Question

Given the production function
Q = A Kα Lβ Nγ
where Q is the rate of output and K, L, and N represent inputs of capital, labor and land, respectively, determine:
(a)The specific conditions under which returns to scale would be increasing, constant, and decreasing.
(b)The equation for the marginal product function for each input

Answer 1

1. If the functions such as the output increases with the same proportional change as all of the existing input then the return of scale is constant, when the output increases by a less proportional change of all the inputs it is called the decreasing rate of return and lastly when the output output increases with a higher proportion change than all the inputs, it is called the increasing rate of return.
2. Q = A Kα Lβ Nγ

hence the Marginal product function is $Marginal product= Total production/Total units$