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

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 + 0.5AX2
and

CY = 10 + 2AY + 0.5AY2

where the subscripts are used in the same way as in Box
10.2.

(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
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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 + 0.5AX2
and

CY = 10 + 2AY + 0.5AY2

where the subscripts are used in the same way as in Box
10.2.

(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
sidepayment to the other to obtain Pareto improvements for each with
cooperation?

(d) Obtain the privately optimising 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?

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