EEP101/ECON125 Spring 00Prof.: D. ZilbermanGSIs: Malick/McGregor/St-PierreKey toPROBLEM SET 21.There are three polluting firms in the economy with marginal benefit curves given by: MB1= 75 –(5/4)q1 for firm 1, MB2 = 75 – q2 for firm 2, and MB3 = 75 – (3/4)q3 where qi (i=1,2,3)is theamount of emissions produced by each firma)The MB curve tracks the aggregate level of emissions. At any level of valuation (MB1 = MB2= MB3 = MB), aggregate emissions can be obtained by summing horizontally the three firms’curves. Analytically, you need to find the inverse of the MB equationsq1= 60 - 4/5 MB; q2= 75 - MB; and q3= 100 - 4/3 MB, and sum quantities:q1 + q2 + q3= Q = 235 – (47/15) MB; or inversely, MB = 75 – (15/47) Q = 75 – 0.32 Q(decimals are rounded off) Your graph should look like the following:2351007564.1303MB (aggregate)B2Q*/311.460Q*34.175v* = t*emissionsMSC1$b)Remember that “qi” does notrepresent the output of each firm, but instead the quantity ofpollution it emits. Firm 1 is more efficient in reducing that pollution. Intuitively, it is lessdependent on emitting pollution than others to create profits (think of emissions as inputs).Alternatively, reducing emissions would cost it the least.c)The optimal level of emissions (Q*) can be obtained by equating the marginal social costcurve with the aggregate MB curve: MSC = 30 + Q = MB = 75 – (15/47) Q , which impliesQ* = 34.1 (and MB* = 64.1).d)Since marginal benefits of emissions are already net of marginal costs, the optimal tax onemissionsis simply equal to the aggregate MB at the optimum quantity, which is MB* = 64.1.To find out the amount of emissions produced by each firm (q1*, q2*, and q3*) given the tax,simply substitute MB* = tax = 64.1 into the equations you calculated in part a. On the graph,those qi* quantities (8.7, 10.9, and 14.5, respectively) are at the intersections of the horizontalline running from the equilibrium point B to the left and each of the three MBicurves.
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