Question

Consider a situation where the world consists of two countries, X, and Y. The total benefits (B) and total costs (C) of greenhouse gas emissions abatement (A) for each country are given by the functions listed below. Utility is defined as the difference between the benefits and cost of greenhouse gas abatement. Notice that the benefits of greenhouse gas abatement for each country is determined by the combined total amount of greenhouse gas abatement by both countries. This is because of the nature of climate change as a transboundary pollution problem.

BX = 8(AX + AY)

BY = 5(AX + AY)

CX = 10 + 2AX + 0.5AX2

CY = 10 + 2AY + 0.5AY2

Obtain the non-cooperative equilibrium levels of greenhouse gas emissions abatement for country X and country Y that maximizes each country’s utility. The non-cooperative solution is found where each country independently maximizes its utility, i.e., that is, each country ignores the behavior of the other country in its utility maximizing choices.

Answer 1