The most relevant field here is International Monetary Economics.

After TAing a class on the subject, I became convinced that most people (including economists) would be better off ignoring money most of the time, and just following where the goods went. So think of this as a transfer of $1000 worth of goods from the US to Kenya.

You could get the official answer with an IS-LM-BP model and some masochism.

More seriously, this does make me want to look into theoretical work on the macroeconomics of charity. On the empirical side, the best evidence is that even average (poorly targeted and managed) foreign aid has positive effects on country-level growth.