Let Failure The Coase Theorem Notice that the amount of the externality produced at the efficient point depended on how property rights were assigned. If the smoker started with the property rights, more smoke is generated at the efficient allocation. With starts with property rights -the the externality is produced at the efficient allocation. Consider the last example: A Recall that quasi-linear preferences have indifference curves that are parallel translates of each other s"smoke is produced whatever property rights are assigned. Only m varies between efficient allocations This is the Coase theorem the efficient externality level is independent of the initial distribution Market- Market Failture Production Externalities fish f. The firm aste w in the sea, reducing fish yields. Cost (e, w)=c(e) u)and c,(f, u)=c(f)+u- respectivel ence profits are given respectively by: Te =Pee-d(e)+u(1-u) and T, =prf-cf)-w2 Since the electricity firm alone chooses w it will keep producing waste (which reduces cost ) until no more profits be made from doing so. The benefit increases until w =0.5 and decreases thereafter. 0. 5 the marginal benefit of waste is equal to its marginal cost(zero). Both firms set MR=MC to derive f-pe =c(e)and p=c(') Is this efficient? No. The electricity firm is producing too much waste, damaging the fishing firmMarket — Market Failure 3 The Coase Theorem • Notice that the amount of the externality produced at the efficient point depended on how property rights were assigned. If the smoker started with the property rights, more smoke is generated at the efficient allocation. • With quasi-linear preferences, it does not matter which consumer starts with property rights — the same amount of the externality is produced at the efficient allocation. Consider the last example: ....................................................................................................................................................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................................................................................................................................................... . ....................................................................................................................................................................................................................................................................................................................................................................................................................... ................................................................................. . ............................................................................... ................................................................................. . ............................................................................... A s B m • • x 0 x s ∗ • Recall that quasi-linear preferences have indifference curves that are parallel translates of each other. • s ∗ smoke is produced whatever property rights are assigned. Only m varies between efficient allocations. • This is the Coase theorem — the efficient externality level is independent of the initial distribution. Market — Market Failure 4 Production Externalities • Suppose there are two firms, one producing electricity, e, and one producing fish f. The electricity firm dumps toxic waste w in the sea, reducing fish yields. Costs are ce(e, w) = c(e) − w(1 − w) and cf (f, w) = c(f) + w 2 respectively. • Hence profits are given respectively by: πe = pee − c(e) + w(1 − w) and πf = pf f − c(f) − w 2 • Since the electricity firm alone chooses w it will keep producing waste (which reduces cost) until no more profits can be made from doing so. The benefit increases until w = 0.5 and decreases thereafter. • At w ∗ = 0.5 the marginal benefit of waste is equal to its marginal cost (zero). Both firms set MR = MC to derive optimal e ∗ and f ∗ — pe = c 0 (e ∗ ) and pf = c 0 (f ∗ ). • Is this efficient? No. The electricity firm is producing too much waste, damaging the fishing firm