Consider a competitive industry that extracts a valuable min

Consider a competitive industry that extracts a valuable mineral from deep underground. The industry faces market demand for the mineral given by P 200-2Q and extraction incurs a constant marginal private cost and average cost of 20. Suppose that the government realizes that by g minerals the industry is seriously harming and contaminating underground aquifers. The marginal external cost imposed by the activity is equal to E 3Q. What is the Pigouvian tax imposed on firms that pushes the industry to produce at the socially efficient level of output? 0 20 36 90 108 540

Solution

Option (4).

Output is socially optimal and efficient when Price = Private marginal cost + MEC

200 - 2Q = 20 + 3Q

5Q = 180

Q = 36

When Q = 36,

Pigouvian tax = MEC = 3Q = 3 x 36 = 108