I don't think this works. Presumably cash has a lot more utility than rice or shoes, for example. These people can always use more money (i.e. bank loads in your example), but once they have x shoes or y rice, the utility of new shoes or rice is very low.
> Presumably cash has a lot more utility than rice or shoes, for example.
It has a lot more fungibility, which should also mean that the marginal utility of cash drops slower (as a function of total utility from that source) than for rice or shoes.
