2Types of externalities Consumption externalitiesConsumption of a good by agent A has a direct impact on agent B’s utilityE.g., smoking, loud music, tidy garden, etc.Production externalitiesActions by agent A have a direct impact on agent B’s production possibilitiesE.g., bee-keeper and apple orchard, polluting firm and fisherman, etc.
3Missing markets The endowment point is not Pareto efficient. Person BwBxyThe endowment point isnot Pareto efficient.Allowing trade permitsa Pareto improvementwByContract curveEndowmentwAyPerson AxwAx
4Room-mates 2 agents A and B There are two “goods”: Stuff – i.e., money: mA and mB : Endowments = $100Smoke – concentration: 0 ≤ s ≤ 1A is a smoker: uA(mA,s)B is a non-smoker: uB(mB,t), where t = 1-sNote: s + t = 1
13The Coase Theorem Coase Theorem: If property rights are well-defined,bargaining over the externality is possiblewith sufficiently low transaction coststhe outcome will be efficientWhen preferences are quasi-linear, the allocation of property rights has no impact on the equilibrium quantity of smoke (s*)
14Using demand curves Let’s assume quasi-linear preferences A’s utility: uA(m,s) = mA + v(s)A’s marginal benefit from smoke is v’(s)B’s utility: uB(mB,t) = mB + w(t)B’s marginal benefit of less smoke is w’(t)
15Example: smoking A’s utility: uA(m,s) = mA + ln(s) mA = 50 B’s utility: uB(mB,t) = mB + 2ln(t)mB = 150What are equilibrium s, t, mA, and mB if A has the right to smoke as much as he wants?What if B has the right to clean air?
16Agent AAgent Bw(t)v(s)Slope = marginalutility of less smoky airSlope = marginalutility of smoky airstv’(s)w’(t)st
17Marginal costs and benefits Pareto efficiency requires v’(s) = w’(t)A’s marginal benefitLooks like a demandcurveB’s marginal costof smokeLooks like a supplycurvePigouviantax on smokers1ss*1-s=t
18Pigouvian taxDefinition: A tax on activities with negative externalitiesDouble benefitReduce harm from negative externalitiesFund useful government spendingEspecially beneficial when Coase theorem does not apply
19Example: smoking A’s utility: uA(m,s) = mA + ln(s) mA = 50 B’s utility: uB(mB,t) = mB + 2ln(t)mB = 150‘what sort of government tax on smoking x would lead to an efficient outcome?What are mA and mB in this outcome?
20Allocating pollution amongst firms Suppose one unit of pollution is to be allocated between two firmsFirm A’s marginalbenefitFirm B’s marginalbenefitPigouvian taxon pollution1ss*1-s
21Pollution permitsIf A has all the permits, it sells 1-s* to B, at price p*If B has all the permits, it sells s* to A, at p*Only difference is which firm earns the profits from permit salesFirm A’s marginalbenefitFirm B’s marginalbenefitp*1ss*1-s
22Why don’t people cooperate? Two firms could merge so as to internalize the costs they impose on each otherRoom-mates can agree on smoking limits, or switch partnersBut there may be transactions costs that limit agents’ ability to tradeE.g., if the market is one-sided – one polluter and many pollutees