# Acceleration principle (1917)

Formulated by American economist John Maurice Clark (1884-1963), acceleration principle is one of the basic pillars of modern macroeconomic theory and is an important tool in understanding the development of business cycles.

The acceleration principle links investment to output, each level of which needs a specific amount of capital. If output (and the amount of machinery required to make it) is expected to rise, the amount of capital within an economy must be increased. The accelerator equation is:

I = Α Δ t

where I is net investment in year t, alfa is the accelerator coefficient and delta t is the annual change in income.

The acceleration principle has been proposed as a theory of investment demand as well as a theory determining the supply of capital goods. When combined with the multiplier, it has played a very important role in models of the business cycle as well as in growth models of the Harrod-Domar type. The acceleration principle has been used to explain investment in capital equipment, the production of durable consumer goods and investment in inventories (or stocks). In general, it has been used to explain aggregate investment, although it is sometimes used to explain investment by firms (micro-investment behaviour). The main idea underlying the acceleration principle is that the demand for capital goods is a derived demand and that changes in the demand for output lead to changes in the demand for capital stock and, hence, lead to investment. Its distinctive feature, then, is its emphasis on the role of (expected) demand and its de-emphasis on relative prices of inputs or interest rates.
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 AC 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 ∆l/∆Y or the capital- output ratio.

It depends on the relevant change in output (∆T) 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:

Igt = v (Yt – Yt-1) + R

= v ∆Yt + R

where Igt is gross investment in period t, v is the accelerator, Yt is the national output in period t, Yt-1 is the national output in the previous period (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)t R must be deducted from both sides of the equation so that net investment in period t is

Im = v (Yt-Yt-1)

= v ∆Yt

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.

Operation of the Acceleration Principle: v = 4

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 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 despite net investment being negative, the replacement investment is taking place at a uniform rate.

Also see: business cycle, Harrod-Domar growth model, trade cycle

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