Three Stages of Production and Laws of Returns to Scale

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Three Stages of Production

The short run production function under the law of variable proportions can be described by dividing it into three stages, as each is important from the standpoint of resource allocation for the firm.

 

 

 

Stage I

During this stage TP_L and AP_L are increasing.

The MP_L starts to decline however, remains greater than AP_L.

At the end of the stage, AP_L reaches at its maximum and equals to MP_L.

Thus, Stage-I begins form the origin and ends when AP_L and MP_L are equal (at point B in the figure AP_L = MP_L).

 

Stage first is also called the stage of increasing returns.

This stage appears in the short run production because of division of labour, increase in efficiency of variable factor, fuller utilization of fixed factor of production, etc.

 

Stage II

During the Stage-II, TP_L is increasing.

Both AP_L and MP_L are declining.

The MP_L is less than AP_L however the MP_L remains positive.

Thus, Stage-II is the stage of diminishing returns from both the marginal and average productivity points of view.

The stage starts when AP_L equals MP_L and ends when MP_L becomes zero or TP_L reaches at its maximum.

In figure Stage-II spreads in the ranges of uses of inputs between the point of AP_L = MP_L to point MP_L = 0.

In terms of the figure at point B, AP_L = MP_L and MP_L is zero at point C.

 

The rationale behind the stage is that the labour input is already sufficiently large.

In that case, if labour is still added, there will not be any chance of further specialization.

Over staffing or crowded labour brings the disadvantages of division of labour and reduces their productivity.

 

Stage III

During this stage, MP_L is negative; TP_L and AP_L are declining but remain positive.

In figure stage-III starts from point C where MP_L equals zero.

 

The stage occurs because of excessive utilization of fixed factor-capital, over load for management and disadvantages of division of labour and so on.

It is said that “too much cooks spoil the broth”. 

So, too much labour with scarce capital gives negative return.

 

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Stage of Operation of the Firm

As we discussed mainly three stages of law of the law of variable proportion, it is important to explain which stage is the appropriate stage of production?

The answer is very straight that production always occurs in stage II where diminishing return operates for a rational producer.

In stage I, there is increasing returns till the maximum AP.

There is further possibility to increase profit beyond this stage.

Thus, producer does not stop production in this stage.

In stage III there is negative returns.

Operation beyond the situation causes fall in output with increase in input which causes loss to the producer.

Therefore, production does not occur in this stage.

It means, production occurs only in stage II where producer maximizes profit.

 

 

Laws of Returns to Scale

Return to scale is the long run concept of production theory.

It is also known as the long-run production function.

In long run, all the factors of productions are variable.

The producer has sufficient time period to manage all the factors which were fixed in short run.

 

The long run production function can be written as:

Q = f(C, L, T)

Where:

Q = quantity output

C or K = capital input

L = labour input

Over the long run, all factors of productions are variable.

 

In the long-run all inputs are variable.

They can be varied in the same/equal proportion or in different proportions.

However, to simplify our analysis here, we assume that they are varied in fixed proportion throughout the production process.

 

The law is concerned with the question on how output responds to the change in all inputs together.

Suppose that all inputs were doubled: would output be doubled or not?

This is the question of the law of returns to scale.

In other words, the law of returns to scale states that if both inputs are to be varied in a fixed proportion, then the production functions shows three types of relationship in the long-run.

They are:

·         Increasing Returns to Scale (IRS)

·         Constant Returns to Scale (CRS)

·         Decreasing Returns to Scale (DRS)

 

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Increasing Returns to Scale (IRS)

If percentage change in output is more than the percentage change in inputs, then the production function exhibits increasing returns to scale.

In this scale, one percentage increase in all inputs leads to more than one percentage increase in output.

For example, if all inputs are increased by 10%, this would bring more than 10% increase (assume 15% increase) in output.

It can be explained with the help of the data given in table.

 

Increasing Returns to Scale

Units of Labour (L)	Units of Capital (C or K)	Total units of inputs	Total units of Output	Results
1L	1C	1L + 1C	200	Increasing Returns
2L	2C	2L + 2C	500
4L	4C	4L + 4C	1,200

 

As shown in the table, one unit of labour and one unit of capital can produce 200 units of output.

As both inputs i.e. L and C are increased by 100%, that is, they are made 2L and 2C then the corresponding total output is 500 units which is more than 100%.

So, output has increased by more than the percentage increase in inputs which exhibits increasing returns to scale.

 

During the scale, marginal productivity of inputs increases as scale increases.

 

Constant Returns to Scale (CRS)

If there is equal percentage change in inputs and output, then the production scale is known as constant returns to scale.

In this scale one percentage increase in inputs increases the output by exactly one percentage.

Over the scale marginal product remain constant.

 

For example, if all inputs are increased by 100% and output also increases exactly by 100%, it is constant returns to scale.

Over the scale marginal product remain constant.

It can be explained with the help of table.

Constant Returns to Scale

Units of Labour (L)	Units of Capital (C ort K)	Total units of inputs	Total units of Output	Results
1L	1C	1L + 1C	200	constant Returns
2L	2C	2L + 2C	400
4L	4C	4L + 4C	800

 

As shown in the table, one unit of labour and one unit of capital can produce 200 units of output.

As both inputs L and K are increased by 100%, that is, they are increased to 2L and 2C then the corresponding total output is 400 units.

It is increased by exactly 100%.

So, inputs and output has increased by the same percentage.

This tendency of increasing output equal to the change in inputs is called CRS in production.

 

Decreasing Returns to Scale (DRS)

If output changes by less than the proportionate change in inputs, then the production scale is known as decreasing returns to scale.

Here, one percentage increase in inputs leads less than one percentage increase in output.

In this scale, marginal productivity declines as scale increases.

 

For example,

If 100% increase in inputs leads less than 100% increase in output; this is decreasing returns to scale.

In this scale, marginal productivity declines as scale increases.

It is shown in table.

Decreasing Returns to Scale

Units of Labour (L)	Units of Capital (C or K)	Total units of inputs	Total units of Output	Results
1L	1C	1L + 1C	200	Decreasing Returns
2L	2C	2L + 2C	300
4L	4C	4L + 4C	5000

 

As shown in table, one unit of labour and one unit of capital can produce 200 units of output.

When both inputs L and C are increased by 100%, that is they are increased to 2L and 2C then the corresponding total output is 300 units.

It is increased by less than 100%.

So, output has increased by less than percentage increase in inputs.

Again,

As inputs are increased by 100%, that is when they are increased to 4L and 4C from the previous level of 2L and 2C, corresponding increase in output is by less than 100%, output increases to only 500 units from the previous level of 300.

This tendency of increasing output with change in inputs is called DRS in production.

 

All the three returns to scale are shown summarized in figure:

 

 

Thus in increasing returns to scale marginal product will be rising with the increase in inputs; it will remain constant under constant returns to scale and decline in the case of decreasing returns to scale.

 

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