LAW OF VARIABLE PROPORTIONS

Reasons for stage 2 - Diminishing returns to a factor

(1) Fixity of the Factor: Fixity of the factor(s) is the principal cause behind the law of diminishing returns. As more and more units of the variable factor are combined with the fixed factor, the latter gets excessively utilised. It suffers greater wear & tear and loses its efficiency. Hence, the diminishing returns. (2) Imperfect Factor Substitutability: Factors of production are imperfect substitutes of each other. More and more of labour cannot be continuously used in place of capital. Accordingly, diminishing returns are bound to set in if only the variable factor is increased to increase output. (3) Poor Coordination between the Factors: Increasing application of the variable factor (along with the fixed factor) eventually disturbs the ideal factor ratio. This results in poor coordination between the fixed and variable factors. Hence, the diminishing returns.

Reasons for Stage 1 - Increasing returns to a factor

(1) Fuller Utilisation of the Fixed Factor: 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 remains underutilised) additional units of the variable factor add more and more to total output, or marginal product of the variable factor tends to increase. (2) Division of Labour and Increase in Efficiency: Additional application of the variable factor (Labour) enables process-based division of labour. Specialised workers may be used for different processes of production. This increases efficiency or productivity of the variable factor. Accordingly, marginal productivity tends to rise. (3) Better Coordination between the Factors: So long as fixed factor remains underutilised, additional application of the variable factor tends to improve the degree of coordination between the fixed and variable factors. As a result, marginal product (MP) increases and total product (TP) increases at the increasing rate.

Graphical illustration of the law of variable proportions

(i) 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 a factor. (ii) When MP is rising, TP tends to rise at an increasing rate. This occurs till point K on the TP curve. This corresponds to the situation of increasing returns to a factor. (iii) Beyond OL units of labour, MP tends to decline, and TP increases only at diminishing rate. This occurs between E and S on MP curve, and between K and T on TP curve. This corresponds to a situation of diminishing returns to a factor. (iv) When employment of labour exceeds OS units, MP becomes negative. Accordingly, TP starts declining. This is a situation of negative returns to a factor, occurring beyond point T on TP curve and beyond point S on MP curve.

Reasons for Stage 3 - Negative Returns to a Factor

1. Limitation of Fixed Factor: The negative returns to a factor apply because some factors of production are of fixed nature, which cannot be increased with increase in variable factor in the short run. 2. Poor Coordination between Variable and Fixed Factor: When variable factor becomes too excessive in relation to fixed factor, then they obstruct each other. It leads to poor coordination between variable and fixed factor. As a result, total output falls instead of rising and marginal product becomes negative. 3. Decrease in Efficiency of Variable Factor: With continuous increase in variable factor, the advantages of specialization and division of labour start diminishing. It results in inefficiencies of variable factor, which is another reason for the negative returns to eventually set in.

Law of variable proportions

A short period production law also called returns to a factor. It says that the marginal product rises with a rise in the employment of a factor (keeping other factors constant). But after reaching a certain level of employment, it starts falling.

Example of the law of variable proportions

Consider a situation when land is a fixed factor and labour is a variable factor, and the farmer is producing wheat. Since land is a fixed factor, he can produce more of wheat only by using more and more of labour. Every additional unit of labour employed on the given land will not yield the same amount of additional output of wheat. If MP of labour was to remain constant (no matter how much of labour is employed), 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 any food problem (or the problem of unemployment). The fact of the matter is that MP must eventually diminish. The logic is simple: always there is some ideal factor ratio (optimum factor ratio or most appropriate factor ratio). Once the ideal ratio is reached, any increase in L would mean excessive employment of the variable factor.

Stage 1 - Increasing returns to a factor

In the first phase, every additional variable factor adds more and more to the total output. It means TP increases at an increasing rate and MP of each variable factor rises. As seen in given schedule and diagram, one labour produces 10 units, while two labours produce 30 units. It implies, TP increases at increasing rate (till point 'Q') and MP rises till it reaches its maximum point 'P', which marks the end of first phase.

Stage 2 - Diminishing returns to a factor

In the second phase, every additional variable factor adds lesser and lesser amount of output. It means TP increases at a diminishing rate and MP falls with increase in variable factor. That is why this phase is known as diminishing returns to a factor. The second phase ends at point 'S', when MP is zero and TP is maximum (point 'M') at 52 units. 2nd phase is very crucial as a rational producer will always aim to produce in this phase because TP is maximum and MP of each variable factor is positive.

Stage 3 - Negative Returns to a Factor

In the third phase (starting from 6 units of labour), the employment of additional variable factor causes TP to decline. MP now becomes negative. Therefore, this phase is known as negative returns to a factor. In Fig 5.1, the third phase starts after point 'S' on MP curve and point 'M' on TP curve. MP of each variable factor is negative in the 3rd phase. So, no firm would deliberately choose to operate in this phase.

Reasons behind the law of variable proportions

Optimum ratio of factors reached. All factors are utilized optimally. Efficient use of factors achieved. All factors are efficiently used. More usage of factors will result in over-exploitation.

Postponement of the law

Postponement of the law of variable proportions (the situation of diminishing MP) is possible under two situations, as under: (i) When there is improvement in technology used in the process of production. So that greater output is achieved with the same inputs. (ii) When some substitute of the fixed factor is discovered. So that the constraint of the fixed factor is removed. However, such a situation is very rare, if not impossible.

Tabular illustration of the law of variable proportions

Table 1 shows that as more and more units of labour (Variable Factor) are used, MP (Marginal Product) tends to rise till 3 units of labour are employed. In this situation, TP (Total Product) increases at the increasing rate. This is a situation of increasing returns to the factor. But, with the application of 4th unit of labour, situation of diminishing returns sets in: MP starts decreasing and TP increases only at the decreasing rate.

Assumptions of the Law

The law of variable proportions is based on certain assumptions. These are as follows: (i) Ratio in which factors of production are combined can be changed. (ii) Units of the variable factor are homogeneous or equally efficient, and are increased one by one. Thus, the law of diminishing returns sets in not because latter units of the variable factors are less efficient than the former ones. It sets in because the ideal factor ratio is disturbed (iii) State of technology does not change.

Constant proportions

When all factors are changed in a fixed proportion. In the long run, all factors become variable. Both L and K are variable factors. Output is increased by increasing the application of both the factors.

Variable proportions

When one factor is a fixed factor and the other is a variable factor, production function may be specified as under: QX = f(L,_K) Here, QX= Output of Good-X. L = Labour, a variable factor. K = Capital, a fixed factor. In this type of production function, output can be increased only by increasing the application of L (the variable factor). The following equations illustrate this point further:

CAN MP EVER RISE?

Yes, MP of the variable factor can rise, but only in a situation when the fixed factor is not fully utilised. If ideally, 4 full time workers are needed to cultivate 2 hectares of land, MP L 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.

Can TP increase even when MP is decreasing?

Yes, TP increases even when MP is decreasing. Because MP is an addition to TP. When MP is decreasing, only an addition to TP is decreasing, not the TP as such. TP continues to increase, though at a diminishing rate. TP starts declining only when MP is negative.