Let us make an in-depth study of the Accelerator. Learn about:- 1. Meaning of Accelerator 2. Working of Accelerator 3. Importance 4. Conclusion.

### Meaning of Accelerator:

The multiplier and the accelerator are not rivals: they are parallel concepts. While multiplier shows the effect of changes in investment on changes in income (and employment), the accelerator shows the effect of a change in consumption on private investment.

Hayek explained the central idea of this principle in these words:

“Since the production of any given amount of final output usually requires an amount of capital several times larger than the output produced with it during any short period (say a year) any increase in final demand will give rise to an additional demand for capital goods several times larger than the new final demand.”

The Principle of Acceleration states that if the demand for consumption goods rises, there will be an increase in the demand for the equipment, say machines, which produce these goods. But the demand for the machines will increase at a faster rate than the increase in demand for the product.

The accelerator, therefore, makes the level of investment a function of the rate of change in consumption and not of the level of consumption. In other words, the accelerator measures the changes in investment goods industries as a result of long-term changes in demand in consumption goods industries.

The idea underlying the accelerator is of a functional relationship between the demand for consumption goods and the demand for machines which make them. The acceleration coefficient is the ratio between induced investments to a given net change in consumption expenditures.

v =∆//∆C

Symbolically where v stands for acceleration coefficient; ∆I denotes the net changes in investment outlays; and ∆C denotes the net change in consumption outlays. Suppose an additional expenditure of Rs. 10 crores on consumption goods leads to an added investment of Rs. 20 crores in investment goods industries, then the accelerator is 2. The actual value of the accelerator can be one or even less than that.

In actual world, however, increased expenditures on consumption goods always lead to increased expenditures on capital goods. Hence acceleration coefficient is usually greater than zero. Where a good deal of capital equipment is needed per unit of output, the acceleration coefficient is very much more than unity.

In exceptional cases, the accelerator can be zero also. Sometimes it so happens that production of increased consumer goods (as a result of a rise in their demand) does not lead to an increase in the demand for capital equipment producing these goods.

The existing machinery also wears out on account of over use, with the result that the increased demand for consumer goods cannot be met. It actually happened in India and Turkey during the Second World War.

Additional investment funds were not available. In the absence of induced investment and acceleration effects, the increased demand for consumption levelled off and the accelerator, which measures the effects of induced investment (in investment goods industries) as a result of changes in consumption did not seem to work during all-these years.

The factual basis of the acceleration principle is the knowledge that fluctuations in output and employment in investment goods industries are greater than those in consumption goods industries. Accelerator has greater applicability to the industrial sector of the economy; and as such it seeks to analyse the problem as to why fluctuations in employment in the capital goods industries are more pronounced than those in the consumption goods industries.

There would be no acceleration effects in an economy which used no capital goods. But that situation is very rare. The more capitalized the methods of production are, the greater must be the value of accelerator.

The principle of acceleration is basically a concept related to net investment. Therefore, we must derive an expression linking the accelerator with net investment. We know that gross investment has two components: net investment plus replacement of capital wearing out due to depreciation. We can write

Gross Investment = Igt= V(Yt-Yt-1) +R

which means that the quantum of gross investment in period t depends upon the value of acceleration effects of the change in income in the previous period and the need for replacement of capital.

Inet =V(Yt-Yt1)

Thus, net investment in period t is which means that net investment depends only on the rate of change of income and the accelerator (V).

#### Multiplier and Accelerator Distinguished:

For a clear grasp of the concept of accelerator, it is useful to distinguish between multiplier and accelerator. Multiplier shows the effect of a change in investment on income and employment whereas accelerator shows the effects of a change in consumption on investment. In other words, in the case of multiplier, consumption is dependent upon investment, whereas in the case of accelerator investment is dependent upon consumption.

Further, multiplier depends upon the propensity to consume and accelerator depends upon durability of the machines. In other words, the former is dependent upon psychological factors, while the latter is dependent upon technological factors. However, even accelerator is psychological in its origin because it is linked to induced investment but it becomes highly technical on the operational plane. The accelerator shows the reaction (effect) of changes in consumption on investment and the multiplier shows the reaction of consumption to increased investment.

Further, another very important point of difference between the multiplier and accelerator is in their working backwards. Multiplier works as rigorously in the reduction of income as it does in its increase. But the working of the accelerator is restricted in the downward direction to the rate of replacement of capital because businessmen can at the most disinvest to the extent of not replacing the wearing-out capital.

### Working of the Accelerator:

It is interesting to analyse the working of the Principle of Acceleration.

Accelerator depends primarily upon two factors:

(i) The capital-output ratio, and

(ii) The durability of the capital equipment.

A numerical example will clarify the dependence of acceleration value on the durability of the machine, capital-output ratio being given.

The following table 11.1 is meant to make two things clear about the accelerator:

(i) Given the same percentage change in consumption, the percentage change in induced investment depends directly on the durability of the machine. Greater is the life (durability) of the machine, greater the value of the accelerator;

(ii) Accelerator does not depend upon the change in the absolute level of consumption; it depends upon the rate of change of consumption.

In Case I in the Table, we assume that we need 100 machines to produce 1000 consumer goods (capital-output ratio being 1:10). Further we presume that the life of the machine (durability) is 10 years. Thus, after 10 years, the machine has to be replaced and 10 machines have to be replaced in each period in order to maintain the flow of 1000 consumer goods. This is called ‘Replacement Demand.’

Now suppose there are 10% rise in the demand for consumer goods in period I (as shown in case I); the change in consumption will be of 100 such goods and we will need 110 machines to produce these goods (at the constant capital- output ratio of 1: 10). Thus, we need 20 machines in all, 10 machines being the addition to the stock of capital and 10 machines for replacement.

