multiplier:

The working of the multiplier can be understood with the help of an example as given in Table-2.

Suppose, the MPC is 0.5. Thus, according to the formula of multiplier, K = 1/(1 – MPC) = 1/(1 – 0.5) = 2. Again suppose that investment is increased by Rs. 100 crores. This means the income (of those who get this increased investment) also increases by the same amount. Of this Rs. 100 crores, Rs. 50 crores are saved and Rs. 50 crores are spent on consumption (MPC = 1/2).

The induced consumption of Rs. 50 crores leads to an increase in income by the same amount (i.e., Rs. 50 crores) in period 2. In the same manner, income increases by Rs. 25 crores in period 3, by Rs. 12.5 crores in period 4 and so on till the total income has increased by Rs. 200 crores (i.e., 2 times the initial investment of Rs. 100 crores).

Reverse Working of Multiplier:

Multiplier works both in the forward direction as well as in the backward direction. If investment decreases, the multiplier operates in the reverse direction. A reduction in investment leads to contraction in income and consumption which, in turn, causes cumulative decline in income and consumption level till the contraction in total income is the multiple of initial decrease in investment.

Suppose, investment decreases by Rs. 20 crores. With MPC = 0.5 and K = 1/(1-MPC) = 2, there will be net reduction in income to the extent of Rs. 40 crores.

The higher the MPC the greater the value of multiplier and the greater the cumulative decline in income. Or, in other words, the higher the marginal propensity to save (MPS), the lower is the size of the multiplier and the smaller is the cumulative decline in income (because K = 1/MPS).

Thus, a higher multiplier would cause greater jerks and shocking decline of income whenever the investment falls. But, there is one ray of hope. Since MPC is always less than one, multiplier is never infinity. Just as consumers do not spend the full increment of income on consumption, similarly, they do not curtail the consumption expenditure by the full amount of decrement of income.

Figure-2 illustrates the reverse operation of multiplier. SS curve is the saving curve which is drawn on the assumption of MPS = 0.5. In this case, multiple K = 1/MPS = 1/0.5 = 2. SS saving curve intersect I₀I₀ investment curve at point E₀, giving the initial equilibrium level of income OY₀.

When investment declines from I₀ I₀ to I₁I₁ (i.e., by I₀ I₁ or ∆I amount), income also declines from OY₀ to OY₁ (i.e., Y₀Y₁ or ∆Y amount). The decrease in income is double the decrement in investment (Y₀Y₁ = 2 I₀I₁ or ∆Y = 2∆I).

Assumptions of Multiplier:

The working of multiplier is based on a number of assumptions. As these assumptions are not fulfilled in the actual world, they limit the operation of multiplier.

Main assumptions are as follows:

(i) There is no induced investment. Multiplier specially applies to autonomous investment which is free from profit motive.

(ii) Marginal propensity to consume remains constant during the adjustment process.

(iii) Consumption is a function of current income.

(iv) The output of consumer goods is responsive to effective demand for them.

(v) There is surplus capacity in the consumer goods industries to meet the increased demand for these goods as a result of a rise in income following the increased investment.

(vi) Other factors and resources of production are easily available in the economy.

(vii) The new higher level of investment is maintained for the completion of the adjustment process.

(viii) There is net increase in investment. In order words, increase in investment in one sector is not offset by a decline in investment in some other sector.

(ix) There are no time lags involved in the multiplier process. An increase in investment instantaneously leads to a multiple increase in income.

(x) There is a closed economy implying the absence of international trade.

(xi) Multiplier process operates in the industrialized economy.

(xii) There is no change in the prices of commodities and raw materials, etc.

(xiii) The situation of less-than-full employment prevails in the economy.

Leakages of Multiplier:

In actual practice, the operation of multiplier is affected by a number of factors. Given the MPC, the whole of the increment of income in each period may not be spent on consumption. This is because there are several leakages from the income stream as a result of which the process of income propagation is slowed down.

