There is a specific relationship between the marginal product of labor and the average product of labor. For the following parts of this question, use the following general function: TP=Q= f(K,L). Assume a short-run time frame. Using any other production function, other than the general function will not be accepted.
a. What are the average product and marginal product of labor curves associated with the general production function specified above? Show the two curves on the same diagram.
b. Show mathematically that the marginal product of labor curve intersects the maximum point of the average product of labor curve.
c. Demonstrate mathematically that the maximum point of the average product of labor curve falls on the downward sloping portion of the marginal product of labor curve.