Suppose that in the absence of any corrective measures, the economy generates 750 megatonnes (Mt) of GHG emissions (E) per year. The damage created by an additional Mt of emissions is called the marginal damage. Assume the marginal damage function is MD = 0.04 E. Thus, if E = 750 Mt, the additional damage to society associated with one more Mt of emissions is $30. The marginal abatement cost, the additional cost associated with a one Mt reduction in emissions, is given as MAC = 45 - 0.06 E. When there is no abatement, E = 750 Mt and the marginal cost of abatement is zero. MD and MAC are illustrated below. Emissions are measured on the horizontal axis in megatonnes per year and the vertical axis is measured in dollars.

a. If E = 600 Mt, how much abatement (emissions reduction) has occurred? What is the marginal cost associated with lowering emissions by an additional Mt when E = 600? What is the marginal benefit of an additional Mt reduction in emissions when E = 600 (i.e., what is the marginal damage prevented)?

b. If E = 600, calculate total abatement costs as the area below the MAC curve between 600 Mt and 750 Mt. Calculate total benefits from lower emissions as the area under the MD curve between 600 Mt and 750 Mt.

c. For this economy, what is the socially optimal level of emissions, E*? (Hint: From an efficiency standpoint, emissions should continue to be reduced as long as the marginal benefit from emissions reductions exceeds the marginal abatement costs.)

d. Suppose the government imposed a tax on emissions equal to $12 per Mt of greenhouse gas emissions. How does the tax affect total emissions in the economy? Is the tax sufficient
to reduce emissions to E*? Why or why not? 

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$per Mt MD MAC 0 100 200 300 400 500 600 700 750