Suppose the production function for widgets is given by
q = KL- .8K2 - .IV,
where q represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labor input.
a. Suppose K- 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= 10, graph the MPL curve. At what level of labor input does MPL = 0?
c. Suppose capital inputs were increased to K - 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?