Question

Environmental Economics

The table below shows the marginal abatement costs of three firms for various levels of emissions. Each firm is currently emitting 10 tons per week, so total emissions are 30 tons per week. Suppose we wish to reduce total emissions by 50 percent, to 15 tons per week.

Emissions (tons/week)	10	9	8	7	6	5	4	3	2	1	0
Marginal abatement costs ($/ton):
Firm A	0	1	2	3	6	10	14	18	23	30	38
Firm B	0	2	3	7	12	18	25	36	42	48	56
Firm C	0	6	12	18	24	30	36	42	54	69	86

        a.     Calculate the total cost of reducing emissions (TAC) to 15 tons per week with an equi-proportional decrease in emissions. Show your calculation, clearly indicating the emission level and TAC for each firm. Keep in mind that the above table shows the MAC, not the TAC.

        b.    Calculate the total cost of reducing emissions (TAC) to 15 tons per week in a manner that meets the equimarginal principle. Again, show your calculation, clearly indicating the emission level and TAC for each firm.

        c.     What is the difference in the overall TC of abatement between the equimarginal allocation compared to the equi-proportional allocation and which is lower?

Answer 1

Equiproportional Decrease will be equal decrease for each firm i.e. 5 units per firm

Total abatement cost for first five unit for firm A=1+2+3+6+10=$22 for B=2+3+7+12+18=$42,For C=6+12+18+24+30=$90 Hence, Total abatement cost through equiproportional Decrease=90+42+22=$154 (a)

b) in equimarginal decrease decrease is done with last unit reduced having same marginal cost across firms

Total unit needs to be reduced =15 now 7th unit of reduction from A cost $18 which is same for 5th unit in B and3rd unit in C so total abatement of unit=7+5+3=15 which is what the target was, Hence cost for A=1+2+3+6+10+14+18=$54, For B=2+3+7+12+18=$42 and for C=6+12+18=36 so, Total abatement cost=54+42+36=$132

c) Equimarginal abatement cost is lower than equiproportional by 154-132=$22