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Question: 2 tax quantity control and permit two power plants provide...

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2. Tax, Quantity Control and Permit. Two power plants provide power to Bradford residents: plant UN and plant DC. Both plants burn coal to produce electricity, and consequently produce smog as a by-product. The total benefit of smog abatement to Bradford is 100(xv x). The UN power plant could reduce its smog at a total cost of where xu indicates the total number of units of smog abated by UN The DC plant is slightly less efficient, and its total cost of reducing smog by aois: (a) Calculate the socially efficient levels of abatement for each power plant Bradford considers giving plants subsidies for smog abatement. How much subsidy (per unit of smog abated) should be given in order to reach the abatement amounts you calculated in part (a)? (b) (c) Write down each plants optimization problem under the subsidy, and show that each will privately choose the socially optimal abatement amount. (d) Suppose that instead of taxation, Bradford tries to regulate quantities. However, it cannot write a separate law for each plant, so it simply declares that both power plants must cut down on smog by ao1. Show that this is not efficient with BOTH math and intuition.

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