Willingness to pay

The basic idea is pretty simple, although implementation can get complicated. Remember that what we're trying to do is to maximize utility. Suppose I have $100 in my pocket. Suppose also, and this is true, that there is Phragmites australis (an invasive plant) in Lord's Cove on the Connecticut river. I'll use $E_0$ to symbolize having the Phragmites so I don't have to write it out all the time, and I'll symbolize the utility associated with that state of the world as $U(\$100, E_0)$. Now I'd be happier if there weren't any Phragmites in Lord's Cove, so if I let $E_1$ symbolize the absence of Phragmites in Lord's Cove, then clearly

$$U(\$100, E_0) < U(\$100, E_1) \quad .$$

But if I would really be happier if there weren't any Phragmites in Lord's Cove, then I'd probably be willing to pay a little bit to get rid of it. So, just as a thought experiment, let's suppose the following three statements are true

$$\begin{eqnarray*} U(\$100, E_0) &<& U(\$90, E_1) \\ U(\$100, E_0) &=& U(\$75, E_1) \\ U(\$100, E_0) &>& U(\$50, E_1) \quad. \end{eqnarray*}$$

How much would you conclude that I am willing to pay to remove Phragmites from Lord's Cove? $25, because if I had to take more than $25 out of my wallet (leaving me with less than $75), my utility would be greater by keeping my $100 and living with the Phragmites. That's the idea behind ``willingness to pay'':

$$U(Y, E_0) \equiv U(Y - WTP, E_1) \quad ,$$

where $WTP$ is the willingness to pay.

So what do you think about willingness to pay as a method of valuation, ignoring all the complications of how to combine answers from different people?

Well, what do you think about the fact that I'm willing to pay $25 to get rid of Phragmites in Lord's Cove. You're probably thinking to yourself ``He's really cheap. He's got a cushy job as a Professor. He must be raking in the dough. Surely he could afford to pay a lot more than $25 to get rid of Phragmites.'' Well, you're right (except about the cushy part). I could afford to pay a lot more than $25 to get rid of Phragmites. In fact, if I were sure we'd be able to get rid of the Phragmites, I'd probably be willing to pay quite a bit more. But suppose I were a homeless person who had been out of work for four years and was completely dependent on handouts from strangers for my income. Then I probably wouldn't be willing to pay even $25 to get rid of Phragmites, because I just wouldn't have the money.

That thought experiment illustrates a significant limitation of using willingness to pay to determine values: Those who are wealthy will be willing to pay a lot more for outcomes they value than those who are poor simply because the wealthy are able to pay more. That doesn't seem right. Why should a wealthy person's desires count more than those of someone who's poor?