A firm produces an output Q that generates environmental damages according to the

Transcription

1 Old Exam Solutions (Part ) Question (worth points) A firm produces an output Q that generates environmental damages according to the following marginal damage function: MD ( Q) Q. The firm s marginal benefit schedule is given by MB ( Q) Q, and the firm s marginal private cost of production is MPC ( Q) for all output levels. a) Plot the relevant curves in the space below, and label your diagram clearly. ( points) $ MB - Q MD Q MPC Q [one point for each curve, and for adequate labeling.]

2 b) Solve explicitly for the level of output, Q, that the firm would choose in the absence of regulation. Please show your calculations. ( points) The firm s profit-maximizing output level, Q, solves MB(Q) MPC(Q) or Q Q. c) Suppose the government introduced a Pigouvian subsidy as a means of regulating the polluting firm. What level would the subsidy be set at? In answering this part of the question, please explain how the Pigouvian subsidy should be set, and show your calculations. ( points) First, we need to solve for the efficient output level. In order to do this, we need to calculate the MSC, where MSC MPC + MD Q +. Q*, the efficient level of output, is found where MB(Q) MSC(Q), or Q Q +, implying Q* /.

3 The Pigouvian subsidy should be set equal to MD(Q*), so s /. d) What would the total amount of subsidy paid by the government be? Please show your calculations. ( points) The total subsidy s * (firm output reduction), where Firm output reduction Q Q* /. Therefore the total subsidy 9/ ¼. Question (worth points) a) In circumstances in which the Coase Theorem holds, is government intervention necessary in order to solve environmental problems? Please explain. [Two sentences.] ( points) Under the Coase Theorem, voluntary agreements umong interested parties are sufficient to solve externality problems. In such circumstances, government intervention is not necessary. b) If a regulator wishes to minimize the expected losses associated with the incorrect setting of a regulatory instrument, under what circumstances should a quantity instrument be chosen? Please explain, giving an example of a quantity instrument. [Two sentences.] ( points) A regulator should choose a quantity instrument if the absolute value of the slope of the MC schedule exceeds the absolute value of the slope of the MB schedule, according to Weitzman s rule. Generally speaking, that will minimize the expected loss associated with any incorrect setting of the regulatory instrument. c) Explain clearly the sense in which a permit trading scheme is optimal. [One sentence.] (5 points) A permit trading scheme is optimal in the sense that it will always attain a given emissions target at the lowest total abatement cost to society.

4 Notes: As we discussed in lecture, permit trading schemes always achieve one form of efficiency: they always minimize total abatement costs subject to hitting a given pollution target. This is the sense in which any permit-trading scheme is optimal. Permit trading schemes do not, in general, attain overall efficiency. Please note the form of the question: it is asking you to give the sense in which a permit trading scheme is optimal. It also makes clear that the perfect answer can be given in just one sentence. Your answer should be of the form: A permit trading scheme is optimal in the sense that recalling our class discussion about the different senses of efficiency in the context of environmental policy making. Question (worth 0 points) Consider an industry in which two polluting firms, firm I and firm II, have identical downward-sloping marginal benefit of pollution emissions curves. To regulate the firms, the regulator introduces a permit trading scheme. a) Suppose both firms have the same initial permit allocation. What is the permit trading equilibrium, and why? [One sentence.] ( points) The permit trading equilibrium will involve no trades, because both firms have the same marginal benefits of emissions at the initial permit allocation. Each firm will emit an amount equal to its initial permit allocation, and the equilibrium permit price will be equal to either firm s marginal benefit of emissions at that emissions level. b) Now consider an alternative situation in which firm I is allocated e I e T I permits and firm II is allocated e II e T II permits, where e T T II e I and e T II < e 0. (These permit allocations are illustrated in the diagram below.) What will the permit trading equilibrium be, and why? Please give a verbal explanation and also illustrate your answer clearly in the diagram. [Note: you must provide both to earn the points.] (6 points) $ MB A A

5 P emissions T e I + e T II Note here that the two firms have different marginal benefits of emissions, given the initial permit allocations, with firm I having a higher marginal benefit than firm II. Thus firm I will have an incentive to buy, due to its higher valuation, and firm II will have an incentive to sell. In equilibrium, two conditions hold:. the amount bought equals the amount of permits sold. Thus, suppose firm I buys A units. Then firm II will sell A units.. Further, in equilibrium, marginal benefits must be equal across both firms. These two conditions are both satisfied if A (et_ii et_i)/. Question (worth 7 points) The electricity generation industry produces significant pollution emissions. Suppose it has N firms with low marginal benefit of emissions schedules, and N firms with high marginal benefit of emissions schedules. To regulate emissions, a permit trading scheme operates in this industry. (Throughout this question, take the supply of permits to be fixed.) Conditions in other sectors of the economy affect entry into and exit from the industry. Consider a situation in which other sectors became less profitable relative to the electricity generation industry.

