Question

A total cost function has been estimated and is TC = 100 + 15Q1 + .5Q12 + 20Q2 + .1Q22 + .25*PL. If Q1 = 10 and Q2 = 20, what is the marginal cost of production for Q1?

Answer 1

Marginal cost = MC

This is the derivative of TC with respect to Q1.

TC = 100 + 15Q1 + .5Q12 + 20Q2 + .1Q22 + .25*PL

Hence,

MC of Q1 = (d/dQ1) (100 + 15Q1 + .5Q12 + 20Q2 + .1Q22 + .25*PL)

                  = 0 + 15 + (0.5 × 2) Q1 + 0 + 0 + 0

                  = 15 + Q1

Since the value of Q1 is 10,

MC of Q1 = 15 + 10

                = 25 (Answer)

Note: the value of Q2 is not required here, since Q2 is already omitted through the derivative.