The world consists of two countries, X which is poor and Y which is rich. The total

benefits (B) and total costs (C) of emissions abatement (A) are given by the functions Bx

= 8(Ax + Ay), By = 5(Ax + Ay), Cx = 10 + 2Ax + 0.5Ax^2 and Cy = 10 + 2Ay + 0.5Ay^2, where

the subscripts are used to denote the country in which the abatement takes place.

(a) Obtain the non-cooperative equilibrium levels of abatement for X and Y.

(b) Obtain the cooperative equilibrium levels of abatement for X and Y.

(c) Calculate the utility levels enjoyed by X and by Y in the non-cooperative and

cooperative solutions. Does the cooperative solution deliver Pareto

improvements for each country, or would one have to give a side-payment to

the other to obtain Pareto improvements for each with cooperation?

(d) Obtain the privately optimizing level of abatement for X, given that Y decides to

emit at the level of emissions that Y would emit in the cooperative equilibrium.

(You should find that the answer to d) above is that X does the same amount of

abatement that she would have done in the non-cooperative case. What

property or properties of the cost and benefit function used in this example

cause this particular result?)

(e) Suppose that Y acts as a 'swing abater', doing whatever (non-negative) amount

of abatement is required to make the combined world abatement equal to the

combined total under a full cooperative solution. How much abatement is

undertaken in the two countries?