a. The marginal cost (MC) is the change in the TC for a unit change in output; that is, it is the rate of change of the TC with respect to output. (Technically, it is the derivative of the TC with respect to X, the output.) Derive this function from regression (5.32).
b. The average variable cost (AVC) is the total variable cost (TVC) divided by the total output. Derive the AVC function from regression (5.32).
c. The average cost (AC) of production is the TC of production divided by total output. For the function given in regression (5.32), derive the AC function.
d. Plot the various cost curves previously derived and confirm that they resemble the stylized textbook cost curves.
For Information: Refer to the cubic total cost (TC) function given in Eq. (5.32).