Externalities, II. Philip A. Viton. May 29, Philip A. Viton CRP 781 () Externalities II May 29, / 24

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1 Externalities, II Philip A. Viton May 29, 2012 Philip A. Viton CRP 781 () Externalities II May 29, / 24

2 Introduction I We have seen that in the presence of externalities (joint impacts + market failure) privately optimizing individuals will adopt the wrong (ie not Pareto-Optimal) levels of the activity: In the case of a positive externality they will choose a level that is too low. In the case of a negative externality they will choose a level that is too high. How can planners intervene so as to obtain the Pareto-Optimal levels? Philip A. Viton CRP 781 () Externalities II May 29, / 24

3 Introduction II The optimal level of an activity is where (where + means vertical addition). MC priv = MB priv + MB oth But with market failure, an individual will adopt a level of the activity where MC priv = MB priv Philip A. Viton CRP 781 () Externalities II May 29, / 24

4 Internalization I One solution is to force the individual to confront a different level of costs, MC priv + Z = MB priv such that he or she will now make the correct decision. Clearly, we want Z = MB oth because with Z set this way, the individual will confront MC priv MB oth = MB priv MC priv = MB priv + MB oth and will choose the correct level of the activity. This is known as internalizing the externality. Philip A. Viton CRP 781 () Externalities II May 29, / 24

5 Internalization II The essential idea is to ensure that people make their decisions based on the full impacts of their actions (that is, in our examples MC priv weighted against This is known as Philip A. Viton CRP 781 () Externalities II May 29, / 24

6 Internalization III The simplest way to do this (conceptually) is via fees and subsidies. This would involve a subsidy in the case of a positive externality to encourage an actor to do more of an activity that provides an external benefit to the community.. The subsidy would be equal to the value of the marginal benefit (MB oth ) that the actor provides to the community (neighbors) via the level of the activity chosen by his or her level of the activity. It would involve a charge ( user fee ) in the case of a negative externality, to encourage the actor to do less of an activity that provides an external cost to the community. The fee schedule in this case would be minus the marginal benefit MB oth (since MB oth is negative) that the actor provides to the community. Philip A. Viton CRP 781 () Externalities II May 29, / 24

7 Internalization IV For the house-painting (positive externality) example, Columbus has an approximation to such a subsidy system : it will loan you tools (ladders etc) for free to help you paint or maintain your house. But this subsidy is not geared to the level of the activity: it is a constant, not MB oth which varies with the level of the activity. Philip A. Viton CRP 781 () Externalities II May 29, / 24

8 Pollution Example I Consider a factory located in an urban area, emitting noxious fumes/particles as part of its production process. Is there an externality here? Arguably yes, since: Pollution will affect the factory owner herself (and she will take this into account). The pollution will also affect the neighbors, and this is an impact that typically the factory owner will not take full account of. (Though she might take partial account of it, if for example, the neighbors are workers in the factory, and their getting sick affects the factory s productivity). This is the non-existence-of-markets aspect of the pollution problem. In other words, pollution gives rise to a standard negative externality. The same argument applies for example to pollution emitted by cars, rather than by factory owners. Philip A. Viton CRP 781 () Externalities II May 29, / 24

9 Pollution Example II Let s pursue the factory pollution example a bit more. From the point of view of the factory owner (producer) the freedom (ability) to pollute is an input just like any other input. The more pollution the factory can emit, the more output can be produced. We can therefore think of the marginal product of the pollution emitted: the increase in output per unit of additional pollution, holding all other inputs constant. The value of the marginal product of pollution (VMP P ) is the output price multiplied by the marginal product of the pollution. It represents the factory owner s marginal revenue obtained by allowing it to add one more unit of pollution to the air. We represent VMP P as a downward-sloping curve, reflecting a diminishing marginal product. Philip A. Viton CRP 781 () Externalities II May 29, / 24

10 Pollution Example III $ VMP P pollution With no internalization of the externality, the factory will increase the pollution it emits until the VMP P is zero (ie until increasing pollution levels results in no revenue gain). If it faces a marginal cost of p per unit of pollution, it will increase pollution levels until the marginal cost of emitting one unit more of pollution (ie, p) equals the marginal benefit (the VMP P ) of doing so. Philip A. Viton CRP 781 () Externalities II May 29, / 24

11 Optimal Pollution I From a public policy standpoint, the optimal amount of pollution should balance the negative impact on the community against the benefit of allowing the polluter to emit noxious chemicals into the air (where the benefit is the value ot the community of producing the factory s output). Philip A. Viton CRP 781 () Externalities II May 29, / 24

12 Optimal Pollution II Represent the marginal cost (ie the negative of a negative MB comm ) to the community (as a function of pollution levels) by MC comm. Arguably, the MC comm is low at low levels of pollution (with little existing pollution, allowing a bit more probably won t have much impact). But when the air is already highly polluted, adding a bit more to the pollution will probably have large cost (health) impacts on the community. So MC comm is likely to be upward sloping. The Pareto-optimal level of pollution is where the marginal benefit to the producer (ie VMP P ) equals the marginal cost imposed on the community, MC comm. Note that the optimal pollution level is not zero. Philip A. Viton CRP 781 () Externalities II May 29, / 24

