Law of Variable Proportion (Short Run Production Analysis)

Law of Variable Proportion, also known as the Law of Diminishing Marginal Returns, describes the relationship between inputs and output in the short run when one factor of production is varied while others are kept constant. As the quantity of the variable input (e.g., labor) increases, the total output initially rises at an increasing rate, then at a diminishing rate, and eventually may decline.

This law operates in three stages:

1. Increasing Returns: Adding more of the variable factor leads to a more than proportionate increase in output due to better utilization of fixed resources.

2. Diminishing Returns: Output increases but at a decreasing rate, as the fixed factors become overutilized.

3. Negative Returns: Adding more of the variable input may result in a fall in total output, as overcrowding or inefficiency sets in.

Assumptions

Law of variable proportions is based on following 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.

Short Run Production Analysis

The short run is a period of time in which at least one input used for production and under the control of the producer is variable and at least one input is fixed.

That is, in the short run, the output quantity can be increased (or decreased) by increasing (or decreasing) the quantities used of only the variable inputs. This functional relationship (of dependence) between the variable input quantities and the output quantity is called the short run production function.

We have to remember here, of course, that in the short-run, the firm uses a particular combination of fixed inputs, and its short-run production function is obtained in respect of that combination.

Therefore, in this case, the firm’s short-run production function may be written as:

q = f(x, y̅)        

The short run production function is one in which at least is one factor of production is thought to be fixed in supply, i.e. it cannot be increased or decreased, and the rest of the factors are variable in nature.

In general, the firm’s capital inputs are assumed as fixed, and the production level can be changed by changing the quantity of other inputs such as labour, raw material, capital and so on. Therefore, it is quite difficult for the firm to change the capital equipment, to increase the output produced, among all factors of production.

In such circumstances, the law of variable proportion or laws of returns to variable input operates, which states the consequences when extra units of a variable input are combined with a fixed input. In short run, increasing returns are due to the indivisibility of factors and specialisation, whereas diminishing returns is due to the perfect elasticity of substitution of factors.

Significance of the three Stages:

The three stages of the Law of Variable Proportion hold important significance in understanding production efficiency and decision-making for businesses:

1. Increasing Returns (Stage 1):

• Significance: This stage highlights the underutilization of fixed factors. As more of the variable input (like labor) is employed, output increases at an accelerating rate, improving efficiency. Businesses benefit from economies of scale in this phase, as each additional unit of input generates higher returns.

• Application: Firms are encouraged to increase the variable input to fully utilize fixed resources.

2. Diminishing Returns (Stage 2):

• Significance: Output continues to grow but at a decreasing rate. This stage indicates that the optimal use of fixed factors is approaching. Firms experience diminishing marginal returns as the efficiency of adding more variable inputs decreases.

• Application: Businesses must be cautious in adding further inputs and aim to operate in this stage, where resources are optimally utilized.

3. Negative Returns (Stage 3):

• Significance: In this stage, adding more of the variable input decreases total output due to overutilization or inefficiency. It signals that fixed resources are being overburdened, and additional inputs lead to disorganization or wastage.

• Application: Firms should avoid this stage, as it leads to inefficiency and reduced productivity.

Example:

Law of Variable Proportion with an example of a production process, such as a small bakery increasing the number of workers (labor) while keeping the size of the bakery (capital) constant.

Explanation:

• Stage 1 (Increasing Returns): From 1 to 2 workers, the total output increases significantly, with each additional worker producing more cakes than the previous one.

• Stage 2 (Diminishing Returns): From 3 to 6 workers, the total output continues to grow, but at a decreasing rate. Each additional worker contributes fewer cakes than the previous one.

• Stage 3 (Negative Returns): By the 7th worker, total output falls, meaning the extra worker reduces overall productivity due to overcrowding or inefficiency.