Question

  

A steel producing firm has a demand function given as p=30-q.the cost function facing the firm is given as C=200+Q² This firm emit its waste into a river and it cost the fish farmers C=20+2.5Q² to clean the river.

required

Market competition equilibrium price and quantity

Socially efficient equilibrium price and quantity

Amount of corrective (pigovian) tax per unit

Answer 1

Demand function is p = 30 - Q and so MR = 30 - 2Q. Cost function is C = 200 + Q2 so MPC (Marginal private cost) = 2Q

This firm emit its waste into a river and it cost the fish farmers C=20+2.5Q2 to clean the river. Marginal external cost is MEC = 5Q. Marginal social cost MSC = MPC + MEC = 2Q + 5Q = 7Q

Market outcome has MR = MPC

30 - 2Q = 2Q

Qm = 7.50 and Pm = 30 - 7.5 = 22.50

Socially efficient outcome has MR = MSC

30 - 2Q = 7Q

Qe= 3.33, Pe = 30 - 3.33 = 26.67

Amount of corrective (pigovian) tax per unit = MEC = 5*3.33 = 16.65 per unit