9.2 Suppose the production function for widgets is given by q kl $ 0:8k2 $ 0:2l 2 , where q represents the annual quantity

9.2 Suppose the production function for widgets is given by q ¼ kl $ 0:8k2 $ 0:2l 2

, where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input.

a. Suppose k ¼ 10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point?

b. Again assuming that k ¼ 10, graph the MPl curve. At what level of labor input does MPl ¼ 0?

c. Suppose capital inputs were increased to k ¼ 20. How would your answers to parts

(a) and

(b) change?

d. Does the widget production function exhibit constant, increasing, or decreasing returns to scale?