# Principle of Acceleration Coefficient

## Introduction

The principle of acceleration coefficient shows the relationship between the demand for consumer goods and the demand for capital goods i.e. capital investment. The relationship between the two was first stated by the American economics professor T.N. Carver in 1903. However, the term ‘acceleration principle’ was introduced in economics only in 1917 by J.M. Clark.

The principle states that the increase in demand for consumer goods leads to a rise in demand for capital goods i.e. the factors of production, that are essential in the production process. But, the proportion of demand for capital investment or the factors of production will be highly magnified in comparison to the proportion of demand in consumer goods.

For instance, when the demand for particular good increases in the market, the demand for factors of production, suppose machinery will increase at a higher rate than the demand for the product. According to Kurilara, “The accelerator coefficient is the ratio between induced investment and an initial change in consumption expenditure.”

Symbolically,

Where,

α= Accelerator coefficient;

ΔI= Net change in investment;

ΔC= Net change in Consumption expenditure

If the consumption expenditure increases by \$1o million leading to an increase in investment of \$30 million, the accelerator coefficient is 3.

The accelerator coefficient is usually greater than zero because the increase in expenditure of consumption goods will eventually lead to an increase in the capital goods requirement. In an economy, a unit of output requires a good deal of capital assets and equipment. This is the reason acceleration coefficient remains positive i.e. greater than unity.

Economists J.R. Hicks provided a broad interpretation of the coefficient as the ratio of induced investment to changes in output. So, the accelerator coefficient can be expressed as the capital-output ratio.

Symbolically,

Since, the demand for capital goods is not just affected by consumer demand, but also by national output demand, accelerator coefficient is dependent on the relevant change in output (ΔT) and change in investment (ΔI).

Subsequently, capital stock required is affected by the change in the requirement of total output in the economy, the change is expressed as

ΔI= α ΔY,

Where, α= Acceleration coefficient

For instance, if a factory machine is valued at \$ 3 million that produces output worth \$ 1 million, then we can calculate α as 3. This means that if a producer wants to produce an output of \$ 1 million each year, he should invest \$ 3 million on the factory machine.

Another thing to consider in the economy is a gross investment which is equal to the replacement investment (investment made to replace the obsolete machinery) plus net investment. Considering replacement investment to be constant, gross investment varies with the level of output.

The principle of acceleration can be expressed as

Igt= α (Yt – Yt – 1) + R

= α ΔYt + R

Where,

Igt= Gross Investment in period t;

Yt= National output in period t;

Yt – 1= National output in the previous period (t – 1);

R= Replacement Investment

When R is deducted from both side of the equation, net investment is obtained.

In= α (Yt – Yt – 1)

= α ΔYt

If, Yt > Yt – 1, net investment is positive in the period t

Yt < Yt – 1, dis-investment occurs in the period t

## Operation of Principle of Acceleration

Period in Years Total Output (Y) Capital Required Replacement Investment (R) Net Investment (In) Gross Investment (Ig)
(1) (2) (3) (4) (5) (6)
t 100 400 40 0 40
t + 1 100 400 40 0 40
t + 2 105 420 40 20 60
t + 3 115 460 40 40 80
t + 4 130 520 40 60 100
t + 5 140 560 40 40 80
t + 6 145 580 40 20 60
t + 7 140 560 40 -20 20
t + 8 130 520 40 -40 0
t + 9 125 600 40 -20 20

The table above shows the trend in output, capital stock, net investment, and gross investment over a period of ten years. Suppose α= 4, the capital requirement is four times the level of output in the period.

Replacement investment is considered to be 10% of capital stock, so, it is shown as 40 for each year. On the other hand, net investment is α times change in the level of output between the current year and previous year.

The table shows that net investment is dependent on the change in the level of output when the value of the accelerator is given. And, as long as the demand for output is increasing, net investment is progressive.

However, net investment declines and reaches negative if the demand for final goods and services decline. This is shown in the table.

## Assumptions of the Principle

The principle of acceleration coefficient is based on the assumptions that

1. Capital- output ratio is constant
2. Resources have ease of access
3. Demand for consumer goods continue to rise
4. Factors of production are efficiently utilized
5. Rise in final output immediately increases net investment
6. Capital and credit facilities are available in abundance

## Criticisms

Although the acceleration principle effectively explains the output-capital relation, it is not free of criticisms. Some of the limitations of the principle are:

### Inelasticity of resources

The principle assumes that resources are found in abundance. But this is only possible when the economy has some level of unemployment. But at full employment level, industries that produce capital goods are not able to expand the resources because of the insufficient availability of the resources.

### Varying capital-output ratio

The principle assumes capital-output ratio to be constant. However, in today’s modern dynamic economy, the ratio of capital and output change with the change in expectations of the investors and also due to various improvements in the methods of production.

### Ignorance of technological changes

Technological changes can bring about capital saving or labor saving in the economy. Depending on this, the volume of investment may differ. But this phenomenon is ignored by the acceleration principle.

### Idle capacity of factors of production

The principle of acceleration assumes that there are no idle machinery or equipment in the economy. But, if there is some machinery lying idle, then the increase in demand will not lead to investment, rather it leads to the utilization of the idle resources.

### Temporary demand is ignored

Increase in demand is sometimes temporary, but the principle assumes that demand is always permanent. So, in case of a temporary increase in demand, producers meet the demand by intense utilization of the existing resources rather than investing in new materials. So the acceleration will not materialize.

### Inelasticity of credit and capital supply

The principle assumes cheap credit availability during the time of collecting resources for the rise in the requirement of induced investment. If the credit facilities are not easily accessible, interest rates sore up. This results in less or no investment of capital goods and acceleration coefficient will not function.

### Internal sources of funds are ignored

Although the principle implies that firms are dependent on external sources for the required investment fund. But, in reality, firms are more dependent on the internal sources of financing such as the profit earned by the firm. Profits are one of the major determinants of investment that are ignored by the acceleration principle.

### Timing of investment is not explained

The acceleration principle assumes that an increase in demand has an immediate effect on the volume of investment. But it fails to consider the time frame between which the firms and investors need to generate enough amount for investment. So, the time lag before which a new investment can be made is not explained by the principle of acceleration coefficient.