Question

2. The table shows the emissions of two sources and the marginal abatement costs (MCC, 1,000/week) Emissions 12 1 10987654320 tons/week MCC. Source! | Ο | 1 | 2 | 3 | 4|ST 8 10T 14T 24|38|70 MCC: Source0 2 4 6 10 14 20 25 31 38 5894 160 Suppose that initially each source is emitting at the uncontrolled level (12 tons a week) so total emissions are 24 tons. Now assume that we want to reduce overall emissions to half the present level, or a total of 12 tons a week. There are two ways to allocate emission control. a. Calculate the total costs of decreasing emissions equiproportionally (each source reduces by 50 percent). b. Calculate the total costs with a decrease that meets the equimarginal principle

Answer 1

Marginal abatement cost is 1000€ per week.

a. In uncontrolled situation total emission is 12 tons + 12 tons = 24 tons per week. If the target is to reduce the emission by 50% then total emission should be 12 tons per week. If we reduce from both source by 50% then from source 1 there will be 6 tons of emission and from 2 there will be 6 tons of emission. If we reduce from source 1 total abatement cost will be 0+1+2+3+4+5 = 15 i.e 15,000€ per week. It is because if we allow upto 6 tons per week so from 7 ton of each source we need to consider the abatement cost. So from source 1 the total abatement cost will be 15000€. Now from source 2 the total abatement cost will be 0+2+4+6+10+14 = 36 i.e 36000€ per week if we also allow 6 tons of emission from source 2. So total cost of decreasing equi proportionately fro both source is 15000+36000= 51000€ per week.

b) Now according to equi-marginal principle we know that we need to reduce the emission from each source so that their marginal abatement cost is same. Here we need to reduce the emission by 12 tons. Now total emission reduce will be 12 tons so that their marginal abatement cost is same. By analysing the table we can say that if we allow 4 tons of emission from source 1 and 8 tons of from source 2 we see that their marginal abatement cost that time are same i.e both are 10 i.e 10000€ per week. Then total cost of abatement from source 1 if we reduce 8 tons will be 0+1+2+3+4+5+6+8 = 29 i.e 29000€ per week. From source 2 if we reduce by 4 tons then total abatement cost from source 2 will be 0+2+4+6 = 12 i.e 12000€ per week. So from both source the total abatement cost will be 29000+12000 = 41000€ per week.