I see, via Yet Another Sheep, that nonstandard analysis has spread to mathematical economics. Robert Anderson has a book manuscript available, Infinitesimal Methods in Mathematical Economics which explains how to apply nonstandard analysis to approximate economies with large numbers of agents. The main technique is Loeb measures, which is something that I plan on writing a post on, once I actually know anything about them.
Anderson’s book is certainly not the first appearance of nonstandard analysis in economics. He also wrote a chapter (39) in the handbook of mathematical economics on nonstandard analysis in economics (presumably his textbook is an outgrowth of this chapter?). That chapter has a lot of references to previous literature using NSA.