Bjorn Lomborg is at it again, asking how to best spend $1 billion in new funding to fight AIDS/HIV.
The answer, for the few first million at least, is almost certainly to lobby for more HIV/AIDS funding. The funding has gone from in the low tens of millions or so to around $5 billion in the U.S. alone thanks to lobbying efforts led by Bono, Jeff Sachs and ONE Campaign.
But the real point of that story isn't that Lomborg will answer his own question wrong, it is that the government budget constraint on aid spending isn't fixed. We can spend more on aid if we want to.
If you've read Mountains Beyond Mountains this is the point that Paul Farmer makes (though he is opaque) at the end of the book, arguing that it is worth the cost to fly a dying child from Haiti to Boston if that is what it takes to keep her alive. I think Farmer is wrong about that but the key piece in his argument is that cost-benefit analysis is based on the premise of trade-offs with a static budget constraint. It's true that you "can't spend the same dollar" saving a child by flying to Boston and saving 10,000 children who have anthrax or measles. But you could spend different dollars on the two goals and a good cost-benefit analysis needs a theory of political economy to endogenize spending on aid. Don't hold your breath waiting for it.