Law of Variable Proportion

The law of variable proportion states that as more and more units of variable factors are applied to the given quantity of a fixed factor, the total product may increase at an increasing rate initially, but eventually it will increase at a diminishing rate.

Explaining the above law by taking an example:

A farmer is producing wheat, he has land as a fixed factor and labour as a variable factor.

Since land is a fixed factor, he can produce more of wheat only by using more and more of labour.

Will every additional unit of labour employed on the given land yield the same amount of additional output of wheat?

No, it can never happen. If MP (marginal product/additional output) of labour was to remain constant, then a country like India would have produced more and more of wheat using more and more of labour on the same piece of land. It would have never faced the problem of food.

So MP eventually dimnish.This is due to the fact that, there is some ideal ratio of factors of production.

If L (labour) and K (capital) are the two factors and K is constant than ideal ratio is struck by varying the use of L.

If ideally, 4 full time workers are needed to cultivate 2 hectares of land, MP_L (marginal product of labour) may increase when initially less than 4 workers are employed.

MP should be maximum when 4 workers are employed, and must start diminishing when more than 4 workers are employed.

If the number is increases further, we reach a point when another additional unit of labour adds nothing to total output i.e. MP = 0. MP may even become negative.

Tabular explanation of the Law.

Units of Land	Units of Labour	Total Product	Marginal Product
1 1 1	1 2 3	2 5 9	2 3 4	Increasing MP Implying increasing returns to a factor
1 1 1	4 5 6	12 14 15	3 2 1	Diminishing MP Implying Diminishing returns to a factor
1 1	7 8	15 14	0 -1	Negative MP Implying Negative returns to a factor

The table above shows that:

1) As more and more units of labour (variable factor) are used, MP (marginal product) tends to rise till 3 units of labour are employed and TP(total product) increases at the increasing rate.

This is a situation of increasing returns to the factors.

2) With the application of 4^th unit of labour, MP starts decreasing and TP increases only at the decreasing rate.

This is a situation of decreasing returns to the factors.

3) Diminishing MP reduces to zero. Total output is maximum (15), when marginal output is zero.

4) Eventually, MP may be negative. TP starts declining (from 15 to 14) when 8^th unit of labour is employed. This is a situation of negative returns to the factors.

Diagrammatic explanation of the Law.

Law of Variable Proportion

1) MP tends to rise till OL units of labour are used.

This corresponds to point E on the MP curve.This is a situation of increasing returns to the factors.

When MP is rising, TP tends to rise at an increasing rate.

This occurs till point K (point of inflexion- It is the point from where slope of TP changes.

Up to this point, TP has been increasing at increasing rate but after this point TP increases at diminishing rate) on the TP curve.

This is a situation of increasing returns to the factors.

2) Beyond OL units of labour, MP tends to decline, and TP increases at diminishing rate.

This occurs between point E and S on MP curve and between K and T on TP curve.

This is a situation of decreasing returns to the factors.

3) When employment of labour exceeds OS units, MP becomes negative.

Accordingly TP starts declining.

This is a situation of negative returns to the factors, occurring  beyond point T on TP curve and beyond point S on MP curve.

Causes Of Increasing returns:

1) Fuller utilisation of Fixed Factors : In the initial stages, fixed factor(such as machine) remains underutilised.Its fuller utilisation calls for greater application of the variable factor(labour).

Hence, initially(so long as fixed factor remain underutilised) additional units of the variable factors add more and more to total output, or marginal product of the variable factor tends to increase.

2) Increased efficency of the variable factor : Additional application of the variable factor(labour) causes process based division of labour  that raises efficency of the factor.

Accordingly, marginal productivity of the factor tends to rise.

3) Better coordination between the factors : So long as fixed factor remains underuttilised, additional application of the variable factor tends to improve the degree of coordination between the fixed and variable factors.As a result, total output increases at the increasing rate.

Causes Of Dimnishing returns:

1) Fixity of the factor : As more and more units of variable factor is combined with the fixed factor, the latter gets excessively utilised.

It suffers greater wear and tear and loses its efficency.Hence, dimnishing returns.

2) Imperfect factor substitutability : factors of production are imperfect substitute of each other. More and more of labourcannot be continiously be used in place of additional capital, hence dimnishing returns.

3) Poor coordination between the factors : Continuous increasing application of the variable factor along with fixed factor beyond a point crosses the limit of ideal factor ratio.

This result in poor coordination between the fixed and variable factors. Hence, dimnishing returns.

Causes Of Negative returns:

1) Overcrowding : If we keep on adding variable factor with the given quantiy of a fixed factor, this will lead to overcrowding on the fixed factor(excessive variable factor on the given quantity of fixed factor). There will be lower availability of tools and equipment per worker. Productivity will fall.

2) Management Problem : Use too much of variable factor creates the problem of effective management, it will become difficult to manage them, leading to decrease in efficency.