Assuming that I precisely know which charity does how much good, I thought for a long time that it is most efficient to spend all my charity budget on this single charity. However, last week I thought that utility can be expressed as a function of how much money every charity has. So rather then spending everything on one charity, I should allocate my money based on the gradient of the utility function in it's current state (provided the utility function is smooth around this state). I would appreciate some (hopefully mathematically not challenging) comment.

Thanks.

This answer holds for almost all situations a small donor might encounter.

The most common exception I can think of: A charity is running a special campaign where dollars are more valuable until a certain point (for example, they are eligible to get their next $5000 in donations matched dollar-for-dollar, but no further matching past that, so your 5001st dollar suddenly has half the impact of the first dollar, and you might start giving elsewhere at that point).

There are other situations I've encountered with the same kind of artificial limit. Faceb... (read more)