Thus, a 10% rise in the demand for consumer goods leads to a 100% rise in the demand for investment goods (machines). This is what the principle of acceleration is intended to show. Accelerator shows that a small increase in consumption is likely to result in manifold increase in investment (called induced investment).

Table 11.1

Value of the Accelerator Depends on the Durability of the Investment Goods and the Rate of Change of Consumption Expenditure

Assumptions: (i) Capital-output ratio 1: 10 for all the Cases.

Now in case II, where the life of the machine is 20 years, other things being the same, a rise in the demand for consumer goods in the first period leads to 200% increase in gross investment.

Further, in case III, when the life of machine is 5 years, a 10% rise in the demand for consumer goods results merely in an increase of 50% in gross investment. It is, therefore, clear that:

Greater the durability (life) of the machine, the greater the value of the accelerator and higher the acceleration effect; smaller the durability, lower the value of the accelerator and lower are the acceleration effects.

In case IV, where we presume the life of the machines to be 10 years and capital-output ratio constant at 1: 10 (i.e., we need 100 machines to produce 1000 goods), we find that a 10% rise in demand in period I in consumption goods sector leads to 100% increase in gross investment, whereas in period V, when the demand for consumer goods does not rise and remains constant at 1000, there is a decline of 50% in gross investment.

Thus, we find that, even when there is no decrease in the demand for consumer goods, there is likely to be a decline in gross investment. The case demonstrates the sensitivity of investment to a cessation of economic activity. It is to be noted that it is the falling off in the rate of increase in consumption and not a decline in the absolute level of consumption which causes the contraction in the demand for machines.

Further, in case V, presuming the life of the machine to be 10 years, we find that we need machines to produce 1000 consumer goods. But when there is a fall in the demand for consumer goods to the extent of 10% in period I, we need 90 machines to produce 900 consumer goods.

There is 100% fall in the net investment caused by 10% fall in consumption. If, however, the demand for consumer goods falls by 20%, we would need 20% less machines and correspondingly we can expect the rate of investment to fall by 200%. But there is a saving grace.

At the most what the producers can do is to produce no new machines at all, i.e., not to replace existing machines. They may allow some of the existing plants and equipment to wear out. Thus, when the economy is moving downwards, the fall in investment becomes confined to the demand for replacement and that can at the most fall to zero.

In other words, value of the accelerator during downward swing is limited by the inability of the demand for investment goods to fall below the value of replacement (depreciation) demand.

We can state this proposition as follows:

A decline in investment resulting from a decline in the demand for consumption goods cannot exceed the rate of depreciation. A decline in consumption which induces a decline in investment in excess of the depreciation figure simply gives rise to excess idle capacity.

Thus, the so-called ‘accelerator’ is a more complicated tool than the multiplier, for it depends upon the change in the rate of consumption, which, in turn, depends upon highly capricious investment in the short period at any rate. Therefore, as long as the basic conditions (technological and structural) favouring investment prevail, the acceleration principle serves as an indicator of the consumption-based inducement to invest.

### Importance and Limitations of the Accelerator:

The introduction of the Principle of Acceleration enables us to understand the process of income generation more clearly. No doubt, a certain level of income (or employment) could be attained by multiplier action alone. But along with accelerator the process of income propagation is speeded up. When accelerator and multiplier join hands, more violent fluctuations in income occur in upward and downward directions.

Firstly, this multiplier-accelerator interaction enables us to throw light on one of the most important features of business cycle. This feature is that the investment goods industries fluctuate more violently than the consumption-goods industries. It has helped us to show that small demand changes in consumption-goods industries lead to considerably enlarged changes in investment-goods industries.

Secondly, the multiplier-accelerator interaction has profoundly increased our understanding of business cycles. Prof. Hicks’ theory of the business cycle is based primarily on the principle of acceleration.

Further, Prof. R.F. Harrod has based his theory of Steady Growth on the acceleration principle. Harrod’s analysis of economic growth grew out of his analysis of business cycle as a dynamic economic phenomenon.

Despite its great theoretical importance, its qualifications indicate that attempts to apply very simplified models using the acceleration principle are likely to give misleading results. The presumptions of a fixed ratio of consumer to capital goods, of constant replacement demand, of no excess capacity, of permanent demand are lacking in realism. In other words, acceleration theory is valid only so long as all machines are in use (no excess capacity), overtime is excluded, the relation between production factors is not altered (unchanged technology), sufficient raw materials and labour are present and the entrepreneurs command the necessary financial means.

Since this is not the case generally, the simple concept of accelerator as we have studied it is of little significance. Many attempts to measure the accelerator have yielded little result. Entrepreneurs’ behaviour is to be explained through numerous other factors, especially future expectations play a particularly important part. More realistic assumptions would virtually lead to results significantly different from those obtained under simplifying assumptions.

### Conclusion:

The theory of accelerator is based upon the idea that income and the stock of capital goods increase in flexible proportion. This is not the case where fundamental changes in technology are changing both the capital-output ratio and durability of the machines. Economic growth, furthermore, is not only dependent on capital. The accelerator is not adequate to explain changes in aggregate investment.

Only under special circumstances and in the short run there is a proportional relationship between output and the stock of capital goods. The acceleration principle is less general in application than the multiplier; whereas the latter operates in both the forward and backward directions, the accelerator is effective only in the upward direction (in the downward direction it works only to the extent that replacement investment is not provided for).

Thus, it is clear that at least three basic conditions must operate for a ‘pure’ accelerator model:

(i) Existing capacity is fully utilised,

(ii) Finances are adequate to permit satisfaction of accelerator-generated demand,

(iii) The change in output is thought to be non-temporary.

Such requirements obviously limit the generality of the principle.