1.Suppose the production function for widgets is given by

q = kl -0.8k²- 0.2l²,

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 maximum? How many widgets are produced at that point?

b.Again, assuming that k = 10, graph the MP_L curve. At what level of labor input does MP_L = 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?