The law of returns to scale is concerned with the scale of production. The scale of production of a firm is determined by the amount of factors units.
In the long run all factors are variable. The firm therefore can expand its production by using more of all inputs. When there is increase in the quantity of all factors in the long period, keeping the factor proportion constant, there is increase in the scale of production.
The concept of returns to scale explains the behavior of output when changes are made in the scale of production. Thus, the relationship between quantities of output and the scale of production in the long run when all inputs are increased in the same proportion, is called law of returns to scale. In case all inputs are increased in the same proportion and the scale of production is expanded, the effect on output may take three forms or stages, such as increasing, constant and diminishing returns to scale.
Suppose, a firm is increasing all its inputs by 10% at a time. As a result, total output will increase. In the first stage total output will increased by more than 10% (more than proportionate) to the increase in inputs. It is a case of increasing returns to scale. If increase in output is proportionate to the increase in inputs (10% in both the cases) in the second stage, it is a case of constant returns to scale. If increase in output is less than proportionate (less than 10%) to the increase in inputs, it is a case of diminishing returns to scale.