13 Optimal Pollution III $ MC comm The Pareto-optimal amount of pollution is E E * VMP P pollution Philip A. Viton CRP 781 () Externalities II May 29, / 24

14 The Policy Dilemma In order to regulate pollution emissions and bring about the Pareto-Optimal amount, the planner needs to know both the community impact (MC comm ) and the benefit of allowing the pollution (VMP P ). We can assume that with some research, the planner can discover the community cost But typically the benefit to the polluter is private information. Moreover, if asked, the polluter has an incentive to exaggerate the positive impact (in order to allow it to continue polluting). How can the planner help here? Philip A. Viton CRP 781 () Externalities II May 29, / 24

15 The Coase Solution I Suppose that negotiation between the polluter and the community (represented, eg, by the planner) is costless. Ronald Coase suggested that any assignment of property rights plus costless bargaining between the parties will lead to the right solution. This amounts to assigning ownership in the resource in question (here, air) The important feature of Coase s suggestion is that any assignment of property rights (that is, assignment to either party) will result in the Pareto-Optimal solution. But note that this is asserted to work only with costless bargaining. Philip A. Viton CRP 781 () Externalities II May 29, / 24

16 Coase Solution II p 1 $ MC comm VMP P pollution Suppose the community owns the right to pollute the air. Then it will insist on zero pollution But at this level the cost to the community of allowing a bit more pollution (ie MC comm (0)) is essentially zero, while the benefit to the polluter (= p 1 ) is large. The polluter would therefore be willing to pay a fee of anything less than p 1 to pollute a bit As long as the fee was greater than zero the community would go along Philip A. Viton CRP 781 () Externalities II May 29, / 24

17 Coase Solution III p 1 p 2 $ E 1 E * MC comm VMP P pollution Suppose the polluter emits level E 1 Then the benefit to the polluter of being able to emit a bit more is VMP P (E 1 ) = p 1 The cost to the community of allowing this would be MC comm (E 1 ) = p 2 Since p 1 > p 2 the polluter could persuade the community to allow him to pay at least p 2 and allow him to pollute at level E 1. This would continue until the optimal pollution level E was reached. Philip A. Viton CRP 781 () Externalities II May 29, / 24

18 Coase Solution IV p 2 $ VMP P MC comm E 2 pollution Conversely, suppose the property right was owned by the factory. Then it would adopt pollution level E 2, where VMP P was zero. But then the community could offer anything up to p 2 to get the factory to emit a bit less. This would be acceptable to the polluter because that last bit of pollution has essentially zero value (VMP P is zero). The community could continue to do this, and the factory owner would agree until the Pareto-Optimal level is reached. Philip A. Viton CRP 781 () Externalities II May 29, / 24

19 Coase Solution, Summary In either way of assigning the property rights, bargaining between the parties eventually results in the Pareto-Optimal level of the impact. Note that we have assumed that negotiation is costless: when this is not true, we do not arrive at the Pareto-Optimal answer. This also relies on small numbers being involved: it is perfectly reasonable for the polluter to negotiate with the City Council or state EPA: it clearly will not work as well if he has to negotiate with individual affected people. Philip A. Viton CRP 781 () Externalities II May 29, / 24

20 Another Approach Suppose the Coase approach is not available to us. Remember that it involves an assignment of property rights to one actor or another; and this may be legally or politically infeasible. Can we construct another way to get the polluter to do the right thing in light of the fact that we do not know all the facts (ie the VMP P )? Philip A. Viton CRP 781 () Externalities II May 29, / 24

21 Iterative Scheme I p 1 p 2 $ E 2 E 3 E 1 MC comm VMP P pollution In the picture, VMP P is shown dashed to indicate that it is not known to us. Suppose we observe pollution level E 1. We announce a price to pollute based on MC comm, which we do know. The polluter takes this price as given and sets p 1 = VMP P based on his private information. This results in his polluting at level E 2. Philip A. Viton CRP 781 () Externalities II May 29, / 24

22 Iterative Scheme II When we observe pollution levels at E 2 we revise our price. $ Based on MC comm we set the new cost of polluting to p 2. At this new price, the polluter sets p 2 = VMP P (privately) at determines pollution level E 3. p 1 p 2 E 2 E 3 E 1 MC comm VMP P pollution Note that E 3 is less than E 1 : we have succeeded in reducing pollution. If you continue this, you will eventually arrive at the optimal level (where VMP P = MC comm ). Philip A. Viton CRP 781 () Externalities II May 29, / 24

23 Iterative Scheme III We have found a way to arrive at the Pareto-Optimal level of pollution without our having to know the private VMP P. The polluter has no incentive to misrepresent this data to us. In fact, he never tells us his VMP P ; rather, he just reveals several points on it by his behavior. The polluter s determination of his pollution level via price = VMP P is dictated by pure selfishness (ie profit-maximization). Philip A. Viton CRP 781 () Externalities II May 29, / 24

24 Caveat Will this always work? No: you can adjust the slopes of the curves to come up with an example where at the end of one complete iteration E 3 > E 1. In this case the adjustment process blows up and will not result in a Pareto Optimum. On the other hand, when this happens, it will be obvious fairly quickly. Nonlinear functions can complicate this even further: in this case, you can just try it and see if it converges or not. Philip A. Viton CRP 781 () Externalities II May 29, / 24