Problem%20Set%206%20-%20%20Answerkey - Economics 131 Fall...

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Unformatted text preview: Economics 131: Fall Quarter 2009 Problem Set #6 Answer Key Question 1 The government of Babbage found out that the pollution level in its river Tiva is too high. In an effort to deal with this problem, the president brought the brightest minds among economists and ecologists in the country together to discuss possible policy options. The ecologists agreed on passing a new law where each firm can only produce a certain level of pollution. The economists disagreed with the ecologists and said that imposing a tax can get the target level of pollution. (a) In theory, assuming that you can get all information you need and given a target level of pollution, which policy is efficient? Explain clearly. The policy that the economists proposed is efficient because it sets the marginal abatement costs of all different firms equal to each other, whereas the command-and-control policy proposed by the ecologists generally leads to inefficiency, because (i) it is more costly to abate the same amount using the command-and-control policy and (ii) it is not dynamically efficient, as it does not incentivize using a more efficient technology. Note that the only case when the ecologists and the economists will lead to the same allocation of abatement levels across firms if one had firms with identical marginal abatement cost curves and identical starting levels of abatement. (b) In practice, is the policy you propose in A necessarily going to get you to the target level of pollution? The difficulty in implementing the tax policy is that one needs to know the marginal abatement cost curves of all firms in the market, which is generally impossible in practice. However, a cap- and-trade policy can be used instead. Question 2 So far, we have applied our tools to different environmental questions: (a) Rainforests (b) Water pollution (c) Bioprospecting For each of the above, (i) Explain what an economist defines as optimal for the specific question. If there are different ways of analyzing the problem, such as in the case of pollution one can think of pollution abatement vs. pollution level, please explain both and show how they are "mirror" images of each other. (a) Rainforest - Single harvest: V(t+1)-V(t)=rV(t), i.e. MB from delaying harvest by an additional period is equal to the marginal cost of delaying the harvest by an additional period Multiple harvest: (MBl(x)+MBg(x))/r=MH(x), i.e. where the present value of the marginal benefit of preservation equal the present value of marginal benefit of harvesting. (b) Water Pollution The efficient level of water pollution is defined by the MSC of pollution=MSB of pollution, similarly, the MSB of abatement=MSC of abatement. A policy to achieve a target level of pollution is efficient if for all firms 1,2,....,n, marginal abatement cost is the same, i.e. MACi=MACj for all firms i,j=1,2,...,n. This is why a tax policy or a cap-and-trade policy works in this context (c) Bioprospecting The process of bioprospecting has to stop when the expected marginal net benefit of an additional trial is equal to 0, i.e. V(n+1)-V(n)=(1-p)n(pR-c)=0 (ii) What is the main rule that we use to define optimality in all of these cases? In general, we use the idea of MB of an additional unit=MC of an additional unit. If different individuals are in a market, efficiency is defined by equating the MB or MC of all individuals. If the trade-off is between two different things that can provide benefits, then equating their MB curves will leave to the right solution. If there is a stream of benefits, then we should look at the present value. If there is uncertainty about costs and benefits, then we take the expected value of marginal net benefit. Question 3 Dangerous levels of harmful pollutants are being released into Hayden Lake. A portion of the pollution comes from one large steel refinery. The remaining pollution comes from fertilizer runoff used on two nearby farms. Assume the marginal benefit, in dollars/year, of each unit of pollution, x - tons/year, produced by the refinery is given by . Assume the aggregate marginal benefit to the farmers for each unit of pollution released is given by , where XF is the combined pollution generated by both farms. The social marginal cost of the pollution is given by . Currently no policies are in place to reduce the level of pollution. a) How much pollution will the refinery generate each year? How much pollution will the farms generate each year? b) How much surplus does the refinery receive from being allowed to pollute at the business as usual level? How much surplus do the famers receive? c) What is the total social cost of the business as usual level of pollution? What is the total economic surplus? The pollution generated by the refinery (a point source polluter) can be freely measured. The pollution from each farm (non-point sources) cannot be directly measured however. Therefore, the local government decides that it will impose a pollution tax on the refinery. d) At what level should the tax be set to maximize the total economic surplus? (Hint: since pollution generated by farmers is not taxed, the pollution they generate will remain unchanged from the business as usual case. Therefore, the social marginal cost of an additional unit of pollution from the refinery is given by .) The efficient level of pollution from the refinery (given the farms continue to pollute 50 tons) is 50 tons. To achieve this efficient level of refinery pollution, the tax should be set equal to the SMC created by the 50th ton of pollution from the refinery (which is the 100th ton of total pollution. Therefore, the tax on pollution from the refinery should be set at $50/ton. e) What is the total economic surplus under the tax policy solved for in part (d)? The refinery owner argues that a more efficient outcome could be reached if the government imposes some form of pollution regulation on the famers as well. Recall, the government cannot observe the amount of pollution each farmer produces. Therefore, a pollution tax cannot be imposed on the farmers. Instead, the government decides to require the farmers to use a fertilizer that does not create any pollution. f) With the new regulation on the farmers in place, at what level should the pollution tax imposed on the refinery be set? To achieve the new level of efficient pollution from the refinery, the tax should be set at $33.33/ton. This is equal to the SMC and the MB to the refinery from polluting 66.67 tons. g) Using the combined regulation and tax policy, what is the total economic surplus? Question 4 In the previous problem, we saw that it can be difficult to use a market mechanism (a tax, subsidy, or cap and trade policy) to reach the efficient level of pollution from non-point sources. If the pollution generated by each specific source cannot be directly measured, could a market mechanism still be used? If so, how? What other considerations besides economic efficiency must be considered in choosing between command and control regulations (technology standards for example) and market mechanisms? A market mechanism, which would require attributing the pollution to each specific farm, could still be used even if the pollution could not be directly measured. One method would be to estimate the pollution created by each farm. Additional topics that must be considered in choosing between multiple possible policies are listed on pages 246 and 247 of the text. These include fairness, environmental impact, administrative ease and costs, and political acceptability. ...
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