Not disagreeing with you, but from my perception of economics as a field, biodiversity is not a topic that attracts a lot of attention. Working on biodiversity topics does not lead to a top 5 journal publication or a job in a prestigious institution for an economist. I doubt there is a strong incentive for economists to take on this problem. On the other hand, ecologists have been working on biodiversity for a long time. Of course, a collaboration between economists and people who work on biodiversity would seem most effective.
It's not a difficult problem to cost though is it, if we continue on the path we are on and destroy all biodiversity, we'll have killed the planet that sustains us and the side effects will quickly destroy our civilization. Thus the cost is infinite.
We can't survive without other life on earth, and life on earth dies without enough biodiversity.
What is "enough" though? 30%, 50%, 90%? And how much are we willing to spend to hit each of those targets. We're obviously not going to spend "infinite" economic resources to protect biodiversity and we've long since accepted that we are willing to sacrifice a bit of 'nature' for a bit of 'comfort' and that won't change. We're now negotiating how much we are willing to give up to save how much of nature, and that is, demonstrably, a very difficult problem.
I think it may be helpful to invert the framing of your question - you allude to spending economic resources to protect biodiversity, but aren't we actually talking about spending biodiversity (and other natural resources) to gain economic resources?
Your framing takes acquiring economic resources (a.k.a. the destruction of natural resources) for granted, assuming that we're losing, or giving up, something by opting to not destroy some portion of the natural environment for economic gain. Aren't we losing, or giving up, something every time we choose to gain economic resources by destroying part of the natural environment?
Logically, both framings are valid, but they don't appear wholly equivalent to me. Perhaps I'm missing something, but economic resources seem far more fungible than natural resources, which seems to imply that the latter framing may be more appropriate.
This difference, highlighted here, in this essentially ephemeral internet-space, may seem to occupy the border between semantic and pedantic, but I think it will take on a fundamental role in determining humanity's future prospects. How we define our relationship to the earth determines how we live. Your framing of the economic/environmental calculus seems to represent the status quo, but I don't think it represents a sustainable future for humanity. If/how/when the status quo shifts, I have no idea, but it does seem (from my limited vantage point, anyway) that more and more people are developing sympathy for the notion that modern society doesn't optimize for human well-being.
