Tackling Negative Externalities from Smog: Two power plants provide power to all of Ontario: a Nanticoke plant and a Lennox plant. Both power plants burn coal to produce electricity, and consequently produce smog as a by-product. The Nanticoke power plant could reduce its at a total cost:
TCN(Qn) = 5(QN)^2
where QN indicates the total number of units reduced by Nanticoke. The Lennox plant is
slightly less efficient and its total cost for cutting down on smog by QL is: TCL(QL)=7(QL)^2 +10QL
The Ontario government hires a team of environmentalists who calculate that the total benefit of smog abatement to the Ontario province is 100(QN + QL):
1. Calculate the socially optimal level of smog reduction for each power plant.
2. Suppose Ontario government considers imposing a tax on power production.
(a) What tax should it impose to reach the abatement amounts you calculated in (1)?
(b) Write down each firmâs optimization problem under the tax, and show that each will privately choose the socially optimal abatement amount.
3. Suppose that instead of taxation, the Ontario government tries to regulate quantities. However, it cannot write a law for each firm, so it simply declares that all Ontario power plants must cut down on smog by 1 unit each year. Show that this is not efficient.
4. Suddenly, an economist is voted in as Premier of Ontario. She declares that Lennox power plants must cut down on smog by 5 units overall. Additionally, she declares that firms will be able to competitively trade permits that will allow them NOT to abate. One of the Premierâs old classmates from graduate school runs the Nanticoke power plant, so the Premier grants Nanticoke 5 permits and Lennox 0 permits. As a result, Lennox is expected to abate by 5 units, and Nanticoke (since it owns all the permits) is not expected to abate at all.
(a) Lennox will surely want to buy some of Nanticokeâs permits. Explain intuitively why this trade might happen.
(b) Denote the number of permits that firm i â {N, L} eventually holds as Yi (so that Qi = 5âYi), and denote the competitive price of permits as PY . Derive the amount of permits that Nanticoke will eventually hold as a function of PY . Calculate the amount of permits that Lennox will hold as a function of PY .
(c) Using the fact that YM + YN = 5, calculate PY .
(d) If the new mayor had divided the permits up differently, what outcomes would have
changed and what would have stayed the same?
