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
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.