Consider an industry consisting of two firms (j=1 and 2) that produce a consumer good and pollution. The abatement cost and damage functions are:

(a) Determine the firms’ marginal abatement cost curves.

(b) Determine the socially optimal allocation and level of pollution. Now let a₁=10, b₁=1, a₂=12, and b₂=0.5. Suppose the environmental authority aims to establish an aggregate emission level of E=16 units.

(c) What is the unregulated market emission level for each firm?

(d) What is each firm’s abatement cost and the aggregate abatement cost if the government requires e_j=8 for each firm?

(e) What is the tax rate the government should charge in order to achieve the target of E=16 units? What is each firm’s abatement cost and the aggregate abatement cost if the government charges this tax rate? What is each firm’s tax bill?

(f) Suppose instead the government freely issues tradable emission permits, with each firm receiving an initial endowment of 8 units. If the permit market is competitive, what is the market price for permits? How many does each firm buy or sell? What is each firm’s total cost (abatement plus net permit expenses)?
(g) Suppose instead the government auctions off 16 permits. What is the competitive auction price? What is each firm’s total cost (abatement plus permit expenses)? What are government revenues?
(h) What would be the per unit subsidy needed to achieve a total of E=16 units? What baseline emission level, below which the firms receive a subsidy, should the government set? What is each firm’s total cost (abatement minus subsidy receipts)? What is the government expenditure?

(i) Construct a table summarizing the following for each policy option: total abatement cost, total industry cost, and government revenue (expense).

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C(e) = f(a,-be) /2b, ve, sa, Ib,, a, b, >0 0 otherwise D(E)=E d> 0. 2