Question

Suppose the marginal cost for water production in a small country is 20 + Q, and the demand for water is P = 80 – 2Q, where P is the dollar price and Q is the tons of water produced. Suppose the processing procedure generates pollution, which incurs damage to the environment described by a marginal function of MEC = Q. (The externality does not directly harm producers or consumers.)

A.) What quantity will the market tend to without any intervention?

B.) What price will the market tend to without any intervention?

C.) What is the socially optimal quantity?

D.) What is the socially optimal price?

E.) Does the competitive equilibrium incur any deadweight loss? If so, how much? If none, enter 0.

F.) If the government intends to impose a production tax to reach the socially optimal level of pollution, how much should the tax be? (how much per unit, assuming a constant per-unit tax: not total tax revenue)

Answer 1

A) Equilibrium Quantity without intervention:

Qd=Qs

20+Q=80-2Q

Q*=60/3=20

Equilibrium quantity=20

B) Equilibrium Price without intervention:

Equilibrium Price =20+20=$40

C) Socially optimal condition: At equilibrium,

MC+MEC=Demand

20+Q+Q=80-2Q

4Q=60

Q*=60/4=15

Socially optimal quantity= 15

D. Socially optimal Price= 80-2*15= $50

E) No, competitive equilibrium doesn't incure any deadweight loss. As the efficient equilibrium Quantity is achieved.

F) Tax=MEC=Q=$15 per unit