Law of Variable Proportion (Short Run Production Analysis)
Law of Variable Proportions occupies an important place in economic theory. This law is also known as Law of Proportionality.
Keeping other factors fixed, the law explains the production function with one factor variable. In the short run when output of a commodity is sought to be increased, the law of variable proportions comes into operation.
Therefore, when the number of one factor is increased or decreased, while other factors are constant, the proportion between the factors is altered. For instance, there are two factors of production viz., land and labour.
“As the proportion of the factor in a combination of factors is increased after a point, first the marginal and then the average product of that factor will diminish.” Benham
“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
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.