A competitive refining industry produces one unit of waste for each unit of refi

Question

A competitive refining industry produces one unit of waste for each unit of refined product. The industry disposes of the waste by releasing it into the atmosphere. The inverse demand curve for the refined product (which is also the marginal benefit curve) is Pd = 24 ? Q, where Q is the quantity consumed when the price consumers pay is Pd. The inverse supply curve (also the marginal private cost curve) for refining is M P C = 2 + Q where M P C is the marginal private cost when the industry produces Q units. The marginal external cost is MEC = 0.5Q where MEC is the marginal external cost when the industry releases Q units of waste. a. What are the equilibrium price and quantity for the refined product in an unregulated free market? b. How much of the chemical should the market supply at the social optimum? c. How large is the deadweight loss from the externality? d. Suppose the government imposes an emissions fee of $T per unit of emissions. How large should the emissions fee be if the market is to produce the economically efficient amount of the refined product?

Explanation / Answer

If there is no correction for the externality, the equilibrium will occur at the point where the marginal benefit curve,

P^D= 24-Q

intersects the marginal private cost curve,

MPC Q = +2 . This occurs at

24-Q=2+Q

Q =11

At Q =11, price is P =13.

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b) At the social optimum marginal benefit,

P^D=24- Q, will equal marginal social cost,

MSC= MPC+ MEC

This occurs where 2

24 –Q=(2+Q ) +0.5Q

Thus, the social optimum is to produce Q = 8.80 .

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c) At the uncorrected equilibrium, the marginal social cost is

MSC = 2 +1.5(11)= 18.5 .

Thus, the deadweight loss will be 0.5(11 -8.80)(18.5 -13) =6.05

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d) The emissions fee of $T should be set to shift the MPC curve so that it intersects the marginal benefit curve at Q = 8.80 , the socially optimal quantity.

At Q = 8.80 the marginal benefit is P =15.2 and the marginal private cost is MPC = + = 2 8.80 10.80 .

Therefore, the optimal tax is T =15.2- 10.8 =4.4

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