University of Waterloo Macroeconomics Problem Set


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Problem Set 5
1. 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 B X = 8(AX +
AY), BY = 5(AX + AY), CX = 10 + 2AX + 0.5AX2 and CY = 10 + 2AY + 0.5AY2, 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?
2. The construction of a hydroelectric plant in a wilderness valley is under consideration. It
is known that the valley contains an insect species found nowhere else, and the project
includes relocating the insects. It is not known whether they can be successfully located.
The pay-off matrix is:
H: Hydroelectric
C: Coal-fired
F: favorable
U: unfavorable
where F and U stand for favorable and unfavorable, H is the decision to go ahead with the
hydroelectric plant, C is the decision to proceed instead with a coal fired plant, and the
cell entries are Net Present Value millions of $s. Favorable is the state of nature where
species relocation is successful, unfavorable is where it is not. Ascertain the decisions
following from adopting:
(a) the principle of insufficient reason,
(b) the maximin rule,
(c) the maximax rule.
Derive the regret matrix and ascertain the implications of the minimax regret rule, and
compare the outcome with that arising from the safe minimum standard approach.

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Explanation & Answer:
2 Questions


noncooperative equilibrium

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