The following cubic equation is a long-run production function for a firm:
Q = -0.002K3L3 + 6K2L2
Suppose the firm employs 10 units of capital.
i. What are the equations for the total product, average product, and marginal product of labour curves?
ii. At what level of labour usage does the marginal product of labour begin to diminish?
iii. Calculate the marginal product and average product of labour when 10 units of labour are being employed.
Now suppose the firm doubles capital usage to 20 units.
iv. What are the equations for the total product, average product, and marginal product of labour curves?
v. What happened to the marginal and average product of labour curves when capital usage increased from 10 to 20 units? Calculate the marginal and average products of labour for 10 units of labour now that capital usage is 20 units. Compare your answer to part iii. Did the increase in capital usage affect marginal and average product as you expected?