TLDR: you don’t want a metric that goes to infinity in the case of human extinction

There’s a fun graph in this FT article, which is from a Dallas Fed paper on what might happen to per-capita GDP growth with AI. The point the authors make is that there’s a lot of potential upside as well as downside: the future could be quite good (very fast per-capita GDP growth in the “end-of-scarcity” case), or quite bad (per-capita GDP goes to 0 in the human extinction case)

The problem is that the graph is wrong? GDP growth should also go to infinity in the human extinction case?

per-capita-GDP = (amount of stuff produced by economy) / (number of humans in existence)

If skynet produces a bunch of nukes that then results in human extinction, the top stays nonzero (>0 nukes) but the bottom goes to 0 (0 humans) = infinity?

So I’ve gone ahead & modified the graph from the FT article to more accurately reflect this point:

linear

In conclusion: instead of per-capita GDP growth (which actively promotes human extinction), maybe just focus on overall GDP growth (which is merely indifferent to it).