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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 Â‘swing abaterÂ’, 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

+70

+20

U: unfavorable

-20

+20

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

Tags:

macroeconomics

noncooperative equilibrium

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