1    Part 1:

Consider a group consumers who consume two types of goods, a numeraire good, Z, with price 1 and a consumption good X with price P . The latter produces pollution.  Consumers can be “green” or“non-green” reflecting their envrionmental preferences.  There are Mg  green consumers and Mn non-green consumers and let M = Mg + Mn .

Each green consumer i has preferences

M

Zi + γ log (Xi ) − ⇤ X log (Xj )

j=1

and each non-green consumer k has preferences

M

Zk + Γ log (Xk ) − λ X log (Xj )

j=1

where ⇤ >  λ  and Γ >  γ .  Also assume throughout that γ − (Mg ⇤ + Mn λ) > 0. All consumers have an endowment Yi  of the numeraire. [Note that P log (Xj ) is the sum of (log of) consumption across all consumers.]

1. Explain how these preferences capture the negative externality from pollution. (2 marks)

2. In what sense do the assumptions that ⇤ > λ and Γ > γ capture what it means to be a green consumer? (2 marks)

3. Derive the demand for good Xi  for each type of consumer and show that green consumers buy less of good X than non-green consumers. (2 marks)

4. Suppose we measure welfare as the sum of utilities. What is the level of consumption of good X for each type of consumer which maximizes welfare? Explain why this di↵ers from your answer to part 3 (6 marks)

5. Let c be the marginal cost of producing good x.  Suppose that the government chooses to regulate the price of this good and legislates a price for each type of consumer of

γ − ⇤     

Pg  = cγ − ⇤Mg  − λMn

for green consumers and

Γ − λ          

Pn  = cΓ − ⇤Mg  − λMn

for non-green consumers. How will this a↵ect demand by both types of consumer?  Will this achieve the welfare-maximizing consumption of good X? Is this a workable policy? Explain. (6 marks)

6. Will producers who are competing with each other to supply good X have an incentive to ask the government to regulate the price due to the externality? (2 marks)