The market for wheat is characterized by the following inverse demand and supply equations:
P = 540 - 1.5Q
P = MC = 3Q
Where P is the price per metric ton of wheat and Q measures the daily quantity of wheat in metric tons. Because of fertilizer runoff, the external marginal cost is constant at $90 per metric ton of wheat. What is the socially optimal quantity of wheat?
A) 80 metric tons
B) 360 metric tons
C) 100 metric tons
D) 240 metric tons

Question

Quizplus · Accepted Answer

To find the socially optimal quantity, we need to account for the external marginal cost. The social marginal cost (SMC) is the sum of the private marginal cost (MC) and the external marginal cost. So, SMC = 3Q + 90. Set the inverse demand equal to SMC: 540 - 1.5Q = 3Q + 90. Solving this equation gives Q = 100 metric tons.

The Market for Wheat Is Characterized by the Following Inverse