According to Peterson, “Income that is not spent for currently produced consumption goods and services may be regarded as having leaked out of income stream.” Or, in other words, leakages of multiplier constitute that portion of prior income which has been lost to the income stream.

Important leakages are described below:

I. Saving:

Saving constitutes an important leakage to the process of income propagation. Since marginal propensity to consume is less than one (MPC < 1), the whole of the increment of income is not spent on consumption. A part of it is saved and peters out of the income stream, thereby limiting the value of multiplier.

The whole of saving forms a leakage and the size of multiplier is inversely related to the marginal propensity to save (MPS). According to the formula of multiplier (i.e., K = 1/MPS = 1/Leakage), the higher the MPS, the greater the leakage and the lower the value of multiplier.

II. Debt Cancellation:

If some of the income received by the people is used for paying off old debts, that part peters out of the income stream and becomes leakage.

III. Imports:

Net imports form another leakage in the domestic income stream. If there is an excess of imports over exports, a part of the increased domestic income as a result of increased investment will flow out to foreign countries.

IV. Price Inflation:

Price inflation is another important leakage from the income stream of an economy. When there is a rise in prices of consumption goods, a major part of the increased income is dissipated on higher prices, instead of promoting consumption, income and employment.

V. Hoarding:

If people have a tendency to hoard the increased income in the form of idle cash balances, they will reduce the expenditure on consumption in the economy. This will constitute another leakage, restricting the value of the multiplier.

VI. Purchase of Old Shares and Securities:

If people purchase old stocks and securities with the newly earned income, this type of financial investment will reduce consumption and restrict the value of multiplier.

VII. Taxation:

Taxes reduce the disposable income of the tax payers, discourage consumption expenditure and lower the size of the multiplier.

VIII. Undistributed Profits:

If a part of profits of the company is not distributed to the shareholders in the form of dividends and is kept in reserve fund, it forms a leakage from the multiplier process.

Effect of Leakages:

The leakages interfere with the smooth flow of income stream and thereby lead to the slowing down of the pace of multiplier. Had the entire higher income been spent and none saved, the process of income generation will go on endlessly.

The effect of leakages (e.g., saving) can be understood with the help of the example given in Table- 2. In that table, it is clearly shown that when investment is increased by Rs.100 crores in period 1, income also increases by the same amount in the same period. But, in the subsequent periods, only half of the increased income is consumed (because of MPC = 0.5). Other half is saved (because of MPS = 0.5). The saved portion becomes a leakage in the multiplier process.

Figure-3 shows the effect of leakage. C₀ is the basic consumption in each period. Initial investment (i.e., ∆I) made in period 1 leads to induced consumption (C₁ + C₂ +C₃ + …) in subsequent periods which goes on decreasing by half the amount in each period because of MPC = 0.5. S₁ + S₂ + S₃ (= shaded area) are the total savings in each period which indicate leakage from the multiplier process. As a result of leakage, income in each period increases only by the amount of induced consumption.

Criticisms of Multiplier:

Keynes’ concept of multiplier has been criticised on the following grounds:

I. Limitations and Qualifications:

The ‘ideal’ multiplier operates on the basis of a number of assumptions, like the availability of consumer goods, maintenance of investment, net increase in investment, autonomous investment, closed economy etc. These assumptions may not be found in practice. Thus, the ‘actual’ multiplier may be greatly restricted and will be different from the ‘ideal’ multiplier.

II. Mere Tautology:

According to Haberler, Keynes’ concept of multiplier is a mere tautology. In other words, the definition of multiplier is a mere tautology. In other words, the definition of multiplier as K =1/1-MPC is simple truism; it does not tell anything. As Hansen has pointed out, “Such a coefficient is a mere arithmetic multiplier (i.e., a truism) and not a true behaviour multiplier based on a behaviour pattern which establishes a verifiable relation between consumption and income. A mere arithmetical multiplier, 1 / (1-(∆C/∆Y)) is tautological.”

