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3 Externality There are two people, Alice and Bob. Alice consumes quantity {EA of good ac, with utility function lnzrjA 6A (with BA to be explained; notice that the ln applies only to an). Bob consumes quantity $3 of good 3:, with utility function lan eB (with 63 to be explained, and with the ln applying only to :63). Each has income I and the price of cc is 1. If Alice consumers quantity 23A of good x, she generates an equal quantity of noxious fumes, which we denote 63 (and hence 23 : xA). Alice does not care about the fumes, but they impose disutility on Bob. However, at cost p per unit, Alice can reduce the amount of fumes she produces. Hence, we can think of Alice's budget constraint as xA+p(;vA 7 6B) : I Alice can spend all of her income on a\" if she does nothing about the fumes, and otherwise has her effective income reduced by 19 times the quantity by which she reduces her fumes. (We assume that Alice cannot generate extra fumes, and cannot generate negative amounts) Similarly, if Bob consumes 233 of quantity it, he generates quantity 8,4 = 333 of infernal racket. 30b is not bothered by the noise, but the noise adversely affects Alice. 30b can reduce his racket at cost p, so that his budget constraint is 333 +P(IB * 8A) : I 3.1 Find the utilitymaximizing consumption bundles for Alice and Bob. 3.2 ls the allocation you found in 3.1 efcient? Explain precisely why not. Find an eicient allocation for Alice and Bob. 3.3 Suppose that Alice consumes her part of an ecient allocation. What would it be best for Bob to do? In light of this, is this situation like a prisoners\" dilemma? 3.4 Suppose you are a regulator charged with overseeing fumes and rackets. Pro pose a policy that would lead to an efcient allocation, and nd the resulting allocation