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The Fireyear and Goodstone rubber companies whose factories produce finished rubber and sell it in tothe highly competitive world market at a fixed price of $60 per ton. The process of producing a ton ofrubber produces a ton of air pollution that affects the environment. This 1:1 relationship betweenrubber output and pollution is fixed at both factories.Let the output of FireÃ¢â‚¬Âyear and GoodÃ¢â‚¬Âstone be QF and QG, respectively. The cost formulas for each firmare as follows:
FireÃ¢â‚¬Âyear Total cost: C = 300 + 2(QF)2Marginal cost is MC = 4QFGoodÃ¢â‚¬Âstone Total cost: C = 500 + (QG)2Marginal cost is MC = 2QGTotal pollution emissions generated are EF + EG = QF +QG. The marginal damage of pollution is constantper unit of E at $12
a) In the absence of regulation, how much rubber would be produced by each firm? What is theprofit for each firm?
b) The local government decides to impose a Pigouvian tax on pollution in the community. What isthe proper amount of such a tax per unit of emissions? What are the post regulation outputsand profits of each firm?
c) Suppose instead of an emissions tax, the government observes the outcome in part (a) anddecides to offer a subsidy to each firm for each unit of pollution abated. What is the efficient perunit amount of such a subsidy? Again calculate the levels of output and profit for each firm.
d) Compare the output and profits for the two firms in parts (a) through (c). Comment on thedifferences, if any, and the possibility of one or both firms dropping out of the market?
a)Profit is maximized where the first order condition is equal to zeroFor Fireyear,Profit function=60Q-(300+2Q2)First order condition=60-4Q60-4Q=04Q=60Q=15Profits= (60*15)-(300+2*152)…
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