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  1. Cost-benefit analysis using net present value (or present discounted value—same thing) calculations:
    A new program to reduce air emissions of particulate matter costs $100 to initiate and $60 per year to operate in each of the next 10 years. As a result of the improved air quality, public health improves. The public health benefits in years 1 through 10 have monetary values as shown in the benefits column of the table below. What is the Net Present Value (NPV) of this initiative if you use the NOMINAL discount rate recommended by the Office of Management and Budget (OMB)1 of (approximately) 3%? Is this initiative worth starting?

    What would NPV be if you use OMB’s recommended REAL rate of discount of 1%? Is the initiative now (or still) worth starting?

    [Please show the formula you would use to calculate NPV, but it is perfectly fine (and a great idea) to copy the table below into a spreadsheet and do the actual calculations there. Hint: you’ll find a suitable formula in the reading for this session.]

Year Benefit Costs
0 100.00
1 240.00 60.00
2 156.10 60.00
3 101.53 60.00
4 66.04 60.00
5 42.95 60.00
6 27.94 60.00
7 18.17 60.00
8 11.82 60.00
9 7.69 60.00
10 5.00 60.00

2. Assessing the cost-effectiveness of noise abatement programs.

Two airlines, Zenith and Nadir are the only two carriers serving a small regional airport, where their jets impose noise pollution on a nearby town. At their current production levels, Zenith emits 600 decibel-hours of noise each day, and Nadir emits 750 decibel-hours per day.

The town has determined that the optimal level of noise pollution per day is 1,000 decibel-hours per day.

Zenith’s total noise abatement cost is TACZ = 20dZ + 2(dZ)2 , where dz is the amount of noise ABATED by Zenith.

Nadir’s total noise abatement cost is TACN = 40dN + 3(dN)2 , where dN is the amount of noise ABATED by Nadir.

(Note that abate means to reduce emissions. So the amount EMITTED by Zenith, for example will be 600-dz, and the amount EMITTED by Nadir will be 750 – dN.)

The town is considering two policy options, either of which would achieve the desired level of noise pollution—that is 1,000 decibel hours, which requires that the two airlines reduce (or abate) 350 decibel hours between them.

Assume that the town cares about achieving the noise level (or noise reduction) reduction at the least cost to society (i.e., to Zenith and Nadir), so your job is to calculate the total cost of achieving the noise reduction under each option.

Option A: Zenith and Nadir each reduce their noise output to 500 decibel-hours per day.

What is the total cost of abatement for Option A?

[Please show your work.]


Option B: The town issues 500 noise pollution permits to each of Zenith and Nadir, but allows them to re-sell the permits to each other, if they so desire. Each permit allows the permit holder to emit one (1) dbh of noise each day. They may not emit more noise than the number of permits they have.

For various reasons, including that this course does not require calculus as pre-requisite, we’ll skip the step of doing a constrained optimization problem to figure out how much noise each firm should use and, therefore how many permits each should use and how many each should sell to/buy from the other.

The upshot of such an analysis is that at the optimal solution, the MARGINAL abatement cost of each firm will be the same. The marginal abatement cost for the two firms are:

MACZ = 20 + 4dZ

MACN = 40 + 6dN

(Those who have had calculus will note that these are the first derivatives of the TOTAL abatement cost curves.)

You now know all you need to know to fill out the table on the next page.

[Two big hints: 1. note in the table below that you are entering just one price for permits. 2. I will tell you that one firm will sell some of its 500 allotted permits to the other firm. That will mean that one firm’s NET abatement costs (after sale of permits) will be less than its total abatement costs, and the other firm’s NET will be higher than its total abatement costs.]

Be sure to answer the questions after the table.

Please fill out the table below for Option B. Show enough of your work in the table itself or in the space (above or) below the table to make partial credit possible.

Zenith Nadir Total for both Firms
Noise Emitted

Noise Abated

Permits bought/sold (indicate which)

Price of permits sold

Put price here
Total Abatement Cost, not counting any purchase/sale of permits

Net Abatement Costs after purchase/sale of permits.

Which option (A or B) should the town pursue, and why?

Finally, please explain in words / logically why Zenith or Nadir ended up selling permits to the other firm.

1 Office of Management and Budget. (2015, November). Discount Rates for Cost-Effectiveness, Lease Purchase, and Related Analyses. Office of Management and Budget. Retrieved from

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