It is impossible to say why exactly Jody purchases Matt's mule, as that information is never presented to us, but there are two theories which seem to make the most sense. It is possible that Jody buys the mule out of compassion, as he knows that it is overworked and abused by its owner. If this is Jody's reasoning, it could serve as proof that there is in fact some goodness in him, despite his treatment of Janie. On the other hand, readers know that Jody exhibits very domineering tendencies toward Janie. Since he knows that buying the mule would impress her, his purchase may be nothing more than another way to control her.