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### The principle of acceleration

The principle of acceleration is based on the fact that the demand for capital goods is derived from the demand for consumer goods which the former help to produce. The acceleration principle explains the process by which an increase (or decrease) in the demand for consumption goods leads to an increase (or decrease) in investment on capital goods.

According to Kurilara, “The accelerator coefficient is the ratio between induced investment and an initial change in consumption expenditure.”

Symbolically, v =∆I /∆C or ∆I = v ∆C where v is the accelerator coefficient, ∆I is net change in investment and ∆C is the net change in consumption expenditure. If the increase in consumption expenditure of Rs 10 crores leads to an increase in investment of Rs 30 crores, the accelerator coefficient is 3.

This version of the acceleration principle has been more broadly interpreted by Hicks as the ratio of induced investment to changes in output it calls forth. Thus the accelerator v is equal to ∆I/∆Y or the capital- output ratio. It depends on the relevant change in output (∆Y) and the change in investment (∆I). It shows that the demand for capital goods is not derived from consumer goods alone but from any direct demand of national output.

In an economy, the required stock of capital depends on the change in the demand for output. Any change in output will lead to a change in the capital stock. This change equals v times the change in output. Thus ∆ I=v∆ Y, where v is the accelerator. If a machine has a value of Rs 4 crores and produces output worth Rs 1 crore, then the value of v is 4. An entrepreneur who wishes to increase his output by Rs 1 crores every year must invest Rs 4 crores on this machine. This equally applies to an economy where if the value of the accelerator is greater than one, more capital is required per unit of output so that the increase in net investment is greater than the increase in output that causes it. Gross investment in the economy will equal replacement investment plus net investment.

Assuming replacement investment (i.e.,replacement demand for machines due to obsolescence and depreciation) to be constant, gross investment will vary with the level of investment corresponding to each level of output.

The acceleration principle can be expressed in the form of the following equation

where Igt is gross investment in period t, v is the accelerator, Yt is the national output in period t, Yt-1 is thenational output in the previousperiod (t—1), and R is the replacement investment.

The equation tells that gross investment during period t depends on the change in output (Y) from period t — 1 to period t multiplied by the accelerator (v) plus replacement investment R.

In order to arrive at net investment (In), R must be deducted from both sides of the equation so that net investment in period t is

If Yt > Yt-1 net investment is positive during period t. On the other hand, if Yt<Yt–1, net investment is negative or there is disinvestment in period t.

#### Operation of the Acceleration Principle

The working of the acceleration principle is explained in Table I.

The table traces changes in total output, capital stock, net investment and gross investment over ten time periods. Assuming the value of the acceleration v=4, the required capital stock in each period is 4 times the corresponding output of that period, as shown in column (3). The replacement investment is assumed to be equal to 10 per cent of the capital stock in period t, shown as 40 in each time period. Net investment in column (5) equals v times the change in output between one period and the preceding period. For example, net investment in period t+3=v(yt+3 – Yt+2), or 40=4(115—105). It means that given the accelerator of 4, the increase of 10 in the demand for final output leads to an increase of 40 in the demand for capital goods (machines). Accordingly the total demand for capital goods (machines) rises to 80 made up of 40 of replacement and 40 of net investment. Thus the table reveals that net investment depends on the change in total output, given the value of the accelerator. So long as the demand for final goods (output) rises net investment is positive. But when it falls net investment is negative. In the table, total output (column 2) increases at an increasing rate from period t+l to t+4 and so does net investment (column 5). Then it increases at a diminishing rate from period t+5 to t+6 and net investment declines from period t+7 to t+9, total output falls, and net investment becomes negative.

The acceleration principle is illustrated diagrammatically in Figure 1 where in the upper portion, total output curve Y increases at an increasing rate up to t+4 period, then at a decreasing rate up to period t+6. After this it starts diminishing. The curve In, in the lower part of the figure shows that the rising output leads to increased net investment upto t+4 period because output is increasing at an increasing rate. But when output increases at decreasing rate between t+4 and t+6 periods, net investment declines. When output starts declining in period t+7, net investment becomes negative. The curve Ig represents gross investment of the economy. Its behaviour is similar to the net investment curve. But there is one difference that gross investment is not negative and once it becomes zero in period t+8, the curve Ig again starts rising. This is because despitenet investment being negative, the replacement investment is taking place at a uniform rate.

#### Assumptions

The acceleration principle is based upon the following assumptions:

1. The acceleration principle assumes a constant capital-output ratio.

2. It assumes that resources are easily available.

3. It assumes that there is no excess or idle capacity in plants.4. It is assumed that the increased demand is permanent.

