Who's Happy in Plato's Republic?

Plato's Republic suggests that everyone is better off being just than unjust, yet scholars have disputed whether Plato actually proves it. It is especially unclear whether the Republic shows that non-philosophers are better off being just. I argue that, despite appearances to the contrary, Plato knowingly offers no convincing proof of this, though it is reasonable to infer from the text that Plato genuinely believes it. Thus, the Republic comes to light as a complex piece of protreptic rhetoric: offering an exhortation ('Be just!') while withholding the rational basis for that exhortation - thus provoking philosophic inquiry rather than concluding it.