III. Mechanical Relationship:

Hazlitt has criticised the theory of multiplier on the ground that it expresses only a mechanical relationship between macro variables. He maintains that there is never any precise, pre-determinable or mechanical relationship between social income, consumption, investment and extent of employment,

IV. Static Concept:

Keynes’ multiplier is a static concept. It shows the process of income propagation from one point of equilibrium to another and that too under static assumptions. It gives little insight into the process by which the economy achieves a new equilibrium. It fails to explain- (a) what happens in between the initial investment and the final increase in aggregate income; (b) how and by what stages of time intervals the final increase in the aggregate income is attained; and (c) how the sequence of events may be hampered by time and other factors.

V. Neglect of Time Lags:

Keynes regards the concept of multiplier as a timeless concept by assuming an instantaneous relationship between income, consumption and investment. In reality, however, a time lag exists between the receipt of income and its expenditure on consumption goods, and then also in producing consumption goods.

VI. Assumption of Consumption Function:

Keynes’ theory of multiplier rests on the simple assumption of linear relationship between consumption and income with the hypothesis that the MPC is less than one and greater than zero. Empirical studies show that the relationship between income and consumption is complicated and non-linear and not as simple as assumed by Keynes.

VII. Exclusive Emphasis on Consumption:

In Gordon’s view, the greatest weakness of the theory of multiplier is its exclusive emphasis on consumption. He maintained that it would be more realistic to use the term ‘marginal propensity to spend’ in place of marginal propensity to consume’ and then to consider the effect of an initial increase in investment, not on consumption, but also on total private investment and government spending.

VIII. Acceleration Effect Ignored:

Multiplier is concerned with the effect of original investment on consumption and income. It ignores the effects of increased consumption on investment. The value of the multiplier will be much greater and achieved much earlier if both the effects, i.e., (a) the effect of investment on consumption (multiplier effect), and (b) the effect of consumption on investment (acceleration effect), are taken into account.

IX. Saving is not Hoarding:

Another fallacy in Keynes’ multiplier theory is the assumption that the entire fraction of a country’s income that is not consumed is hoarded, and no part of this unconsumed income is invested. In reality, saving does not mean hoarding and most of the savings are used for investment

X. Other Critical Comments:

Some of the important comments made by the critics are as follows: According to Hutt, “The conventional multiplier apparatus is rubbish and that it should be expunged from the text books.” To Stigler, “It is the fuzziest part of Keynesian theory.” Hazlitt calls multiplier ‘a worthless theoretical toy’, ‘a strange concept’, ‘a myth’, ‘much ado about nothing’.

Despite these attacks by the critics, the post-Keynesians, like Hansen, Samulson, Harrod, strongly defended the theory of multiplier, introduced many improvements and made the whole analysis dynamic.

The true position regarding the criticism of multiplier can be summed up in the following remarks of Harris, “In the discussion of the multiplier, many economists have gone on fishing expeditions, but though they had many bites, they did not catch any large fish. Indeed, they have added much to Keynes’ relatively simple and unverified presentation.

Importance of Multiplier:

Despite the various qualifications, limitations and weaknesses, the concept of multiplier continues to be of great theoretical and practical importance:

i. Importance of Investment:

The concept of multiplier highlights the importance of investment as the major dynamic element in the process of income generation in the economy.

ii. Income Generation Process:

The theory of multiplier not only indicates the direct creation of income and employment, it also reveals that income is generated in the economy like a stone causing ripples in the lake.

iii. Trade Cycle:

The knowledge of the process of multiplier is of vital importance for understanding different phases of trade cycle and for its accurate forecasting and control.

iv. Economic Policy:

Multiplier is a useful tool in the hands of the policy-makers for formulating suitable economic policies for the achievement of full employment and for the control of business fluctuations.

v. Saving-Investment Equality:

The multiplier process helps to understand how equality between saving and investment is brought about. An increase in investment leads to increase in income. As a result of increase in income, saving also increases and becomes equal to investment.

vi. Deficit Financing:

The theory of multiplier emphasises the importance of deficit financing. Increases in public expenditure by creating deficit budget help in creating income and employment multiple times the initial increase in expenditure.

vii. Public Investment:

The concept of multiplier highlights the special significance of public investment (in the form of government expenditure in public works, and other public welfare activities) in achieving and maintaining full employment.