5. It also assumes that there is elastic supply of credit and capital. 6. It further assumes that an increase in output immediately leads to a rise in net investment.

#### Criticisms

The acceleration principle has been criticised by economists for its rigid assumptions which tend to limit its smooth working. The following are its limitations.

#### 1. Capital-Output Ratio not Constant.

The acceleration principle is based on a constant capital-output ratio. But this ratio does not remain constant in the modern dynamic world. Inventions and improvements in techniques of production are constantly taking place which lead to increase in output per unit of capital. Or, existing capital equipment may be worked more intensively. Moreover, change in the expectations of businessmen with regard to prices, wages, interest may affect future demand and vary the capital-output ratio. Thus the capital-output ratio does not remain constant but changes in the different phases of the trade cycle.

#### 2. Resources not Elastic

The acceleration principle assumes that the resources should be elastic so that they are employed in the capital goods industries to enable them to expand. This is possible when there is unemployment in the economy. But once the economy reaches the full employment level, the capital goods industries fail to expand due to the non-availability of sufficient resources. This limits the working of the acceleration principle. So this principle will not apply in a recession where excess capacity is found.

#### 3. Idle Capacity in Plants

The acceleration theory assumes that there is no unused (or idle) capacity in plants. But if some machines are not working to their full capacity and are lying idle, then an increase in the demand for consumer goods will not lead to the increased demand for new capital goods. In such a situation the acceleration principle will not work.

#### 4. Difference between Required and Real Capital Stock

It assumes no difference between required and real capital stock. Even if it exists, it ends in one period. But if industries are already producing capital goods at full capacity, it is not possible to end the difference in one period.

#### 5. Does not Explain Timing of Investment

The assumption of the existence of full capacity implies that increased demand for output immediately leads to induced investment. The acceleration principle, therefore, fails to explain the timing of investment. At best it explains the volume of investment. As a matter of fact, there may be a time lag before new investment can be generated. For instance, if the time lag is four years, the effect of new investment will not be felt in one year but in four years.

#### 6. Does not consider Availability and Cost of Capital Goods

The timing of the acquisition of capital goods depends on their availability and cost, and the availability and cost of financing them. The theory does not consider these factors.

#### 7. Acceleration Effect Zero for Installed Equipment

It is assumed that no increase in demand for consumer goods has been foreseen and provided for in previous capital investment. If by anticipating future demand, capital equipment has already been installed, it would not lead to induced investment and the acceleration effect will be zero.

#### 8. Does not Work for Temporary Demand

This theory further assumes that the increased demand is permanent. In case the demand for consumer goods is expected to be temporary, the producers will refrain from investing in new capital goods. Instead they may meet the increased demand by working the existing capital equipment more intensely. So the acceleration will not materialise.

#### 9. Supply of Credit not Elastic

The acceleration principle assumes an elastic supply of credit so that when there is induced investment as a result of induced consumption, cheap credit is easily available for investment in capital goods industries. If cheap credit is not available in sufficient quantities, the rate of interest will be high and investment in capital goods will be very low. Thus the acceleration will not work fully.

#### 10. Neglects Profits as a Source of Internal Funds

This assumption further implies that firms resort to external sources of finance for investment purposes. But empirical evidence has shown that firms prefer internal sources of finance to external sources. The acceleration principle is weak in that it neglects profits as a source of internal finance. As a matter of fact, the level of profits is a major determinant of investment.

#### 11. Neglects the Role of Expectations

The acceleration principle neglects the role of expectations in decision-making on the part of entrepreneurs. The investment decisions are not influenced by demand alone. They are also affected by future anticipations like stock market changes, political developments, international events, economic climate, etc.

#### 12. Neglects the Role of Technological Factors

The acceleration principle is weak in that it neglects the role of technological factors in investment. Technological changes may be either capital-saving or labour- saving. They may, therefore, reduce or increase the volume of investment. Further, as pointed out by Professor Knox, “capital equipment may be bulky and the employment of additional plant is justified only when output has risen considerably. This factor is all the more important because usually what is added is a complex of machines and not a machine.”

#### 13. Fails to Explain Lower Turning Point

According to Knox, the acceleration principle is not of much use for explaining lower turning point.

#### 14. Not Precise and Satisfactory

Again, Knox points out that the acceleration, principle is not precise and is unsatisfactory. It is, therefore, inadequate as theory of investment.

#### Conclusion

Despite these limitations, the principle of acceleration makes the process of income propagation clearer and more realistic than the multiplier theory. The multiplier shows the effect of a change in investment on income via consumption while the acceleration shows the effect of consumption or output on investment and income. Thus the acceleration explains volatile fluctuations in income and employment as a result of fluctuations in capital goods industries. But it can explain upper turning points better than lower turning points.