Consider two electric power generation units that each initially emit 100 tons of emissions each. Firm 1 has marginal abatement costs given by: ac1(A1) = 0.5A1 per ton and total abatement costs given by: AC1(A1) = 0.25A^1₂. Firm 2 has marginal abatement costs given by: AC2(A2) = 2A2 per ton and total abatement costs given by: AC2(A2) = A^2₂. Consider values of emissions caps, , from 200 to 100 tons. Suppose that firm 1 receives 25% of all permits and firm 2 receives 75% of all permits under a free allocation. Suppose EB = 6 per ton abated and EB = 6A_t, where A_t = A₁ + A₂ is the total amount abated.

a. Add as a column in Excel the total abatement target for each cap on emissions.

b. Add as a column in Excel the equilibrium permit price for each emissions cap.

c. Add as two columns in Excel (one for each firm), the total amount abated by each firm for each cap.

d. Add as two columns in Excel (one for each firm), the final emissions level for each firm for each cap.

e. Add as two columns in Excel (one for each firm), the number of permits freely allocated to each firm for each cap.

f. Add as two columns in Excel (one for each firm), the net permits demanded for firm for each cap.

g. Add as two columns in Excel (one for each firm), the net costs, NC (equal to total abatement costs for the firm, AC plus the net value of permits demanded, answer from f for the firm times answer from b)) for each firm for each cap.

h. Add as two columns in Excel (one for each firm), the final emissions level for each firm for each cap.

i. Add as a column in Excel the total external benefits from abatement, EB.

j. Add as a column in Excel, total net benefit, which equals total external benefit of abatement (answer from i) less net costs from firm 1 and net costs from firm 2 (answers from g).

k. In Excel, plot the net costs for firm 1 on the y-axis and on the x-axis.

l. In Excel, plot the net costs for firm 2 on the y-axis and on the x-axis.

m. In Excel, plot the total net benefit on the y-axis and on the x-axis.

n. Given the 25/75 free allocation of permits and your answer from k, which level of the emissions cap is preferred by firm 1?

o. Given the 25/75 free allocation of permits and your answer from l, which level of the emissions cap is preferred by firm 2?

p. Given your answer from m, which level of the cap maximizes total net benefit? Is it what you would expect? Is it the Pareto optimal emissions level? Explain your answer.

q. Suppose firm 2 is successful at lobbying the regulator to implement its preferred emissions cap (i.e., your answer from o). What would be benefit/cost to society from implementing this cap relative to no policy? What would be the benefit/cost to society relative to the Pareto optimal emissions level?