Question

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 who live in the valley below, on the “bottom of the fruit bowl with the pits” as the highlanders say.

There are four sources of air pollution. The biggest single source of pollution is the timber mill in the highlands, which produces 50 units of pollution per year. The copra drying and processing activities in the highlands contribute another 20 units of pollution per year. In the lowlands the gin mill produces 20 units per year, and the hog farming produces another 10. If you do the math, you see that there are total emissions of 100 units per year.

The Island Council commissioned a study to examine the benefits that could be derived from reducing emissions from their current total level of 100 units. A consulting company determined that because of their different positions in the bowl, highlanders and lowlanders have very different demands for abatement of the air emissions. Using generally accepted economic methods they found that the demand functions of average individuals in the two areas are QAL = 100 - 11.6532P QAH = 100 - 58.2660P where, QAL and QAH are the reductions in annual emissions, and P is the annual cost of the reductions. However, emissions reductions occur as a result of investments in long term, or semi-permanent, abatement, with project lives of 25 years.

Your job is to:

a. Prove that the social demand curve, QS, for semi-permanent reductions in annual emissions that last 25 years is QS = 100 - 0.000132PS where PS is the NPV of the social cost of making semi-permanent (25-year) reductions in annual emissions, and a seven percent (7%) discount rate is applied. NB: if QS = 10, then the level of emissions would be 90 units per year, for the next 25 years, the abatement is 10 units of emissions per year, accounting for the total of 100 units per year that will occur in the absence of abatement. PS would be the one time capital cost of achieving the 25-year span of annual reductions.

b. What is the total social benefit of reducing emissions by 40 units, (given the social demand function in part 1a, above)?

c. What portion of those benefits go to highlanders?

Answer 1

In the figure above,both the highlands and the lowlands are benefiting from the remedial methods to reduce the air pollution .It is proved that the net present value (NPV) is benefecial to all of them.

b.From the figure ,QRS is the social benefit .

c.Since the highlanders are 30%, 30% of the benefit goes to highlanders.