Suppose that the production function for DVDs is given by Q = KL2 − L3, where Q is the number of disks produced per year, K is machine-hours of capital, and L is man-hours of labor.
a) Suppose K = 600. Find the total product function and graph it over the range L = 0 to L = 500. Then sketch the graphs of the average and marginal product functions. At what level of labor L does the average product curve appear to reach its maximum? At what level does the marginal product curve appear to reach its maximum?
b) Replicate the analysis in (a) for the case in which K = 1200.
c) When either K = 600 or K = 1200, does the total product function have a region of increasing marginal returns?