cemex and holcim are two cement manufacturers durham they produce cement and sell it competi

CEMEX and Holcim are two cement manufacturers in Durham. They produce cement and sell it into a competitive world market at the fixed price of $60 per ton. Producing one ton of cement also produces one ton of air pollution that negatively impacts Durham. Suppose that the one-to-one relationship between cement and pollution production is immutable at both factories. The total cost to CEMEX of producing QC units of cement is 500 + (QC)^2 and the total cost to Holcim of producing QH units of cement is 300 + 2(QH)^2. Total pollution is EC + EH = QC + QH. Marginal damages from pollution are equal to $12 per ton of pollution. In the absence of regulation, how much cement does each firm produce? What are the profits for each firm? And what is total production and total profit? What is the optimal quantity of cement production? Suppose the local government imposes the optimal uniform standard on pollution. How much cement does each firm produce? What are the profits for each firm and total profits? Now suppose the local government allows the firms to trade permits. What is the price of the permits? How much does each firm produce? What are profits for each firm and total profits? Suppose instead that the local government imposes a Pigouvian tax on pollution. What is the amount of the optimal tax? How much does each firm produce? What are profits to each firm? What is the amount of government revenue and what are total profits to the firms? Do the firms prefer the tax or the tradable permits? Would your answer change if the government auctioned the permits rather than allocating them uniformly? If so, how? Finally, suppose the local government knows it has estimated the marginal damages with error. If the true damages are in fact $8, what are the losses under a quantity policy versus a price policy? Which policy should the local government use if it wants to minimize the losses from a mistake?
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