Question: The production function is \(Q={{K}^{3/4}}{{L}^{1/4}}\)

a. Calculate the average product of labor, \(APL\) when K is fixed at 16 units and \(L=16\). How does \(APL\) when L = 81.

b. Find an expression for the marginal product of labor \(MPL\) when K = 16. Then illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor 16 and 81 units of labor.

c. K=16 output price =$100.00 per unit, w=25.00. How many units of labor should the firm hire in order to maximize profits?