Homework 4

Question 1.

Q1a

Suppose that hedonic wage studies indicate a willingness to pay $50 per person for a reduction in the risk of a premature death from an environmental hazard of \(\frac{1}{100,000}\). If the exposed population is 4 million people, what is the implied value of a statistical life?

Q1b

Suppose that an impending environmental regulation to control that hazard is expected to reduce the risk of premature death from \(\frac{6}{100,000}\) to \(\frac{2}{100,000}\) per year in that exposed population of 4 million people. Your boss asks you to tell them what is the maximum this regulation could cost and still have the benefits be at least as large as the costs. What is your answer?

Question 2.

Consider two major economies, Country A and Country B, deciding whether to implement strict mitigation policies. Each country can choose to either “Reduce Emissions” or “Continue Business as Usual (BAU).” The payoff matrix below shows the economic benefits (in billions of dollars) for each country over a 10-year period.

		Country B
		Reduce	BAU
Country A	Reduce	(5,5)	(-2,8)
	BAU	(8,-2)	(1,1)

Q2a.

What is the Nash equilibrium (or equilibria) in this game? Show your work.

Q2b

Explain why this game represents a Prisoner’s Dilemma in the context of climate change policy.

Q2c

If the payoffs represent only economic benefits and ignore environmental costs:

1. What would be the socially optimal outcome?
2. Why do countries tend to deviate from this outcome?

Q2d

Consider implementing a policy mechanism to modify the payoff structure of this climate agreement game.

1. Suggest and explain a specific policy mechanism (e.g., carbon tax, trade sanctions, or technology subsidies) that could alter the payoffs.
2. Provide a new payoff matrix that incorporates your suggested policy mechanism. Show all calculations for the modified payoffs.
3. Prove that under your proposed policy:

• The socially optimal outcome (Reduce, Reduce) becomes a Nash equilibrium

4. Discuss one potential challenge in implementing your proposed policy mechanism in the real world.

Question 3

Two firms are ordered by the U.S. government to reduce their greenhouse gas (GHG) emission levels. Firm A’s marginal costs associated with GHG emission reduction is \(MC_{A} = 20 + 4Q\). Firm B’s marginal costs associated with GHG emission reduction is \(MC_{B} = 10 + 8Q\). The marginal benefit of GHG emission reduction is \(MB = 400 - 4Q\).

Q3a

What is the socially optimal level of each firm’s GHG reduction?

Q3b

Compare the social efficiency of three potential outcomes: (1) mandating equal GHG emission reductions across all firms; (2) imposing a uniform tax per unit of GHG emissions; or (3) mandating equal GHG emission reductions across all firms but allowing the trading of GHG emission permits.