Suppose the Cobb-Douglas production function for a company is given by
z = 300x2/3y1/3
where x is the company's capital investment and y is the size of the labor force (in work-hours).
(a) Find the marginal productivity of x.
(b) If the current labor force is 729 work-hours, substitute y = 729 in your answer to part (a) and graph the result.
(c) Find the marginal productivity of y.
(d) If the current capital investment is $27,000, substitute x = 27,000 in your answer to part (c) and graph the result.
(e) Interpret the graphs in parts (b) and (d) with regard to what they say about the effects on productivity of an increased capital investment (part (b)) and of an increased labor force (part (d)).