Environmental Decisionmaking

Problem Set 7

1) (5 pts) Assume that you are doing a long-range cost-benefit analysis of a recreational facility. The facility will provide an income of $1,000,000 per year indefinitely into the future. The facility will pollute the groundwater, however, and in about thirty years the plume will reach a nearby community and is expected to kill two people per year from then on. The interest rate is 8%, and the EPA currently values human life at about $4 million each. Is this a good investment purely from a cost-benefit perspective? Show your work.

2) (4 pts) How do you feel about the problem in question 4? Now imagine two scenarios. In one scenario, the nearby neighborhood is a poor community whose residents are unlikely to use the facitlity, though a few might take jobs there. In the other scenario, it is only customers who use the facility that take the risk (the contamination is something localized, such as radon in the building itself). Cost benefit analysis might treat these two situations the same. As a policy maker, would you treat them the same? Discuss.

Here I was looking for a discussion that dealt with questions like is it OK for one person to profit off of another person's risk, how do voluntary risks compare to involuntary ones, etc. These are questions that are not answered by CBA, but that you should think about.

3) (4 pts) Assume that you are in charge of the world's last rainforest. Your government is very poor, and there are loggers and drug traders running rampant throughout the forest. You only have money to protect 60% of the total forest, but you can do that indefinitely. However, you are certain that the other 40% will be lost very quickly to illegal loggers. As it is now, there is no value to citizens in that 40% of the forest which is being overrun, because it is too dangerous to go there.

Now, a rich business person comes to you with an idea: he would like to build a theme park with plastic trees (so there is no chance that they will fall on people) and mechanical animals (real animals can be dangerous). This is such a stupid idea, that you are sure nobody will ever visit the park, and so the value of the park to your citizens will be zero once it is built, but this eccentric businessman wants to do it anyway. He tells you here is what he is willing to do: he will hire his own personal police force, and protect the entire forest for the next 20 years. During that time, people will be able to use the forest for anything that is legal, they will be able to take movies and enjoy the animals and all that. But, after 20 years, the whole forest is going to come down to make way for the park.

Question: assuming that the value of the 60% of the forest is 60% of the total value of the forest (i.e. the relationship between forest area and forest value is linear), what is the discount rate above which you will accept this idea based upon a standard future-discounting argument. (You can feel free to use Excel to solve this problem if you can't do it analytically). In other words, at what discount rate is having all of something for 20 years better than having 60% of it forever?

First, let's set up the equation, and then we'll see if we can solve it. This question is asking at which point is having all of something for 20 years the same as having only 60% of it forever. Well, all of X forever is X/r. All of X forever if it starts coming 20 years from now is just this divided by 1+r raised to the 20th power:

(X/r)/(1+r)^20.

Now, after you did this, you should have said to yourself: "Damn, that question is fascinating!!! It means that if I use a discount rate of just 5% (a fairly low value for these problems), then I would rather have all of something for just 20 years and then never have it again, than have 60% of that something forever! Holy TDV, Batman, no wonder we killed off the dodo." Or something along those lines. So, ask yourself: does it make intuitive sense from a social perspective that 60% of something forever is not as good as 100% of it for 20 years? If so, then everything is fine, but if not, then it means that you have a problem with the discount rate. Your answer may help you to think about the next problem.

(3 pts) Give an example of a situation for which it would make sense to use a discount rate of something like 2%, a discount rate of something like 4%, and a discount rate of something like 7% (the long-term return on capital). Assume that these percentages are after inflation.

Discount rate of 2%: something that would have a significant effect on future generations, so that the time preference of money doesn't really make sense. By this I mean that the time preference depends upon who you ask (I might rather have $100 today than in 100 years, but my great grandchildren would certainly rather have it in 100 years than now). Hence, the only reasons why I should discount at all would be a) people in the future will presumably be richer, and b) a little of the money we would save today would get invested and help future generations, just not much of it.

From this perspective, it would make sense to use the long-term return on capital (7%) when I am talking about things where costs and benefits will generally affect the same generation, or if I am specifically talking about long-term investments. You might use a compromise like 4% if it is a mix of the two (or if you don't want to look like a bleeding heart using 2%).

(4 pts) In your own words, explain why a large "voluntary simplicity" movement might call into question the lack of political bias assumed in CBA.

Here your discussion should focus on the idea that if large groups of people decide to eschew consumption to some extent, the people who are not part of this movement will have a proportionately greater influence on economic decisions because they will have more disposable income. Since the decision to avoid consuption is, to some extent, a political decision for many people, this will lead to a political bias in CBA results, especially if they remain focused on WTP.