Law of Proportionality

 Law of Variable Proportions occupies an important place in economic theory. This law is also known as the Law of Proportionality.

“An increase in some inputs relative to other fixed inputs will in a given state of technology cause output to increase, but after a point the extra output resulting from the same additions of extra inputs will become less and less.” Samuelson

Assumptions:

(i) Constant Technology: The state of technology is assumed to be given and constant. If there is an improvement in technology the production function will move upward.

(ii) Factor Proportions are Variable: The law assumes that factor proportions are variable. If factors of production are to be combined in a fixed proportion, the law has no validity.

(iii) Homogeneous Factor Units: The units of variable factor are homogeneous. Each unit is identical in quality and amount with every other unit.

(iv) Short-Run: The law operates in the short-run when it is not possible to vary all factor inputs.

Explanation of the Law:

By keeping land as a fixed factor, the production of variable factor i.e., labour can be shown with the help of the following table:

From the table, it is clear that there are three stages of the law of variable proportion. In the first stage average production increases as there are more and more doses of labour and capital employed with fixed factors (land). We see that total product, average product, and marginal product increases but the average product and marginal product increases up to 40 units. Later on, both start decreasing because the proportion of

workers to land was sufficient and the land is not properly used. This is the end of the first stage.

The second stage starts from where the first stage ends or where AP=MP. In this stage, the average product and marginal product start falling. We should note that marginal product falls at a faster rate than

the average product. Here, the total product increases at a diminishing rate. It is also maximum at 70 units of labour where the marginal product becomes zero while the average product is never zero or negative.

The third stage begins where the second stage ends. This starts from the 8th unit. Here, marginal product

is negative and total product falls but average product is still positive. At this stage, any additional dose leads to positive nuisance because additional dose leads to negative marginal product.

Graphic Presentation:

In the figure, on the OX axis, we have measured the number of labourers while the quantity of product is shown on the OY axis. TP is the total product curve. Up to point ‘E’, the total product is increasing at an increasing rate. Between points E and G it is increasing at the decreasing rate. Here marginal product has started falling. At point ‘G’ i.e., when 7 units of labourers are employed, the total product is maximum while, marginal product is zero. Thereafter, it begins to diminish correspondingly to the negative marginal product. In the lower part of the figure, MP is the marginal product curve. Up to point ‘H’ marginal product increases. At point ‘H’, i.e., when 3 units of labourers are employed, it is maximum. After that, the marginal product begins to decrease. Before point ‘I’ marginal product becomes zero at point C and it turns negative. AP curve represents the average product.

Before point ‘I’, the average product is less than the marginal product. At point ‘I’ average product is maximum. Up to point T, the average product increases but after that, it starts to diminish.

Three Stages of the Law:

1. First Stage: The first stage starts from point ‘O’ and ends up to point F. At point F average product is maximum and is equal to the marginal product. In this stage, the total product increases initially at an increasing rate up to point E. between ‘E’ and ‘F’ it increases at a diminishing rate. Similarly, the marginal product also increases initially and reaches its maximum at point ‘H’. Later on, it begins to diminish and becomes equal to the average product at point T. In this stage, the marginal product exceeds the average product             (MP > AP).

2. Second Stage: It begins from point F. In this stage, the total product increases at a diminishing rate and is at its maximum at point ‘G’ correspondingly marginal product diminishes rapidly and becomes ‘zero’ at point ‘C’. Average product is maximum at point ‘I’ and thereafter it begins to decrease. In this stage, marginal product is less than the average product (MP < AP).

3. Third Stage: This stage begins beyond point ‘G’. Here total product starts diminishing. The average product also declines. The marginal product turns negative. Law of diminishing returns firmly manifests itself. In this stage, no firm will produce anything. This happens because the marginal product of labour becomes negative. The employer will suffer losses by employing more units of labourers. However, of the three stages, a firm will like to produce up to any given point in the second stage only.