# Distinguish between Returns to a Variable Factor and Returns to Scale.

**Returns to a Variable Factor:**

As more and more of input is employed, all other inputs being held constant, normally marginal and average product increase upto a point. Thereafter, marginal product (MP) starts declining and this pulls down the average product also. Let us consider a case, where amount of capital is fixed and the quantity of labour is increased. Then initially MP_{L }will increase as the amount is increased and AP will also be pulled up. Total product increases at an increasing rate.

If the variable input, say, labour is further increased, MP stops increasing after a point. Therefore, the rate of increase of total product shows a tendency to fall. Ultimately MP turns negative and this causes a fall in total product itself.

**Returns to a Scale: **

When all factors are increased simultaneously and ultimately the production of output also changes. Concept of returns of returns to scale is associated with the tendency of production that is observed when the ratio between the factors is kept constant but the scale is expanded.

**When all the factors are increased in the conditions of constant techniques, three production possibilities arise:**

- Output increases in the same proportion as the increase in the amounts of the factors of production —Constant Returns to Scale.
- Output increases in a greater proportion as compared to the increase in the amounts of factors of production — Increasing Returns to Scale.
- Output increase in a smaller proportion as compared to the increase in the amounts of the factors of production — Decreasing Returns to Scale.

In the figure P_{1}, P_{2}, P_{3}….P_{10 }are isoquants. They show 10, 20, 30…, 100 units of output respectively. OS is the scale line which is cut by the isoquants

at unequal distances. Initially, the distance between two consecutive isoquants is small, it then becomes constant, and ultimately increases. It shows that in the first stage when the scale is expanded returns increase, in the second stage they become constant & in the third and last stage, they decrease. It can be seen that Oa > ab > bc > cd..

It means that to enable the firm to rise from isoquants P_{1 }to P_{2 }(so that production increases from 10 to 20 units), the amount of factors required is less than the amount ,required to produce the initial 10 units of output. This position seems to hold true till P_{4} representing increasing returns to scale. When the firm goes from curve P_{4} to P_{5 }to P_{6}, constant returns to scale are obtained as cd = de = ef on the scale line indicates this.

After this, the increasing distance between two consecutive isoquant is an indication that to obtain the same increase in output, factors will have to be increased at a higher and higher rate. On the scale line OS, fg < gh < hi < ij indicate this concept of decreasing returns to scale.