1. Two firms can reduce pollution at the following marginal abatement costs: MC1 = 12Q1 MC2 =...

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1. Two firms can reduce pollution at the following marginal abatement costs: MC1 = 12Q1 MC2 = 4Q2 where Qi is the abatement (pollution control) of firm i = 1, 2. In the absence of regulation, each firm would emit 40 units of emissions. Assume that each firm’s objective is to minimize its compliance costs.

(a) If the government decided to reduce total emissions by 20 units using a uniform emission standard (i.e. each firm reduces pollution by 10 units), what would be the total cost of abatement?

(b) Compare this to the cost-effective allocation of pollution control that reduces emissions by 20 units. How much pollution would each firm abate under a costeffective allocation? What would be the total cost of abatement?

(c) The aggregate marginal cost function for this two-firm industry is: MC = 3Q Show how to derive this function both graphically and analytically. (

d) Suppose the marginal benefit of pollution control is given by: MB = 35 − 0.5Q What is the efficient level of abatement?

(e) What is the relationship between cost-effectiveness and efficiency?

(f) What pollution tax would yield the efficient level of abatement you found in part (d)? If the pollution charge is levied on all units of emissions, how much revenue would the government receive? 1

(g) If instead the government wanted to use a cap-and-trade scheme to achieve the same goal, how many permits should the government issue? In equilibrium, what would be the price of a permit? If all of the permits were auctioned, how much revenue would be raised for the government?

(h) Suppose now that there is considerable uncertainty surrounding the costs of pollution abatement. In terms of our model, take this to mean that the aggregate marginal cost function in part (c) represents expected marginal costs. Actual costs could be much higher or lower. Assume there is no uncertainty regarding marginal benefits. In this situation, would a pollution tax or a system of tradable permits be more efficient?

(i) Suppose now that there is uncertainty regarding both the costs and benefits of pollution control and that the these functions are positively correlated. Would this new information change your answer to part (h)?