Linear Homogeneous Production Function

We describe the production function as
Q = f (L, K)

Now if we increase the inputs L and k by n times, and the output also increase by n times then
 mQ = f (nL, nK)

if m = n, then this means that increase in output is proportion to the increase in the inputs. This indicates the law of constant returns. Such a production function is called linear homogeneous production function. Since, the power or degree of n in this case is 1, it is called linear production function of first degree.

If however m > n, then output increases more than proportionately to increase in input. This is called increasing returns. But when m < n, then increase in inputs leads to a less than proportional increase in output. This shows the law of Diminishing Returns.