Charity as arbitrage

I had an interesting thought occur to me on a walk the other day. While most charity is framed as an act of altruism, it's something we only tend to do when there's a significant difference in value between the good for you and the good for the person you're giving it to. Measured in currency, if you give someone $10 they're $10 better off, and you're $10 worse off. But measured in utility that $10 might be worth a lot more utilons to the homeless guy you give it to than it was to you.

A reasonable measure of altruism would be an exchange rate from your utilons to someone else's. An exchange rate of 1 would mean someone else is exactly as valuable to you as you are. That would imply strange things like not minding if someone steals something of yours as long as it gives them the same utility as it gave you. A number like 0.5 would mean you are willing to sacrifice 50% of what you want to give someone else what they want. In practical terms, I think most people would have a number fairly close to zero. Plenty of people give to charity, but few are willing to sacrifice much to do it.

So how does charity work in a society with such low altruism exchange rates? Ultimately, it relies on arbitrage. Charities act as middlemen between people with a lot of money (where it's not worth much) and people with very little money (where it's worth a lot). They can exploit that difference to do a trade at the point where the money exchange rate matches the utility exchange rate.

I wonder how hard that would be to measure...