Question

Consider a manufactured good whose production process generates pollution. The annual demand for the good is given by Qd = 100 − 3P. The annual market supply is given by Qs =P. In both equations, P is the price in dollars per unit. For every unit of output produced, the industry emits one unit of pollution. The marginal damage from each unit of pollution is given by 2Q.

Find the socially optimal quantity of the good. What is the socially optimal market Price?

Answer 1

Demand = Qd = 100 - 3P

Supply, Qs = P

Marginal damage per unit = P = 2Q

Without damage, output will be produced when Demand = Supply

100 - 3P = P

Q = 25

P = 25

If there is marginal damage per unit, social cost would rise and become more than private cost and reduce the output produced,

100 - 3P = 0.5P

P = 28.57

Q = 14.28

Thus at socially optimum equilibrium level, less output is produced and more price is charged.