Which of the following conditions must hold to ensure that profits are, in fact, at a maximum? A) d(MC(Q))/dQ 0 B) d(MC(Q))/dQ

Question

Which of the following conditions must hold to ensure that profits are, in fact, at a maximum? A) d(MC(Q))/dQ > 0 B) d(MC(Q))/dQ < 0 C) d²π(Q)/dQ² < 0 D) d(MC(Q))/dQ > 0 and d²π(Q)/dQ² < 0

Quizplus · Accepted Answer

Maximum profits occur when the marginal cost is equal to marginal revenue, which means d(MC(Q))/dQ = 0. However, since profits are maximized when marginal revenue exceeds marginal cost, we need d(MC(Q))/dQ < MR, which also implies d(MC(Q))/dQ > 0. Moreover, to ensure that profits are indeed at a maximum, we need the second derivative of profits to be negative, or d2π/dQ2 < 0. This condition can be expressed as d²π(Q)/dQ² < 0, where S1 is the demand curve, U1 is the inverse supply curve , P12 is the price level, and P0 is the fixed cost. Therefore, the correct answer is D.

Which of the Following Conditions Must Hold to Ensure That