Tutorial Notes: Externalities

Transcription

1 Tutorial Notes: Externalities Jeff Hicks October 19, 2017 Vancouver School of Economics, University of British Columbia, 1

2 In this note, I ll go over examples of externalities and the policy approaches covered by Kevin. We will practice the numerical examples in tutorial. Basic Setup We will assume there are two individuals. Consumer 1 consumes a good or undertakes an activity that imposes an externality on consumer 2. We call this externality a. Examples of negative externalities are the amount of sulphur dioxide (SO2) emission, or something simpler like the amount of noise I impose on my neighbor at night. I ll focus on negative externalities for now, but we could similarly think about positive externalties. Let s use an example. Consumer 1 is Bob. Bob is a farmer who use fertilizer. Bob s farm is next to a river. On the river, Jay the fisherman makes his living. Fertilizer runs-off into the river, weakening the stock of fish, which is bad for Jay. Assume that Bob s marginal benefit of fertilizing is MB = 5 a. The marginal cost to Jay of the fertilizer is MC = 2a. These are graphed below. 1

3 Pareto Efficient Outcome The pareto efficient outcome is defined as the level of fertilizer such that in order to improve one person s outcome, we must worsen the other person s outcome. Call this point â. This is the point at which Jay s marginal cost intersects Bob s marginal benefit: MB = MC (1) â = 5 3 (2) 2

4 No Government Action - No Property Rights If left unchecked, Bob will use fertilizer until his marginal benefit is 0 (a = 5). In the absence of property rights, Bob and Jay cannot reach an agreement because it would not be enforceable by the government. Can you think of some examples where property rights are hard to define or enforce? I (Jeff) work in an office with 26 other students. Their talking distracts me. It is an externality imposed on me. But property rights don t exist, so I suffer through it. Obviously, social norms can mitigate the problem. I can send angry glares to my colleagues. But this is imperfect. They still talk. I still talk. Property Rights Property rights can be assigned in two ways: 1. Bob is given ownership over the right to pollute. 2. Jay is granted the authority to restrict Bob s usage of fertilizer. Property Rights Assigned to Polluter (Bob) When property rights are assigned and enforced, the two parties can arrange mutually beneficial agreements. At a, the marginal benefit of the polluter is zero. The marginal cost to the non-polluter is very high. Consequently, the non-polluter (Jay) would be willing to pay the polluter to reduce. This logic is true everywhere to the right of â. To the left of â, the marginal benefit to the polluter (Bob) is higher than the marginal cost to the non-polluter. To persuade the polluter (Bob) to stop, they need to be compensated by at least as much as their marginal benefit. But the non-polluter (Jay) is not willing to pay that much. Property Rights Assigned to Non-Polluter (Jay) Similar logic holds here. Rather than paying the polluter to stop, the polluter would be paying for the right to pollute. 3

5 Quota The government could limit Bob to no more than a = 5. But in practice, for quotas to reach 3 the pareto efficient outcome, the government must know the marginal costs and benefits for all parties involved. This is an extremely high burden of information. And, if the government were to ask Jay and Bob what their costs and benefits were, they would both lie. Tax The government could tax Bob for each unit of fertilizer used. The optimal tax (t) is the difference between private benefit (Bob s marginal benefit) and social benefit (Bob s marginal benefit subtract Jay s marginal cost). So, this two person case, the tax is equal to Jay s marginal cost (at the pareto efficient outcome). So the optimal tax is t = 10/3. Let s examine Bob s choice given the tax. He uses fertilizer until his MB equals the tax ( 10 3 = 5 a a = 5 3 ) Notice again, there is a high burden of information to set the appropriate tax - the government must know Jay s marginal cost curve. But, in more realistic scenarios there are good reasons to prefer taxes for externality problems. Cap and Trade This is similar to the tax and property rights solution. The government will distribute permits for fertilizer. Holding a permit allows Bob (or anyone) to use fertilizer. If Jay holds all the permits to begin with, it will be advantageous for him to sell 5/3 s worth to Bob. They will negotiate a price somewhere between marginal cost and marginal benefit. For the final permit traded, what is the only possible price? Discuss with your class mates. Yet again, this solution requires the government to know what the appropriate amount of permits are, which requires knowing where Bob and Jay s marginal cost and marginal benefit curves cross. This is clearly unrealistic, especially in large economies with millions of potential polluters. The government has to choose how to distribute the permits initially. In practice, they typically just give them to the polluters. Perhaps preferably, they should auction the permits. 4

6 Cap and trade is used in many jurisdictions for carbon and sulphur dioxide emissions. I recommended reading (but it is not required) Goulder (2013) for a good discussion of cap and trade versus taxes in practice. References [1] Lawrence H Goulder. Markets for Pollution Allowances: What Are the (New) Lessons? In: Journal of Economic Perspectives 27.1 (2013), pp