There are two major cities, A and B. Because workers commute from suburbs to cities, traditional work technology generates a negative externality in the form of infectious disease transmission of 4000 new cases per day to other cities, whose healthcare systems then have to treat cases that did not originate within their borders. In order to not overwhelm the health care system, the government mandates a 50 percent reduction in traditional work, which we assume to directly reduce the number of new cases per day by 50 percent as well (so one for one in percent terms). However, the marginal costs of case reduction differ between the two cities, probably because they have different virtual work technology (so imagine City A is New York City, where internet speeds are fast, reliable, and widespread, while City B is New Orleans, whose suburbs do not necessarily have the same infrastructure). Denote by Ri the amount of case reduction for each city i = A, B: MCA = 200 + 5RA MCB = 50 + 10RB Societys marginal benefit from reducing the new cases coming out of New York City and New Orleans is: SMB = 700 5RT where RT = RA + RB. (a) To reach the socially optimal level of pollution, by how much should each firm reduce traditional work, taking into account their different costs of doing so? 4 pts (b) If the government were to give each firm an equal number of traditional work permits to implement your answer in part (a), which city would propose to buy more permits from the other plant, and how many permits will be traded? 3 pts each, so 6 pts (c) If the government were to instead use a tax to achieve the socially optimal level of traditional work reduction, what should the per traditional worker amount of tax be? 5 pts (d) Draw a graph that depicts your answers to parts (a), (b), and (d). (It doesnt have to be to scale.) 5 pts (e) If the government did not allow permits to be traded, what would be the deadweight loss of giving each firm an equal number of traditional work permits? 5 pts (f) If the government implemented the tax you calculated in part (c), what would be the resulting deadweight loss?