### What is the socially optimal level of phosphorus emissions

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Question 1. The steel industry near Hamilton (ON) emits, among other harmful pollutants, carbon monoxide (CO). There are ten identical firms in this industry. Five of them are located near the city (urban area) while five of them are located in the country (rural area). They can install Otters (scrubbers) in their exhausts to clean up part of their emissions. Their abatements costs related to CO clean-up are described by MACi = 600   12Ei, where i = 1,2.........10.The emissions of CO are locally dispersed (no spillovers from one area to the other). Due to higher population and structure density in the city, the marginal damage a unit of CO is causing in the urban area is higher than that in the rural area. More specifically these damages are described by MDU = 0:8E and MDR = 0:6E.

(a) How many units of emission will these ten firms emit if the CO emissions are left unregulated? How many units of emission are released in each of the two areas?

(b) What are the marginal abatement cost functions for each of the two areas? (hint: use horizontal summation for EACH area)

(c) What are the optimal levels of emission in the urban and the rural areas? How many units of emission must be abated (in each area) compared to the unregulated level so that efficiency will be achieved?

(d) If the government sets individual standards equal to the socially optimal levels of emission in each of the two areas, calculate the total cost of compliance per firm in each of the two areas (note that the standards per firm in each area will be set at the same level for all of them since firms are identical).

(e) If the government sets a uniform standard in the two areas equal to E = 190 calculate the loss in the two areas due to over-control (for the rural area) and under-control (for the urban area).

Question 2. There are two agglomerate plants1 in Quebec, along the Saint-Lawrence River. The process of iron agglomeration (pelletization) releases phosphorus in the river causing eutrophication (algae having excess phosphorus to adsorb can grow out of control and absorb a lot of oxygen, thus suffocating other species). The cost of abatement for these two factories is described by MAC1 = 200   0:1E1 and MAC2 = 200   0:4E2. The damages caused in the river can be described by MD = 0:12E.

(a) How many units of phosphorus will these two firms emit if the phosphorus emissions are left unregulated?

(b) What is the socially optimal level of phosphorus emissions in the river?

(c) What is the level of the emission tax consistent with the socially optimal solution? What is the cost of compliance per firm under this tax?

(d) The government is imposing a per-unit of emission tax, t = \$40. How much each of the two firms will emit under regulation? How much is the cost of compliance per firm? What is the social cost due to incorrect level of regulation?

Question 3. Consider a firm emitting a harmful pollutant in the environment. This firm can clean-up its emissions according to an abatement technology described by MAC = 100   2E. The government sets an emission target equal to E = 20. When emissions are regulated the firm can either fully comply with regulations or it can cheat and over-pollute. In the latter case, there is a probability p = (E=100) that the firm will get caught and asked to pay a One F.

(a) What is the cost of full compliance for the firm?

(b) What is the expected cost of compliance when the firm is violating the emission standard by over-polluting?

(c) What is the net marginal benefit for the firm when cheating? How much will the firm decide to emit? (Hint: the answer to the last question would be a function of the One).

(d) How high should the One F be in order for the firm not to have an incentive to over-pollute?

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