Another benefit-cost analysis: cleaning up the Allegan Dam reservoir

There is a dam on the Kalamazoo River at Allegan, known as the Allegan Dam. The dam has created a reservoir, a small lake that could be used for recreation. However, the bottom of this lake is covered with PCBs, polychlorinated bi-phenols, a very dangerous chemical compound. (This compound was used in the manufacture of certain paper products.)

Well, to make a long story short, because of that, the lake is not a place that a person would want to swim in, fish in, or boat on. That is, it can't be safely used as a recreation site. But, if the sediments containing this compound were dredged up and disposed of, the lake would be a great recreation site.

The population of Allegan County is let's say, 50,000 households. And they have been surveyed on their willingness to pay for cleaning up the lake. The average willingness to pay (of a household in this group numbering 50,000) turns out to be $200 a year. Cleaning up the lake is very costly. It turns out that the cost of cleaning up the lake and keeping it clean is $8 million a year.

First questions:

1) Under the compensation principle, should the lake be cleaned up?

2) Why do you answer this question as you do?

Let's dig a little deeper. The households in Allegan County can be divided up into three groups: wealthy, middle-class, and poor. There are 5,000 wealthy households, 35,000 middle-class households, and 10,000 poor households. Everybody in a class has the same willingness to pay and the same income. For each wealthy household, income is $200,000 and WTP is $460 a year.For each middle-class household, income is $80,000 and WTP is $200. For each poor household, income is $40,000 and WTP is $70.

An economist has been asked to suggest an annual tax on county residents to pay for the clean-up. The economist proposes a proportional income tax. That means every household will pay the same percentage of their income as a tax. So, if the tax rate is 1.5%, each wealthy household's tax will be .015 x $200,000 = $3,000; each middle-class household's tax will be .015 x $80,000, etc.

Next questions:

3) What is aggregate household income for the county?

4) What must the proportional income tax rate (as a %)be for tax revenues to just

equal the annual cost of cleaning the lake?

Be aware, with a proportional tax, tax revenues = the tax rate x aggregate income.

Last two questions:

5) If the tax rate just covers the cost of clean-up, whowill end up better off from the project and who will end up worse off from the project?

6) Why did you answer the previous question as you did?

Another benefit-cost analysis: cleaning up the Allegan Dam reservoir There is a dam on the Kalamazoo River at Allegan, known as the Allegan Dam. The dam has created a reservoir, a small lake that could be used for recreation. However, the bottom of this lake is covered with PCBs, polychlorinated bi-phenols, a very dangerous chemical compound. (This compound was used in the manufacture of certain paper products.) Well, to make a long story short, because of that, the lake is not a place that a person would want to swim in, fish in, or boat on. That is, it can't be safely used as a recreation site. But, if the sediments containing this compound were dredged up and disposed of, the lake would be a great recreation site The population of Allegan County is let's say, 50,000 households. And they have been surveyed on their willingness to pay for cleaning up the lake. The average willingness to pay of a household in this group numbering 50,000) turns out to be $200 a year. Cleaning up the lake is very costly. It turns out that the cost of cleaning up the lake and keeping it clean is $8 million a year. First questions: 1) Under the compensation principle should the lake be cleaned up? 2) Why do you answer this question as you do? Let's dig a little deeper. The houscholds in Allegan County can be divided up into three groups: wealthy, middle-class, and poor. There are 5,000 wealthy households, 35,000 middle- class households, and 10,000 poor households. Everybody in a class has the same willingness to pay and the same income. For each wealthy household, income is $200,000 and WTP is $460 a year. For each middle-class household, income is $80,000 and WTP is $200. For each poor household, income is $40,000 and WTP is $70. An economist has been asked to suggest an annual tax on county residents to pay for the clean-up. The economist proposes a proportional income tax. That means every household will pay the same percentage of their income as a tax. So, if the tax rate is 1.5%, cach wealthy household's tax will be 015 x S200,000 = $3,000, each middle-class household's tax will be.015 * $80,000, etc. Next questions: 3) What is aggregate household income for the county? 4) What must the proportional income tax rate (as a %) be for tax revenues to just equal the annual cost of cleaning the lake? Be aware, with a proportional tax, tax revenues the tax rate x aggregate income. Last two questions: 5) If the tax rate just covers the cost of clean-up, who will end up better off from the project and who will end up worse off from the project? 6) Why did you answer the previous question as you did