EEP101/ECON125 Spring 99Prof D. ZilbermanTA's: Malick/Marceau2/23/991PROBLEM SET 2Due Tuesday, March 9, 1999, in class(Late assignments will not be graded)1. Assume there are two polluting firms in the economy with marginal benefit curvesgiven by: MB1= 100 – 2q1 for firm 1, and MB2 = 100 – (2/3)q2 for firm 2, where qi,i =1,2 , is the amount of emissions produced by each firm.a) Find the aggregate marginal benefit curve. (Hint: Find the horizontal sum of theindividual MB curves). Draw each of the three curves in a single graph.b) Which firm is more efficient in reducing pollution? Explain.c) If the marginal social cost curve is given by MSC = 40 + q, what is the optimallevel of emissions (Q*) to be produced? Show both the MSC curve and Q* onthe same graph.d) What is the optimal tax to be levied to achieve Q*? Given this tax, find theamount of emissions produced by each firm, q*1 and q*2. Show these levels onthe same graph.e) Given the optimal tax, what is the total cost of reducing emissions up to q*1 andq*2?f) Suppose that instead of a tax, the government decides to use a uniformstandard equal to Q*/2. What is the level of emissions produced by each firm?Show it on the graph.g) Compare the level of emission produced by each firm under the tax and underthe uniform standard. Which firm produces more/less than before? Comment.h) What is the total cost of achieving the optimal level of emissions under theuniform standard? Compare it to your answer in (e). Which scheme is moreefficient in achieving the optimal pollution level? Explain.i) Under what conditions would a tax or a standard be equally efficient in reachingthe optimal pollution level? Explain.j) Which scheme (tax or standard), do you think, provides more incentives forinvesting in cleaner technologies? Explain.2. Assume there are ten firms in the economy, labeled A through J. Each of thesefirms employs a fixed-proportions technology and produces different quantities of agood (Q). Each firm requires different amounts of labor (L), and each firm producesdifferent amounts of pollution (Z). The following table summarizes this information.EEP101/ECON125 Spring 99Prof D. ZilbermanTA's: Malick/Marceau2/23/992The unit price of the good (P) is $10, the unit price of labor (W) is $10, and the taxper unit of pollution (V) is $8. Given the information above, answer the followingquestions. (Hint: It might be useful to use a spreadsheet)a) Which firm has both the lowest input per output rate and the lowest pollutionper output rate. Provide the numerical value of these rates.b) Which firms are not going to be able to compete at the given prices? Determinethe total aggregate output of the surviving firms? Determine the total aggregatepollution level of the surviving firms?c) Assume that the price of labor (W) increases by two dollars to $12 per unit ofoutput. Which firms are not going to be able to compete now? What effect doesthis increase in W have on the total pollution level of the surviving firms? On thetotal output level of the surviving firms?d) Continue to assume W=12 and P=10, but suppose now that you want toeliminate the tax and use a standard (quota) instead. This standard will restrictthe pollution per output rate allowed to have by each firm.If you want to have the same aggregate pollution level that you had with thetax, what is the maximum level of pollution per output that you would alloweach firm to produce? Which firms are not going to be able to compete underthis standard?e) Compare the aggregate output that you would have under each of the twoalternative policies. Which policy (tax or standard) produces the most outputwhile achieving the same pollution level found in (c)?Output Labor PollutionFirm(Q)( L )( Z )A 21 18 10B 50 32 10C 70 35 10D 60 55 10E 22 5 10F 35 15 10G 18 8 10H 25 16 10I 15 5 10J 95 20 10EEP101/ECON125 Spring 99Prof D. ZilbermanTA's: Malick/Marceau2/23/9933. You have plenty of information about the social costs of pollution, and you are mostcertain that the marginal social cost of pollution is given byMSC = 10 + ¾qwhere q is the pollution level.Unfortunately, you do not have enough information about the marginal benefits ofpollution. Suppose the true marginal benefit curve is given byMB = 50 - ½qbut you do not know this. Instead, you have a recent estimate of the marginalbenefits. The estimated marginal benefit curve is given byMB = 60 - ½qIn other words, you have an overestimation of the true marginal benefits of pollution.In this case,a) Would you use a tax or a standard (quota) to control pollution? Explain.b) Calculate the deadweight loss under each alternative policy.c) Would your answer in (a) be different if the slope of the MB curve were 5/4instead of 1/2? Explain.d) Would your answer in (a) be different if the slope of the MSC curve were 1/2instead of 3/4? Explain.e) Would your answer change if instead of having uncertainty about the MB, wewould have uncertainty about the MSC?