Suppose the production function for widgets is given by:
Q = KL - 0.8K^2 - 0.2L^2
where Q represents the quantity of widgets produced, K represents the annual capital input and L represents annual labor input.
(a) For K = 10, what is the average productivity of labor equal to?
-do i substitute k=10 into Q, and then what do i do to find the average productivity of labor?
(b) At what level of labor input does this average productivity reach a maximum? How many widgets are produced at this point?
(c) Again assuming that K = 10, what is the marginal product of labor equal to?