Question

Part I Suppose that in the market for paper, demand is P=100 - Q. The marginal private cost of producing paper is 10+ Q. However, pollution generated by the production process creates a per unit external harm (i.e., negative externality) equal to 0.5Q (i.e., the level of the externality increases with the quantity produced). 16+1,5 Q (Social cret) 10+Q (private 0 36 45 Top a) What is the (unregulated) market equilibrium and quantity if the externality is not corrected for in this market? b) What is the socially optimal quantity of paper that should be produced? c) Suppose that the government wants to achieve the socially optimal quantity by taxing producers. What should the tax per unit of paper be? (Hint: see the graph below. Be reminded that the tax on producers will cause a parallel shift in the supply curve by the amount of tax. The government can impose a tax so that after tax market equilibrium coincides with the equilibrium you obtained in part (b). To obtain the vertical difference between the new and old private cost curves, notice that the value of the new private cost with tax at Q = 36 is 64. The value of the old private cost at Q = 36 is 46 (Plug Q = 36 into the original private cost function; P= 10 + (36) = 46).

Answer 1

Past I

a. If externality is not corrected market equilibrium occurs where Demand is equal to marginal private cost.

100-Q=10+Q

Q=90÷2= 45

Equilibrium Quantity= 45

Equilibrium price= 10+45=55

b. Socially optimal quantity is produced where demand curve meets marginal social cost.

100-Q=10+Q+0.5Q

Q=90/2.5=36

Socially optimal quantity= Q*=36

C. Tax should be equal to the vertical distance between the marginal private cost and marginal social cost.

At Q =36,

Marginal private cost= 10+36= 46

Marginal social cost= 10+1.5*36= 64

Tax= $64-$46= $18 per unit.