The law of returns to scale is concerned with the study of production function (i.e., input- output relationship) in the long run (when all inputs are variable). Thus, long run production theory or the law of returns to scale studies the behaviour of output in response to changes in scale.
A change in scale means that all inputs or factors are varied in the same proportion, keeping the factor proportions constant. When the quantities of all factors are changed along a particular scale, size of the firm and scale of output will change. The responsiveness of output to such changes in inputs is called returns to scale. Technology is assumed to remain constant.
When a producer increases all the inputs in a given proportion, there are three possibilities, viz., total output may increase more than proportionately, just proportionately or less than proportionately, which occur in that order.
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The law of returns to scale can be explained more precisely through the production function. Production function involving two variable inputs, say, capital (K) and labour (L) can be expressed as Q = f (K, L). Here, ‘Q’ denotes the quantity of commodity produced. Suppose, both ‘K’ and ‘L’ are increased in proportion ‘m’ and the total output increases in proportion ‘n’. The new production function is
nQ= f(mK,mL)
The proportion V may be equalled to, greater than or less than ‘m’. Accordingly, three stages of the law of returns to scale follow:
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(i) If n > m, i.e., increase in the total output is greater than the proportional increase in the inputs, it means that a situation of increasing returns to scale exists. Thus, if inputs are doubled, then the total output is more than doubled. The technology used is such that the requirement of real resources per unit of output tends to decrease. Here,
(ii) If n = m, i.e., increase in the total output is proportional to the increase in inputs, it means that a situation of constant returns to scale exists. To take an example, if all inputs are doubled, then total output is also doubled. In this case,
(iii) If n < m, i.e., increase in the total output is less than the proportional increases in inputs, it means that a situation of diminishing returns to scale exists. For example, if all inputs are doubled, then the total output is less than doubled.