What is socrates account of the virtue of justice in book IV? what are his main reasons for thinking a just person is better off than the unjust?

A just man is for Socrates someone who fulfills his given nature to the utmost of his ability. For him, of course, this nature is an eternal soul. It is not enough to be merely a philosopher or a blacksmith--a just man must be a good philosopher or a good blacksmith. This dedication to cultivating oneself involves the greater power of justice.