ECOS3013 Tutorial 4
Week 5, starting 28 August
Question 1
Consider a firm that produces steel, using coal to generate the heat it needs, which causes C02 emissions.
C02 emissions contribute to the greenhouse effect and climate change, which are public bads. Assume
that aggregate CO2 emissions are at an inefficiently high level – where the aggregate marginal benefit
from reducing emissions is higher than the marginal cost of doing so.
1. Briefly describe some costs that the firm may incur if it tried to reduce CO2 emissions.
2. Describe what we mean by ‘marginal savings from emissions’. Give an intuitive reason that we
assume that the MS curve has a negative slope.
3. Assuming that the firm aims to maximise its profits, does it have incentive to reduce its C02
emissions in the absence of regulation? Explain.
Question 2: Public Bad
Note: this question continues from Question 3 in Tutorial 2.
Sulphur emissions are a public bad. Suppose that the aggregate marginal damage is
MD(e) = 40e
where e is the aggregate emissions. Suppose that the marginal saving from emissions is:
MS(e) = 700− 10e
1. What level of emissions do you expect to occur in an unregulated market? Explain your answer.
Call this level e˜.
2. What is the socially optimal (efficient) level of pollution e∗?
1
3. Use a diagram to show that there is a potential Pareto improvement in moving from e˜ to e∗.
4. Can you think of a way to the move from e˜ to e∗ into a Pareto improvement?
Question 3: Abatement
Sulphur emissions are a public bad. Suppose that the aggregate marginal damage and marginal savings
from these emissions are the same as in Question 2. Abatement is a reduction in emissions. Define A as
the amount of emissions abatement. Let the unregulated emissions level be where abatement is zero (ie:
A = 0 when e = 70).
1. What is the aggregate marginal willingness to pay for abatement when sulphur emissions are at
the unregulated level (and abatement is zero)? Find the aggregate marginal willingness to pay for
abatement as a function of A.
2. Starting from the uncontrolled level of pollution, what is the firm’s marginal cost of abatement as
a function of A?
3. What is the optimal level of A?
4. Compare the optimal outcomes in parts 1. and 2. Are the problems of optimal provision of the
public bad (pollution) and the public good (abatement) equivalent? Explain why or why not.
Question 4: Equimarginal Principle
Assume an economy of two firms. The two firms pollute. Firm one has a marginal savings function of
MS1(e1) = 5− 12e1 where e1 is the quantity of emissions from the firm. Firm two has a marginal savings
function ofMS2(e2) = 11−e2. The aggregate marginal damage to all consumers isMD(E) = 13E, where
E the total amount of emissions (E = e1 + e2).
1. Draw and calculate the firm-level and aggregate marginal savings functions.
2. What is the optimal level of emissions? What is each firm’s marginal saving and emissions level at
the optimum?
3. Explain why one firm has higher emissions than the other at the optimal outcome.