Question

Assume that scientific studies provide you with the following information concerning the benefits and costs of sulfur dioxide emissions: Benefits of abating (reducing) emissions: MB = 500 - 20A Costs of abating emissions: MC = 200 + 5A where A is the quantity abated in millions of tons and the benefits and costs are given in dollars per ton.

a. What is the socially efficient level of emissions abatement?

b. What are the marginal benefit and marginal cost of abatement at the socially efficient level of abatement?

c. What happens to net social benefits (benefits minus costs) if you abate one million more tons than the efficient level? One million fewer?

d. Why is it socially efficient to set marginal benefits equal to marginal costs rather than abating until total benefits equal total costs?

Answer 1

Efficient Abatement Level = 12 million tons

Efficient Marginal Benefit & Marginal Cost = 250

Abatement > Efficient Level : Net social benefit fall ; Abatement < Efficient Level : Net Social Benefit Rise

Socially Efficient setting MB = MC rather than TB = TC , as Net Benefit [ TB - TC] is maximised when MB = MC

Step-by-step explanation:

a. Socially Efficient level of output is when : Marginal Cost of Abatement = Marginal Benefit of Abatement .

MB = MC

500 - 20A = 200 + 5A

500 - 200 = 5A + 20A → 300 = 25A

300 = 25A → A = 300 / 25

A [Efficient Level of Abatement] = 12

b. Putting value of efficient A in MB & MC, we get :

MB = 500 - 20 (12) = 500 - 240 = 260

MC = 200 + 5 (12) = 200 + 60 = 260

c. If one million more abatement than efficient level is done, MC > MB & net social benefit will decrease. If one million less abatement than efficient level is done, MC < MB & net social benefit will increase.

d. Total Benefit & Total Cost are total gain & cost due to all the units of abatement. Marginal Benefit & Marginal Cost are addition to total benefit & total cost by an additional unit of abatement. Net Social Benefit is maximum when difference between TB & TC is maximum, which is so when they are parallel & their slopes MB & MC are equal.