According to Cassels, there are three stages in the production process, when we vary one factor of production, the other factor remaining the same. In stage I, there is increasing average returns to the factor of production, i.e.d(q/l)/dl > 0

i.e. MPL > APL. In stage I, the average product is increasing and the marginal product is greater than the average product. If we refer to figure 4.3 we see that up to the point B on the TP curve, stage I exists. In stage I AP is increasing but MP is first increasing up to A and then decreasing. In stage II, the average product is decreasing and the marginal product is also decreasing, but marginal product is positive. This stage may be called the stage of decreasing returns. The portion of the total product curve between B and C represents this stage. In stage III, total product is diminishing and the marginal product is negative. This stage is called the stage of negative returns. The portion of the total product curve, which lies to the right of the point C, represents this stage.

Let us now discuss the rationale behind the operation of the three stages of production. In the beginning the quantity of the fixed factor of production (which is capital in our case) is abundant relative to the variable factor of production, i.e. labor. Therefore, when more and more units of the variable factor is used, the fixed factor is used more intensively and efficiently. This causes the production to increase at a rapid rate implying increasing AP and MP. But once the point A is reached where the variable factor is used at such a rate that ensures the efficient utilization of the fixed factor, any further increase in the variable factor will cause MP and AP to fall because the quantity of the fixed factor has now become limiting compared to the amount of the variable factor. Again in the stage III the quantity of the variable factor is so large compared to the fixed factor that the formed comes in each other’s way, thereby reducing the efficiency of the fixed factor, which results in a fall in the total product instead of rising. This is the reason behind the negativity of the marginal productivity in this stage. Comparing stage I and stage III, it can be said that, stage III is the mirror image of stage I.

Now the question, which immediately comes in our mind, is that, in which stage would the rational entrepreneur like to be? The answer is the rational entrepreneur will always like to operate in stage II of the production function. Let us analyze the reason behind this.

In stage I, MP and AP both are rising, and MP is more than AP. This has two implications:

  1. A given increase in the variable factor leads to a more than proportionate increase in the output.
  2. The entrepreneur is not making the best possible use of the fixed factor.

In this case the entrepreneur will employ more of the variable factor keeping the fixed factor constant, i.e. a particular portion of the fixed factor remains unutilized.

Considering the stage III we will see that the MP of the variable factor is negative and the TP is also decreasing. Hence the national entrepreneur will not operate in this stage.

However, if we consider stage II, we find that MP and AP are both falling and MP, though positive, is less than AP. Moreover, at this stage, there is less than proportionate change in output due to change in labor. Hence, at this stage the entrepreneur will employ the variable factor in such a manner that the utilization of the fixed factor is most efficient. So this is the stage in which the entrepreneur can use both of the available resources in an optional manner.

Possibility of operation

The law of variable proportions guides us about the possibility of operation. A rational producer will never choose first and third stage for its production he will always operate in the second stage, i.e. the stage of diminishing returns. The producer will not produce in the first and the third stages because in the first stage the fixed factor of production i.e. capital is underutilized and its marginal return is negative and in third stage the variable factor of production i.e. labor is over utilized and thus its marginal return becomes negative. In other words, the marginal return of fixed factor and variable factor is negative in first stage and third stage respective. It is the second stage where the return on both the fixed factors and variables though diminishing is positive. The producer will always produce in second stage.

Returns to Scale Meaning

In the run all factors are variable, hence the expansion of output may be achieved by varying all factor-inputs. When we change all factor-inputs in the same proportion, the scale of production is also changed. The study of the effect of change in the scale of production on the amount of output comes under the head of returns to scale.

Thus, the term returns to scale refers to the changes in output as all factor-inputs change by the same proportion in the long run.

Or, in other words, the law expressing the relations between varying scales of production and quantities of output is called returns to scale. In short, returns to scale refer to the effects of scale relationship.

Three Types

Now the question is at what rate the output will increase when all factor- inputs are varied in the same proportion. There can be three possibilities in this regard. The increase in output may be more than, equal to, or less than proportional to the increase in factor-inputs. Accordingly, returns to scale are also of three types-increasing returns to scale, constant returns to scale and diminishing returns to scale.

S.N. Returns to a Variable Factor Returns to Scale
1 Operates in the short run Operates in the long run.
2 Only the Quantities of factor are varied All factor-inputs are varied in the same proportion
3 Changes in the factor-ratio. No change in the factor-ratio
4 No change in the scale of production Changes in the scale of production.



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