The relation between output and variation in only one input

The relation between output and variation in only one input is return to scale returns to a factor continous

Solution

Returns to scale measures the change in output corresponding to a change in both inputs (not only one input).

Let a production function be Q = f(L, K) where Q: Output, L: Labor and K: capital employed to produce Q.

Let us increase both L and K by N time, such that new output is

Q* = f(NL, NK)

The returns to scalre are determined as follows:

If Q* / Q = N, then there is constant returns to scale (CRS).

If Q* / Q > N, then there is increasing returns to scale (IRS).

If Q* / Q < N, then there is decreasing returns to scale (DRS).