EWU – ECON 450 – Public Finance & Public Policy – Briand
Efficient allocation of pollution abatement. The supply-demand model.
How can inefficiency resulting from an externality be remedied? While output are produced and
sold in a competitive market, pollutants that damage the air quality in the neighborhood are
emitted. Firms can reduce the amount of pollution, but only at a cost. The marginal cost of
abating emissions is upward sloping because the marginal cost of reducing emissions is low for
initial effort in reducing pollution level; it is high for more substantial emissions reduction.
Assume that Firm 1 marginal cost of abatement is given by: MCA1 = 0.5 A, where A is the level
of abatement of the pollutant; Firm 2 marginal cost of abatement is given by: MCA2= A. For
simplicity assume that each level of pollutant not emitted (i.e. each level of abatement adopted)
confers a constant marginal social benefit of $2 per unit.
1. In the space below, plot Firm 1, Firm 2 and the market marginal cost of abatement
assuming the market is composed of only those two firms; also plot society marginal
benefit from increased abatement units of the air pollutant.
2. Determine the efficient level of abatement of the pollutant. Get the exact equilibrium
quantity through calculation. Identify this level on your diagram as A**. Compute the
total cost of abatement, and the total net benefit to society resulting from this allocation.
Policy for pollution abatement. Emission standards.
3. In the space below, re-plot Firm 1 and Firm 2 marginal cost of abatement curves. Assume
an emission standard is imposed on both firms: each has to reduce its emission level by 3
units. Illustrate this abatement standard on your graph; identify it as Astandard.
4. Determine the total abatement cost of this policy.
Policy for pollution abatement. Emission fees.
5. In the space below, re-plot Firm 1 and Firm 2 marginal cost of abatement curves. Assume
an emission fee of $2/unit of pollutant of is charged to both firms. Illustrate this emission
fee on your graph; identify it as Pfee.
6. Determine the level of abatement adopted by Firm 1 and the level of abatement adopted
by Firm 2, identify those levels on your diagram as A1 and A2. Determine the total level
of abatement reached and compute the total cost of abatement incurred to reach it.
Efficient allocation of pollution abatement. The equalization of marginal costs rule.
The efficient allocation of pollution abatement is realized (and the total cost of pollution
abatement is minimized) when the total pollution reduction (i.e. the total abatement) is allocated
between firms such that the marginal cost of abatement is equalized across firms. You will show
this graphically below.
7. In the case scenario considered below, pollutant level has to be decreased by a total of 6
units. The objective is to determine the efficient allocation of this pollution abatement
level across firm 1 and firm 2. In the space below, plot the marginal cost curve of
abatement for firm 1, using origin O1 as the reference point. Plot the marginal cost of
abatement curve for firm 2, using origin O2.
marginal
costs of abatement
for firm 2
(dollar per unit)
marginal
costs of abatement
for firm 1
(dollar per unit)
O1
Abatement level for firm 1
O2
6 units
6 units
Abatement level for firm 2
8. Re-consider the allocation (A1=3, A2=3) from the emission standard scenario and
illustrate on the graph above the total abatement costs associated with it. Can you deduce
graphically which allocation would minimize the total costs of pollution reduction?
Compute its associated total costs.
Policy for pollution abatement. Pollution permit trading system.
Assume that each firm initially emitted a level of 9 pollution units, i.e. a total of 18 units. The
government has decided to reach the acceptable level of 12 units of pollution by using a tradable
permits system. It therefore issues 12 permits, each of which allows the bearer to emit 1 unit of
pollution. For simplicity, assume that the government allocates 6 permits to each polluter. Under
the rules of the permit system, each firm is required to hold a permit for each unit of pollution
released and to undertake abatement on all remaining units.
9. Based on the initial allocation of the permits each polluter-firm must abate 3 units of
pollution. Illustrate this initial condition, termed Round 1 of the permit system, on the
graph below by drawing each firm MCA curve and level of abatement adopted by each.
10. Determine each individual firm abatement cost, and the initial total abatement cost of this
policy.
11. If the permit system did not allow for trading, then the result of this policy would be
identical to an emission standard policy. Now, consider what happens when permits
trading is allowed. Firm 1 has an incentive to buy permits from firm 2 as long as the
purchase price of each permit is less than its MAC1. Likewise, firm 2 has an incentive to
sell permits to firm 1 as long as it can obtain a price greater than its MAC2. Suppose that
in Round 2 of the trading process, the two firms agree on the purchase and sale of one
permit at a price of $2 (make sure that both firms have an incentive to trade at this price).
Illustrate Round 2 of the permit system on the graph below by drawing each firm MCA
curve and the level of abatement adopted by each.
12. Determine each individual firm net abatement cost, after having taken into account the
cost of permit(s) purchased or revenue generated from permit(s) sold. Determine the total
net abatement cost of after Round 2.