Question

A pollutant is found to have the marginal damage function MD=5E, where E= aggregate emissions of the polluation (E1+E2) and marginal damages as a function of emissions reflect society's willingness to pay for environmental quality and improved health that results from a decrease in emissions. There are only two firms that emit this pollutant. Firm 1 has marginal abatement cost curve MAC1=90-5E1 and firm 2's marginal abatement cost curve for the pollutant is given by MAC2=40-2E2. 1) Construct society's marginal abatement cost curve that reflects the minimum cost to society of achieving a given level of emissions abatement. Graph the MAC curve with cost on the vertical axis and emissions on the horizontal axis of your graph. 2a. What is the economically efficient level of emissions? 2b. Explain why you identified this particular level of emissions as being economically efficient. The pollution control authority has set a new emissions target of 19 units of emissions. It is trying to decide whether to use a performance based emissions stand or an emissions trading market to achieve the new emissions target. 3. Suppose a uniform standard is adopted that requires each firm to reduce emissions from the unregulated level to 9.5 units. Calculate the total abatement costs of both firms that result from implementing this uniform standard. 4. Suppose an emissions trading market were created to achieve the proposed 19 units emissions target. a. If both firms were freely allocated permits allowing them to emit 9.5 units each, what number of permits will be held by each firm at the equilibrium in the emissions trading market? b. Calculate the total abatement costs of both firms at the market equilibrium.

Answer 1

Since the pollutant is emitted by two sources, therefore finding an efficient level of emission requires combining two curves to find an overall marginal abatement cost curve.

Note: It is similar to finding the market supply curve when the individual supply curve ( =MC curve ) is given. that is we will do a horizontal summation of the two curves.

doing horizontal summation-:

logic: For efficient abatement we want it to be allocated such that MAC1 = MAC2 ( put both these =MAC )

MAC = 90 - 5 * E1 - - - - - - - Eq1

MAC = 40 - 2 * E2 - - - - - - - Eq2

Also,

E = E1 + E2

using Eq1 and Eq2

E = ( 90 - MAC ) / 5 + ( 40 - MAC ) / 2

10 * E = 180 - 2 * MAC + 200 - 5 * MAC

7 * MACs = 380 - 10 * E

Note: through this we always pick the firm having lowest abatement cost when choosing who should clean the next unit emmision.

Finding an efficient level of emission, do MD = MACS

5E = 380 / 7 - 10 * E / 7

=> E = 380 / 45

=> E = 8.444

2 b. The amount which society is willing to pay for reducing an additional unit of emissions and the amount which companies are willing to spend on cleaning an additional unit of emissions is equals at E = 8.444. This provides satisfaction to both parties without giving extra benefits to anyone of them.

3.

total abatement cost = area under the MAC curve

if uniform standards are followed, then both firms are required to bring pollution from unregulated levels to E = 9.5

therefore,

total abatement cost =  abatement cost born by firm1 + abatement cost born by firm2

total abatement cost = Area ( APR ) + Area ( CPQ )

total abatement cost = 1 / 2 * ( 20 - 9.5 ) * ( 21) + 1 / 2 * ( 18 - 9.5 ) * ( 42.5 )

total abatement cost = 290.875