Question

5. Suppose that Penn Products and Teller Industries are both emitting 30 metric tons of perfluorocarbons (PFCs) into the atmosphere. Regulators wish to reduce emissions to 40 metric tons overall, and plan to achieve this with a system of tradable permits. Penn’s marginal abatement costs are given by MACP = 5eP, where eP is the number of metric tons of emissions that Penn is cutting. Thus, the cost of cleaning up the first metric ton is $5, the second ton costs $10 to clean up, and so on. Teller’s marginal abatement costs are given by MACT = 7.5eT, where eT is the number of metric tons of emissions that Teller cuts.

a. The lowest-cost way to reduce emissions is found when both firms’ marginal abatement costs are equalized. Equate Penn’s and Teller’s marginal abatement costs, and solve for eP in terms of eT. For each metric ton that Teller cuts, how many tons should Penn cut?

b. Because 20 metric tons are to be cut, we know that eP + eT = 20. Use your answer for (a) to solve for eT. How many metric tons will Teller be responsible for cleaning up if the cleanup is done efficiently? How about Penn?

c. Calculate the cost of Teller’s share of the cleanup. Do the same for Penn, and then

compute the total cost of reducing PFC emissions by 20 metric tons.

d. Suppose that Teller cleans up one metric ton less, and Penn cleans up one more ton. Recompute the total cost of the cleanup to determine if the outcome you found in (c) was efficient. Then, double check your work by reversing the situation: Let Teller clean up one additional metric ton, and Penn one fewer ton.

e. If government regulators give Penn and Teller each their own twenty 1-ton pollution permits and allow them to trade, how many permits will end up trading hands, and what price will a permit sell for?

Answer 1

a. For the lowest cost way to reduce emissions, marginal abatement cost of Penn should be equal to marginal abatement costs of Teller.

Thus, for each metric ton that Teller cuts, Penn should cut 1.5 metric tons of emmission.

b. Since 20 metric tons is to be cut form each Teller and Penn, . From part (a) we have,. Substitute the value of eP in the equation to obtain the value of eT.

Compute eP by substituting the value of eT in the above equation: eP+eT=20.

Thus, if the clean up is done efficiently, Teller will be responsible for cleaning up 8 metric tons and Penn will be responsible for cleaning up 12 metric tons respectively.

c. Cost of Teller's clean up can be determined by the marginal abatement cost of Teller, which is given as follows:

Substitute the value of eT as 8 to solve for MACT.

Thus, the cost of Teller's share of clean up is 60.

Similarly,for Penn, the marginal abatement cost is given as:

Substitute the value of eP as 12 to solve for MACP.

Thus, the cost of Penn's share of clean up is 60.

Total cost of reducing the PFC emissions is equal to MACT+MACP.

d. If Teller cleans up one metric ton less, eT will be equal to 8 minus 1.

eT=7

Compute MACT by substituting the value of eT in the equation for marginal abatement cost of Teller.

If Penn cleans up one metric ton more, eP will be equal to 12 plus 1.

eP=13

Compute MACP by substituting the value of eP in the equation for marginal abatement cost of Penn.

Add MACT and MACP to find the total cost of the clean up.

In this case, the total cost of reducing the emissions to 20 metric ton is less in this case than part c, where the total cost was 120.

Now, if Teller cleans up one additional metric ton, eT will be equal to 8 plus 1.

eT=9

Compute MACT by substituting the value of eT in the equation for marginal abatement cost of Teller.

If Penn cleans up one metric ton less, eP will be equal to 12 minus 1.

eP=11

Compute MACP by substituting the value of eP in the equation for marginal abatement cost of Penn.

Add MACT and MACP to find the total cost of the clean up.

In this case, the total cost of reducing the emissions is more than part c, where the total cost was 120.