A moral economy is one that is based on the goodness and fairness
of the people participating in it. Such an economy generally only
works with small groups of people who know each other fairly well and
who aren't likely to try to cheat each other.
Moral economies tend to be "scratch my back and I'll scratch yours"
type of arrangements. They prevent free rider problems by leveraging
the willingness of people to help others and generally follow the
Joseph Heath's The Efficient Society provides an entire
chapter on the moral economy, and he does a much better job of
explaining it than I can.