Question

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).

Answer 1

(a)        MC = B2 + 2B3 Xi + 3B4 X2i

 

(b)        AVC = B2 + B3 Xi + B4 X2i

 

(c)        AC = B1 (1 / Xi) + B2 + B3 Xi + B4X2i

 

By way of an example based on actual numbers, the MC, AVC, and AC from Equation (5.33) are as follows:

 

MC = 63.4776 – 25.9230 Xi + 2.8188 X2i

AVC = 63.4776 – 12.9615 Xi + 0.9396 X2i

AC = 141.7667 (1 / Xi) + 63.4776 – 12.9615 Xi + 0.9396 X2i

 

 

(d)       The plot will show that they do indeed resemble the textbook U-shaped cost curves.