Lectures on Externalities

Transcription

1 Lectures on Externalities An externality is present whenever the well-being of a consumer or the production possibilities of a firm are directly affected by the actions of another agent in the economy. The caveat of directly affected is important because everybody s actions impact everybody else through the price mechanism. Price related affects are known as pecuniary externalities and these have no implications for government intervention. Externalities can go from producers to consumers, consumers to consumers and producers to producers. They can be negative or positive. Externalities are interesting to public finance economists because when they exist, market failure may arise and this may necessitate government intervention.

2 Indeed, government intervention to regulate externalities is very widespread, most notably in the area of the environment. In these lectures we will (i) outline a simple model with an externality to illustrate why they cause market failure; (ii) discuss the Coase Theorem which argues that externalities can be dealt with via negotiation between affected parties provided property rights are clearly specified; (iii) discuss the difference between price and quantity regulations to deal with externalities; (iv) discuss a particular class of externality problems arising from common property resources.

3 A Simple Model of Externalities Many different models of externalites can be constructed - producer-producer, producer-consumer, etc. While we will focus on a consumer-consumer externality, it should be noted that entirely similar conclusions would emerge from any externality model. Consider a community consisting of 2 consumers indexed by i =1, 2 Suppose that there are two goods - a numeraire good z and another good x (think cigarettes) Consumer 1 has utility function u 1 = z 1 + ϕ(x 1 ) where ϕ( ) is increasing, strictly concave and satisfies ϕ(0) = 0.

4 Here z 1 is consumer i s consumption of numeraire and x 1 is consumer i s consumption of the other good. Consumer 2 has utility function u 2 = z 2 ξ(x 1 ) where ξ( ) is increasing, strictly convex and satisfies ξ(0) = 0. Thus, consumer 2 gets no utility from his own consumption of good x, and negative utility from 1 s consumption (for example, 2 is a non-smoker and 1 is a smoker). Suppose that each consumer i has some endowment of the numeraire (or income) y i. Suppose further that the cost (in terms of units of the numeraire) of providing a unit of good x is c. An allocation for this community consists of a description of what each consumer is consuming (z i,x i ) 2 i=1

5 An allocation (z i,x i ) 2 i=1 is feasible if (i) for all ix i 0 and z i 0 and (ii) X i z i + c X i x i X i y i. Efficiency An allocation (z i,x i ) 2 i=1 is Pareto efficient if (i) it is feasible and (ii) there exists no alternative feasible allocation which Pareto dominates it. Proposition 1: An allocation (zi e,xe i )2 i=1 such that > 0foralli is Pareto Efficient if and only if (i) z e i ϕ 0 (x e 1 ) ξ0 (x e 1 ) c (= ifxe 1 > 0), (ii) x e 2 = 0; and (iii) P i z e i + c P i x e i = P i y i. Condition (i) says that the level of 1 s consumption of good x is such that social marginal benefit equals social marginal cost.

6 Social marginal benefit includes both 1 s consumption benefit and 2 s negative disutility from 1 s activities. Market Failure Suppose good x is provided via the market mechanism. Then competition would ensure that the price of a unit of the good were just c. An allocation (z i,x i )2 i=1 is a market equilibrium if and (z 1,x 1 )=argmax{z 1 + ϕ(x 1 ):y 1 cx 1 + z 1 } (z 2,x 2 )=argmax{z 2 ξ(x 1 ):y 2 cx 2 + z 2 }. Proposition 2: Suppose that ϕ 0 (0) > c. Then if (zi,x i )2 i=1 is a market equilibrium it is not efficient. While conditions (ii) and (iii) are satisfied, (i) is not.

7 In the market equilibrium, we have that ϕ 0 (x 1 )=c which implies that x 1 >xe 1. Government Intervention The government can restore efficiency by either imposing a quota or a tax. The quota could be imposed either on Mr 1 s consumption of good x or on firms production of good x. The tax could either be imposed on Mr 1 s consumption or on firms production. The optimal tax is ξ 0 (x e 1 ). This type of tax is known as a Pigouvian corrective tax. Any distributional consequences of the tax could be dealt with by lump sum redistribution.

