Department of Economics
ECON0050, 2023-24 Term 1
Tutorial 1: Feedback Session, Lec. 1-2
This tutorial, or ‘Feedback Session,’ will help you assess your progress thus far and practice the
kind of questions which will show up on the Moodle Quiz for this module. To make the most of
the session, please give these problems your best attempt before attending the tutorial.
On the quiz, you may be asked to solve problems similar to this one and then enter your
numerical answers. Note that, since the quiz will be conducted via Moodle, you will not be
required to draw your own graphs or provide free-response explanations, as in parts (a) and (h),
but these questions will help solidify your understanding of the model—and drawing graphs on
the quiz may help you with your calculations.
1. Policy Solutions to Externalities. In this problem, we’ll mathematically investigate the
optimal ways to reduce pollution. Suppose two coal-fired power plants have the ability to
install carbon capture equipment to reduce, or abate, CO2 emissions.
Plant A has more innovative engineers and can thus abate carbon at a marginal cost (to
the plant) of zero for the first 10 units of abatement and at a marginal cost 𝑀𝐶! = −35 +
3.5𝑞! for 𝑞! > 10, where 𝑞! indicates the reduction in the number of tonnes of carbon
emitted by plant A. Plant B can reduce carbon emissions at a marginal cost to the plant
of 𝑀𝐶" = 10𝑞" . The abatement technology itself does not impose any externalities on
society, positive or negative.
Absent government intervention, neither plant derives any revenue from reducing carbon
emissions, but each tonne of carbon abated has a benefit to society as a whole of £70,
which accounts for all of the future climate change-related damages averted.
a. Graph the private marginal benefit, social marginal benefit, and each plant’s
private and social marginal costs of carbon emissions reduction. [Hint: as in
lecture, the x-axis should represent the amount of emissions reduction]
, Note that the private marginal benefit of abatement for either plant is zero—
absent government intervention, plants do not receive any revenue in
exchange for reducing carbon emissions. The social marginal costs of
abatement at each plant equal the private marginal costs given in the
problem above, since the act of abatement itself does not produce any
externalities.
b. Calculate each coal plant’s profit-maximizing amount of carbon emissions
abatement absent any government intervention, i.e. in the competitive equilibrium.
Since the private marginal benefit of abatement is zero, and reducing
emissions comes at a (marginal) cost, each firm will maximize ‘profits’ by
undergoing zero abatement, 𝒒𝑨 = 𝒒𝑩 = 𝟎.1
c. What is the total social surplus from carbon emissions abatement in this
competitive equilibrium?
Since neither firm undergoes any abatement, social surplus from abatement
is zero.
The government does not know the exact costs faced by each plant – indeed, in the real
world, firms themselves may be reluctant to reveal the details of their production
processes lest they leak to competitors – so regulators instead decide to require what
they estimate as a feasible reduction for the average plant. Specifically, they introduce a
regulation requiring every plant to reduce emissions by at least 20 tonnes.
1
Technically, since the first 10 units of abatement are costless for plant A, plant A would be indifferent
between any abatement level between 0 and 10. On the quiz, any level 𝟎 ≤ 𝒒𝑨 ≤ 𝟏𝟎 would thus earn full
marks, but for the sake of simplicity, we will go forward here assuming firm A chooses 𝒒𝑨 = 𝟎 in the
competitive equilibrium.
