Derive the socially optimal global level of avoided climate

Question

Assignment -

Answer all the questions. If you decide to use diagrams, they should be neatly drawn. On all diagrams, please label your axes and curves.

Background: Assume that the earth's climate is a global, non-excludable public good in that each individual citizen in each country in the world cannot be excluded from the benefits of greenhouse gas mitigation efforts by other countries. For the sake of this example, assume that there two countries in the world, Country One and Country Two. Each Country has its own individual willingness to pay (i.e., marginal benefits) for avoiding climate change damages from greenhouse gas emissions in its own Country. These estimates are:

Country One: P = 550 - Q₁

Country Two: P = 650 - Q₂

Where -

• P is the willingness to pay (i.e., marginal benefits) in $/ton from a reduction in greenhouse gas emissions for each country, and
• Q₁ and Q₂ are the reductions (i.e., abatement) of greenhouse gas emissions (in tons) by Country One and Country Two, respectively.

Assume for simplicity's sake that the marginal cost of reducing greenhouse gas emissions (in $/ton) is constant across the world at $200.

(1) Derive the socially optimal global level of avoided climate change that should be undertaken.

(2) What is Country One's "threat point" (i.e., the level of CO₂ abatement that the Country would undertake considering only its own benefits and costs)? What is Country Two's "threat point"? Assume that both Country One/Country Two can accurately estimate the other Country's benefits and costs of CO₂ abatement. Assume that each individual Country seeks to maximize its own narrow self-interest (i.e., pursues "non-cooperative" behavior), taking into account the other Country's expected behavior. How much CO₂ would Country One and Country Two abate? What are each Country's response functions, and how do the response functions determine how much each Country abates of CO₂ emissions?

(3) Assume that Country Two wants to show "leadership" on climate change. With leadership, Country Two's willingness to pay to avoid climate damage now becomes P = 700 - Q, instead of P = 650 - Q. Given Country Two's show of leadership, how much would Country Two abate? What would be Country One's response in terms of its level of emissions abatement? With Country Two's show of leadership, what would be the combined level of emissions abatement for the two countries? How would the overall level of abatement of the countries now compare to the social optimal global level of abatement?