I Creating a formula for the cost of pollution through time

[grafs50]

Apologies if this is in the wrong section. Wasn't sure where to put it. While this is technically homework, I don't think it fits in the homework section

In a paper I'm writing, I need to estimate the cost to society of future pollution. Reading relevant academic articles, it seems pretty clear that estimating this is basically impossible. I think I've come up with a method to base a reasonable approximation (at least reasonable enough for the paper) given two things: knowing the current level of pollution and the level of pollution at which humanity is likely to die out.

I set the cost of pollution, C(P), where humanity goes extent to infinite (i.e.: no polluting activity is worth extinction)

Then I tried to come up with a formula that would make C(P)=0 when P=0 and C(P)=(1/0) when pollution reached extinction levels. This is what I came up with:

aP/(a-P) where a is the level of pollution at which humanity goes extinct. I'm also assuming that the costs of pollution grow exponentially.

The intuition I'd like to assign to this equation is that, as the level of pollution grows its effects grow linearly (the numerator, and it also begins to effect more and more of the planet.

What's right and what's wrong about this approach?
Thanks in advance.

 

[jbriggs444]

You still have the problem of determining what extinction levels are and a way of measuring pollution as a single scalar value that ranges up to that extinction value.

The approach only considers one cost of pollution, the closeness with which it approaches "extinction levels". It does not consider how much more we have to spend for clean drinking water, breathable air, decreased productivity due to shortened lifespans, development costs to replace submerged real estate, increased medical costs due to pollution-related effects or decreased medical costs due to pollution-related early demise. All of the things that could make the result meaningful to use and difficult to determine.

The approach also does not have a scale in dollars (or Euros or anything else). How can someone make a rational management decision about the wisdom of paying 1 billion dollars and 12 lives for a pollution cost reduction of .001?

 

[Ssnow]

If the cost of pollution grows exponentially you must have that $\frac{d}{dP}C(P)=KC(P)$ where $K$ is a constant ... (is the Maltus law)