Consider a city dealing with a severe ozone problem. Ozone levels are initially

Question

Consider a city dealing with a severe ozone problem. Ozone levels are initially uncontrolled and there are 100 units of ozone in the atmosphere. The ozone results from emissions at 2 sources, each of which is responsible for 50 units. Source 1 can abate its emissions at a marginal cost given by MCA1=2Q1, where Q1 is the amount of abatement by Source 1. Source 2’s marginal cost of abatement is MCA2=4Q2, where Q2 is the amount of abatement by Source 2. Suppose a regulator sets up a tradeable permit system and allocates 20 permits to Source 1 and 20 permits to Source 2. Each permit gives the right to emit 1 unit of ozone. The permits are tradable and currently sell for $80 each.

A) At a price of $80, how many permits will Source 1 want? Will they be a buyer or a seller of permits? Explain.

B) At a price of $80, how many permits will Source 2 want? Will they be a buyer or a seller of permits? Explain.

C) How many units of ozone will Source 1 abate after it has bought/sold permits? What is Source 1’s total cost of abatement?

D) How many units of ozone will Source 2 abate after it has bought/sold permits? What is Source 2’s total cost of abatement?

E) What would the total cost of abatement be if the regulator instead issued 20 non-tradable permits to each source? How does this compare to the total cost of abatement with the tradable permit system? Why are the costs different?

Explanation / Answer

A) At optimum, MCA1 = 2Q1 = 80
Q1= 40
Total abatement is 40 units
Total Emission is 10 units
So Source one will sell permits

B) At optimum, MCA2 = 4Q2 = 80
Q2= 20
Total abatement is 20 units
Total Emission is 30 units
So Source 2 will buy permits

C) Source 1 will abate40 units.
Total Cost of abatement = 40 x 40 = 160
(TC is found by integrating MC)

D) Source 2 will abate 20 units
Total Cost = (2x20) x (2x20) = 160

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