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HW2,SP2000sols

HW2,SP2000sols - EEP101/ECON125 Spring 00 Prof D Zilberman...

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EEP101/ECON125 Spring 00 Prof.: D. Zilberman GSIs: Malick/McGregor/St-Pierre Key to PROBLEM SET 2 1. There are three polluting firms in the economy with marginal benefit curves given by: MB 1 = 75 – (5/4)q 1 for firm 1, MB 2 = 75 – q 2 for firm 2, and MB 3 = 75 – (3/4)q 3 where q i (i=1,2,3) is the amount of emissions produced by each firm a) The MB curve tracks the aggregate level of emissions. At any level of valuation (MB 1 = MB 2 = MB 3 = MB), aggregate emissions can be obtained by summing horizontally the three firms’ curves. Analytically, you need to find the inverse of the MB equations q 1 = 60 - 4/5 MB; q 2 = 75 - MB; and q 3 = 100 - 4/3 MB, and sum quantities: q 1 + q 2 + q 3 = 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: 235 100 75 64.1 30 3 MB (aggregate) B 2 Q*/3 11.4 60 Q* 34.1 75 v* = t* emissions MSC 1 $ b) Remember that “q i ” does not represent the output of each firm, but instead the quantity of pollution it emits. Firm 1 is more efficient in reducing that pollution. Intuitively, it is less dependent 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 cost curve with the aggregate MB curve: MSC = 30 + Q = MB = 75 – (15/47) Q , which implies Q* = 34.1 (and MB* = 64.1). d) Since marginal benefits of emissions are already net of marginal costs, the optimal tax on emissions is 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 (q 1 *, q 2 *, and q 3 *) given the tax, simply substitute MB* = tax = 64.1 into the equations you calculated in part a. On the graph, those q i * quantities (8.7, 10.9, and 14.5, respectively) are at the intersections of the horizontal line running from the equilibrium point B to the left and each of the three MB i curves.
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