Question

The Cherry islands are a small island nation in the Pacific. The population of 10,000 is roughly split between highland inhabitants (30 percent of the total population) who live on the slopes of the mountains, and lowland inhabitants (70 percent of the total population) who live in the valley below.

Air pollution emitted from Cherry has a long residence time and has been causing negative health effects on its citizens. There are 4 major source of pollution: Firm 1 emits 50 units/yr, Firm 2 emits 20 units/yr, Firm 3 emits 20/yr , Firm 4 emits 10/yr. Total emissions is 100 units/yr

The Cherry islands funded a study to examine the benefits they could get from reducing emissions from their current total of 100 units. A consulting company determined highlanders and lowlanders have different demands for abatement of air emissions.

Demand functions of average individuals for reducing emissions:

QL = 100 - 11.6532P

QH = 100 - 58.2660P

where, QL and QH are the reductions in annual emissions, and P is the annual cost (value) of the reductions. These represent individuals’ willingness to pay for one year of emissions reductions in the lowlands (QL) and highlands (QH), respectively. However, emissions reductions occur as a result of investments in long-term, or semi-permanent, abatement, with project lives of 25 years. That means that to come up with a single social benefit(i.e., demand for abatement) function you have to use the above equations to aggregate across three factors: years, then individuals, and finally regions.

The firm then concluded that the the social demand function for emissions reductions for semi-permanent reductions in annual emissions (i.e., reductions over 25 years at 7% discount rate) is

QS = 100 - 0.000132PS

The Islands hired an accounting firm to provide advice about what the appropriate level of emissions reduction would be. I will provide you with the answer and your job is to prove why it is right.

a. The accounting firm states that the efficient level of abatement is QS = 67.4

Answer 1

The consulting firm determined the efficient level of pollution abatement using the social demand function QS = 100 - 0.000132P, concluding that QS = 67.4 represents the level of reduction where demand is optimized over 25 years at a 7% discount rate.

Step-by-step explanation:

The question assesses the efficiency level of pollution abatement for the Cherry Islands, which are experiencing health effects from airborne pollution. The Cherry islands have a population of 10,000 with two main populations of highland inhabitants and lowland inhabitants. The consulting firm determined that the social demand for semi-permanent reductions in annual emissions (over 25 years with a 7% discount rate) is represented by the demand function QS = 100 - 0.000132P. The accounting firm concluded that the efficient level of abatement is when QS is equal to 67.4. This conclusion likely comes from setting the social demand function equal to the amount of pollution that needs to be abated to achieve an efficient level of environmental quality, given the cost value P that society is willing to pay. Using this method, if we substitute QS = 67.4 into the equation, we get: 67.4 = 100 - 0.000132P, solving for P gives us the cost at which the social demand for abatement is optimized. The process demonstrates how economic principles such as demand functions and efficiency can be used to make environmental policy decisions.