Question

Suppose the production function for widgets is given by:

Q = KL - 0.8K2 - 0.2L2

where Q represents the quantity of widgets produced, K represents the annual capital input and L represents annual labor input.

(a) For K = 10, graph the total and average productivity of labor curves.

(b) At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point?

(c) Again assuming that K = 10, graph the MP₁ curve. At what level of labor input does MP_{1 =} 0?

(d) Suppose capital inputs were increased to k=20.How would your answer to parts (a) and (b) change?

(e) Does the widget production function exhibit constant, increasing or decreasing returns to scale?