Public investment is autonomous in nature and avoids the uncertainty and instability of private investment. Public investment is particularly important during depression when private investment is not forthcoming due to very low profitability.

To conclude, the concept of multiplier is one of Keynes’ path-breaking contributions in the sense that it has not only enriched economic analysis but also has influenced economic policy.

Principle of Acceleration:

Keynes’ concept of multiplier is inadequate to account for the total national income induced by the original money spent. It explains the effect of initial investment on consumption and hence on income, but ignores the effect of induced consumption or income on investment. The latter effect is known as acceleration effect. To know the total effect of initial money spent on total income, multiplier effect and the acceleration effect should be combined.

The principle of acceleration was first introduced by J.M. Clark in 1917. Later on the economists like, Hicks, Samuelson and Harrod, further developed this principle to explain the business cycles. The principle of acceleration is based on the fact that the demand for capital goods is derived from the demand for consumer goods.

The acceleration principle explains the process by which a change in demand for consumption goods leads to a change in investment on capital goods. According to Kurihara, “The accelerator coefficient is the ratio between induced investment and an initial change in consumption.”

Symbolically, the coefficient of acceleration is expressed as- v = ∆I/∆C or ∆I = v∆C, where v is the acceleration coefficient, AI is net change in investment and AC is the net change in consumption expenditure. Hicks has broadly interpreted the concept of acceleration as the ratio of induced investment (∆I) to change in income or output (∆Y).

Thus, the accelerator v = ∆I/∆Y (or the capital-output ratio). This implies that the demand for capital goods is not derived from consumer goods alone, but from any demand for output. Now it has become customary to explain the principle of acceleration in terms of final output (Y).

The production of any given demand for final output generally requires for technical reasons an amount of capital several times larger than the output produced with it. Therefore, an increase in the demand for final output will give rise to an additional demand for capital goods several times larger than the new demand for output.

If, for example, a machine worth Rs. 3 lakh produces output worth Rs. 1 lakh, then the accelerator v will be 3 (v = ∆I/∆Y = 3 lakh/I lakh = 3).

Equational Model:

The principle of acceleration can be expressed in the form of equational model given below:

Thus, it is clear from Equations (1) and (2) that gross investment in the economy is equal to net investment plus replacement investment. Assuming replacement investment to be constant, gross investment varies with the level of net investment at each level of output.

Working of Acceleration Principle:

The working of acceleration principle can be explained with the help of an example given in Table-3.

(i) Column (1) indicates a series of time periods.

(ii) Column (2) gives the assumed level of income and output in each period.

(iii) Assuming a constant capital-output ratio or the value of accelerator, v = 2, the required stock of capital in each period is two times the corresponding output of that period, as shown in Column (3).

(iv) The replacement investment in each period is assumed to be equal to 10% of the capital stock in period zero. Thus, it is 20 in each period, (i.e., 10% of 200= 20) as shown in Column (4).

(v) Net investment in any period as shown in Column (5) equals v times the change in output between that period and the preceding period. For example, net investment in period 3= v (Y_t3 – Y_t2) = 2(115-105) = 20. This means that given the accelerator v = 2, an increase in the demand for final output of 10 leads to an increase of capital goods of 20.

(vi) Total demand for capital goods {Column (6)} is equal to the net investment plus replacement investment { (i.e.. Column (4) + Column (5) } in each period. For example, total investment in period 3 = 20+ 20 = 40.

