You cannot cherry pick a single year (a pretty non-representative year given the recession) in which the growth of a few sub-Saharan African countries was faster than the average growth of the stock market.

I didn't cherry-pick anything; that was the first google image result, so it's the one I linked to. I didn't think it's any different from a typical year. Is it? If so, what was special that year? If you're concerned that the US was in a recession, you can simply compare sub-Saharan Africa to the typical 6-7% stock market returns instead of comparing to the GDP growth of the US in that year.

So what you are arguing is that the most efficient use of money to gain QALYs (not the average) has decreased exponentially and faster than the growth of capital over time?

Yes!

That seems very difficult to argue while taking into account increased knowledge and technology. But I have no idea how to calculate that.

I don't claim to be able to exactly calculate it, but some quick back-of-the-envelope calculations suggest that it is true. For example, consider this from slatestarcodex:

http://slatestarcodex.com/2013/04/05/investment-and-inefficient-charity/

[...] in the 1960s, the most cost-effective charity was childhood vaccinations, but now so many people have donated to this cause that 80% of children are vaccinated and the remainder are unreachable for really good reasons (like they’re in violent tribal areas of Afghanistan or something) and not just because no one wants to pay for them. In the 1960s, iodizing salt might have been the highest-utility intervention, but now most of the low-iodine areas have been identified and corrected. While there is still much to be done, we have run out of interventions quite as easy and cost-effective as those. And one day, God willing, we will end malaria and maybe we will never see a charity as effective as the Against Malaria Fund again.

While I don't have the exact numbers, this seems to me to be self-evidently true if you know any history (to the point where I would say it is the onus of the "invest instead of donating" camp to prove this false).