8 Coase Theorem Coase pointed out that the externality problem fundamentally arose from two factors (i) lack of clearly specified property rights and (ii) transactions costs. To illsutrate his point, suppose that we assigned Mr 1 the right to consume as much x as he liked and suppose that there were no transactions costs. Then consumer 2, recognizing Mr 1 s right would offer him a transfer in exchange for him cutting back his x consumption. Mr 1 would agree to the deal provided it made him better off. Assuming a one round bargaining procedure with Mr 2 making a take it or leave it offer, Mr 2 would make an offer (T,x 1 )tosolve max y 2 T ξ(x 1 ) y 1 + T cx 1 + ϕ(x 1 ) y 1 cx 1 + ϕ(x 1 )

9 Clearly, T = cx 1 ϕ(x 1 ) cx 1 + ϕ(x 1 ) and thus, the level of x 1 that 1 would choose solves max y 2 cx 1 + ϕ(x 1 ) ξ(x 1 ) cx 1 + ϕ(x 1 ) which means that ϕ 0 (x 1 ) ξ 0 (x 1 ) c (= ifx 1 > 0). implying that x 1 = x e 1! Alternatively, we could assign Mr 2 the right not to be infringed by Mr 1 s consumption. Then Mr 1, recognizing Mr 2 s right would offer him a transfer in exchange for allowing him to consume x. Mr 2 would agree to the deal provided it made him better off.

10 Assuming a one round bargaining procedure with Mr 1 making a take it or leave it offer, Mr 1 would make an offer (T,x 1 )tosolve max y 1 T cx 1 + ϕ(x 1 ) y 2 + T ξ(x 1 ) y 2 The same conclusion emerges - the negotiated level of x 1 would be efficient. This yields: Coase Theorem: If property rights are clearly specified and there are no transactions costs, bargaining will lead to an efficient outcome no matter how the rights are allocated. The allocation of rights have distributional consequences, but no efficiency consequences. The allocation of rights is crucial because otherwise the participants would be fighting over who should be paying who.

11 What are the transactions costs that Coase had in mind? Most obviously, if there are a large number of citizens impacted by the externality then there will be significant transactions costs to bring everybody to the table and start negotiating. Less obviously if participants have to pay an ex ante cost in order for an agreement to be reached (such as showing up to a meeting) then this can lead to inefficiencies arising for strategic reasons - see Anderlini and Felli Costly Bargaining and Renegotiation Econometrica, In this case an agreement need not be reached even if the surplus created from such an agreement would exceed the negotiation costs. Imperfect information is also a problem. It is natural to assume that the affected parties will not have perfect information about each others benefits and costs.

12 It is well-known that with bilateral asymmetric information, bargaining will not lead to an efficient outcome (Myerson and Sattherwaite, Journal of Economic Theory (1983)). To illustrate these difficulties, let us retrun to our example, but assume that x 1 is a discrete choice; that is, x 1 {0,x 1 }. Further assume that and ϕ(x 1 )=ϕ(x 1 ; θ) ξ(x 1 )=ξ(x 1 ; η) where θ and η are ranom variables with ranges [θ, θ] and [η, η]. Let b(θ) =ϕ(x 1 ; θ) cx 1

13 and s(η) =ξ(x 1 ; η) Let G(b) andf (s) bethecdfsofthevariablesb and s induced by the random variables θ and η. Assume that Mr 2 has the right not to be infringed by Mr 1 s consumption, so that without bargaining the outcome will be x 1 = 0. This outcome will be inefficient whenever b(θ) >s(η) Now consider the bargaining problem, where Mr 1 offers Mr 2 a transfer T in exchange for letting him consume x 1.Mr1knowsb but does not know s. Now Mr 2 will agree if and only if T s. The probability of this is 1 F (T ).

14 Thus, given b, Mr 1 will choose T to solve max(1 F (T ))(b T ) T Note that the objective function takes on value 0 at T = b and is strictly positive at T (s(η),b). Therefore the solution to the problem Tb (s(η),b)ifs(η) <b. T b is such that This implies inefficiency since Mr 2 will reject the offer whenever b>s>t b.