•The law of variable proportions arises because factor proportions change, as long as one factor is held constant and the other is increased.

•Example: we increase the number of labour without increasing the size of the land mass

•Both factors, however, can change in the long run.

•Returns to scale means the quantitative change in output of a firm or industry resulting from a proportionate increase in all inputs.

•One situation is when both factors are increased by the same proportion.

•When a proportional increase in all inputs results in an increase in output by the same proportion, the production function is said to display Constant returns to scale (CRS).

•When a proportional increase in all inputs results in an increase in output by a larger proportion, the production function is said to display Increasing Returns to Scale (IRS).

•Such economies of scale may occur because greater efficiency is obtained as the firm moves from small- to large-scale operations.

•When a proportional increase in all inputs results in an increase in output by a smaller proportion, it indicates Decreasing Returns to Scale (DRS).

•Decreasing returns to scale occur if the production process becomes less efficient as production is expanded, as when a firm becomes too large to be managed effectively as a single unit

•If in a production process, all inputs get doubled. As a result,

•If the output gets doubled, the production function exhibits CRS.

•If output is less than doubled, then DRS holds,

•and if it is more than doubled, then IRS holds.

•Consider a production function *q *= *f *(*x*1*, x*2)

•where the firm produces *q *amount of output using *x*1 amount of factor 1 and *x*2 amount of factor 2.

•Now suppose the firm decides to increase the employment level of both the factors *t *(*t > *1) times.

•Mathematically, the production function exhibits

•**constant returns to scale (CRS) **if we have,

•*f *(*tx*1*, tx*2) = *t.f *(*x*1*, x*2)

•**increasing returns to scale (IRS) **if, *f *(*tx*1*, tx*2) *> t.f *(*x*1*, x*2)*. *

•**decreasing returns to scale (DRS) **if, *f *(*tx*1*, tx*2) *< t.f *(*x*1*, x*2)*.*

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