(vii) Thus it is clear that, given the value of accelerator, total demand for capital goods depends upon the change in the total output. As long as the demand for final goods rises {i.e., Y increases upto period 6 in Column (2)}, net investment is positive {(i.e., upto period 6 in Column (5)}. After period 6, demand for final goods [Column (2)] falls and the net investment [Column (5)] is negative.

(viii) Total output [(Column (2)] increases at an increasing rate from period 1 to period 4 and net investment increases {Column (5)}. Then output increases at a decreasing rate from period 5 to 6 and the net investment declines. From period 7 to 9, total output falls, and the net investment becomes negative.

(ix) The behaviour of gross investment is similar to the net investment. The only difference is that the gross investment is not negative and once it becomes zero in period 8, it starts rising. The reason for this is that despite the net investment becoming negative, the replacement investment continues at the constant rate.

Assumptions and Limitations of Acceleration Principle:

The acceleration principle is based on a number of assumptions which are difficult to be found in the actual world.

The important assumptions and limitations of the principle of acceleration are as follows:

i. Constant Capital-Output Ratio:

The acceleration principle is based on the assumption of constant capital-output ratio. It means that the units of capital required to produce one unit of output remain constant. In the dynamic world, the capital-output ratio changes and therefore the acceleration effect also varies.

ii. No Excess Capacity:

The acceleration principle assumes that there should be no excess capacity in the capital goods industries. If excess capacity exists, an increase in the demand for consumer goods will not lead to any induced investment because the increased demand will be met from the existing capital and machinery.

iii. Permanent Change in Consumption Demand:

The principle of acceleration will operate it the increase in consumption demand is permanent. A purely temporary change in consumption demand will not induce the entrepreneurs to invest in the production of additional capital goods.

iv. Availability of Resources:

The acceleration principle assumes the availability of resources. The supply of resources should be elastic so that the investment in capital goods industries can be increased easily. If tire economy is at the full employment, the capital goods industries will fail to expand because of non-­availability of required reserves.

v. Elastic Supply of Funds:

The acceleration principle assumes elastic supply of cheap credit so that sufficient funds for induced investment are available. If there is shortage of credit, the rate of interest will be high and the investment in capital goods will be low.

vi. Absence of Time Lags:

The acceleration principle assumes that increased output leads to a simultaneous rise in investment. But, in reality, a rise in demand takes a long time to produce its impact on investment level.

vii. Neglect of Expectations:

The acceleration principle neglects the role of expectations on the decision-making behaviour of entrepreneur. Inducement to invest is not influenced by demand alone. It is also affected by future anticipations about stock market changes, political changes, international events, etc.

viii. Neglect of Technological Changes:

The acceleration principle also ignores the role of technological changes on investment. Some technological changes may take the form of capital-saving (or labour-saving) and thus may reduce (or increase) the volume of investment.

Importance of Acceleration Principle:

In spite of certain limitations, the principle of acceleration occupies a significant place in the macro-economic analysis.

The main points of importance are given below:

(i) The principle of acceleration, along with the principle of multiplier, helps to understand the process of income generation more clearly and comprehensively. The concept of multiplier provides only a partial explanation of the income generation process.

(ii) The principle of acceleration explains why the fluctuations in income and employment occur so violently.

(iii) It demonstrates that capital goods industries fluctuate more than the consumer goods industries.

(iv) It is more useful in explaining the upper turning point of the business cycle because what is responsible for a fall in the induced investment is not any absolute fall in the demand for consumer goods but only a decline in its rate of increase.

(v) Harrod has used the coefficient of acceleration in the growth model to show that the economic growth in an economy depends upon the size of accelerator; higher the size of accelerator, higher the growth rate and vice versa.

In the words of Shapiro, “The acceleration principle, however inadequate by itself, clearly emerges us one of a number of major factors that are needed in combination with the multiplier to explain the fluctuations observed in the world of investment spending.”