6 a) What do you anticipate happening to the number of firms in the electricity generation industry and why? [One sentence.] ( points) The number of firms will increase as firms from outside the electricity generating industry seek relatively higher profits by entering this industry. b) Qualitatively speaking, what do you predict will happen to the equilibrium permit price in light of your answer to part a)? [That is, will the price fall or rise?] Explain your answer clearly. [Two sentences.] [Hint: a diagram may be useful here.] (5 points) The permit price will rise. This is because the industry marginal benefit schedule will shift out to the right while the supply curve remains fixed. Question 5 (worth 5 points) A regulator imposes quantity standards on two polluting chemical firms, firm and firm. The first chemical firm has a marginal benefit of emissions schedule where MB 6 e e emissions schedule MB gives the emissions of firm. The second firm has a marginal benefit of 9 e, where e gives the emissions of firm. 5a) Draw the two MB schedules carefully in the space below, labeling your diagram appropriately. ( points) $

7 9 6 emission 6 5b) What emissions level would each firm choose in the absence of any regulation? Please solve for each firm s choice explicitly. ( points) Each firm should choose e where MB MPC or 6 e and 9 e 0 e 0 e 6 6 Thus, both firms would set their emissions equal to 6 in the absence of regulation. 5c) Under the quantity regulation regime, the regulator gets firm to abate by unit and firm to abate by units. What are the resulting marginal benefits of emission levels for each of the two firms? Please show your calculations. ( points)

8 MB MB 6 e MB 9 e MB. where where e 6 5 e 6 5d) Is the solution in part c) the total abatement-cost minimizing solution, and why? [Two sentences.] ( points) At the total abatement-cost minimizing solution, MB s must be equalized. Here, this is not the case. Thus changes in abatement costs can further reduce total abatement costs. 5e) Intuitively, what (if any) adjustments to abatement levels should be made in order to reduce total abatement costs further, and why? [Here, say in what (if any) direction each firm s abatements should adjust.] Explain your answer. ( points) Given that the MB of firm at e exceeds the MB of firm at e 5, a small increase in firm s emissions by an amount ε and a correspondingly small reduction in firm s emissions by an amount ε will serve to reduce total abatements overall. 5f) Solve for the emissions levels of the two firms that minimize total abatement costs. Explain your approach clearly. (8 points) Given we have two firms and the target overall abatement units, we can solve for the relevant emissions levels by deriving the equilibrium outcome under a permit trading scheme. Suppose each firm is given an initial permit allocation of e i. (Clearly, each firm would be abating by two units, so the aggregate abatement target is met.) It is straightforward to derive the permit trading equilibrium. We need to solve for in the diagram below:

9 MB $ MB e 6 Note that solves ( ) ( ) ( ) ( ) or MB MB * * + e and e Thus Now we can check to see whether the respective marginal benefits of emissions across the two firms are equal. (This is a necessary condition for total abatement cost minimization.)

10 MB MB * ( e ) * ( e ) Thus the two marginal benefit levels are equal. Question 6 (worth 6 points) A regulator imposes one performance standard, at Q, on two polluting firms, even though the two firms have different MB curves. (In particular, MB (Q) MB (Q) + C, as in the diagram below.) A policy maker argues that it would be more efficient to reduce the standard, moving it towards Q in the diagram. Please comment. [Hint: in answering this question, you will need to use the information given underneath the diagram.] $ MSC MB MB * Q Q Q Q

11 Note that MB MB + C, implying that the two MB curves are parallel (and hence the arrows drawn on them). Note also that the vertical line extending above Q is in three portions. The top two portions are of equal length, as indicated by the two short horizontal lines. Reducing Q incrementally must increase inefficiency. While the loss triangle on the left gets smaller, the one on the right is now made bigger, and by a more than offsetting amount. Thus the total sum of the losses must increase.

12 Question 7 (worth 7 points) Toronto has two types of residential neighborhood: those in the suburbs and those downtown. In order to assess the benefits of environmental improvements, researchers wish to estimate household valuation of clean air using a hedonic price regression approach. Suppose air quality in location i is measured by Ai, which increases as the air gets cleaner. Suppose also that air quality is cleaner in the suburbs than downtown. The researchers plan to estimate the following hedonic model, with data on house prices (Pi), house size (Hi), neighborhood attributes (Ni), and air quality (Ai): Pi a_0 + a_ Hi + a_ni + a_ai + v_i where v_i represents factors unobserved to the researcher. The true model is Pi a_0 + a_ Hi + a_ni + a_ai + a_xi + e_i, where some variable Xi is omitted. Suppose that Xi measures local traffic congestion (with Xi being higher, the higher the congestion). As congestion rises, so air quality deteriorates. Further, a_ is negative in the true model. Based on this information, if the congestion measure is omitted from the estimated model, what effect will this have on the estimate of a_? Please explain clearly. If the congestion measure is omitted, the estimated coefficient will be biased upward. To see this, note that we would expect the true value of a_ to be positive. Thus a curve with house prices on the vertical and air quality on the horizontal axes would be expected to have a positive slope. Now, where Ai is high on average, we would expect congestion to be low. That will tend to be an additional factor leading to high house prices. Thus the estimated line will pick up (at high levels of Ai) _both_ clean air and low congestion, leading to the coefficient to be overstated, and the estimated line to appear steeper than it actually is. The reverse is true at low levels of Ai, but again leading the estimated line to be steeper than the true line.