Plato on Justice

Plato's interpretation of justice as seen in ‘The Republic' is a vastly different one when compared to what we and even the philosophers of his own time are accustomed to. Plato would say justice is the act of carrying out one's duties as he is fitted with. Moreover, if one's duties require one to lie or commit something else that is not traditionally viewed along with justice; that too is considered just by Plato's accounts in ‘The Republic.' I believe Plato's account of justice, and his likely defense against objections are both clear and logical, thus I will endeavor to argue his views as best as I can.
Plato's view of justice ties in with his view of a perfect world. In Plato's ideal world, the society would be a wise one, wise in understanding that their own position in society is just. This society in turn, must carry out their duties fitted to them by their position. Unfortunately the real world does not function in that manner, Plato understanding that ‘fault' with society tells us that if the society is lacking wisdom, the most wise ones would be philosophers, (473d) and society should consider them to be the authority.
Plato believes that being just is so innately important that everyone is better off being just than unjust, no matter the situation. Plato in 360e-362d uses Glaucon to make this point, Glaucon asks who is better off? The just or the unjust, given the premises that the unjust man is rich, famous, respected, and powerful and that the just man is poor, defamed, and lives a life of suffering. Plato's only real way to answer this is to prove that justice is innately good and that injustice is innately evil; simply prove the poor, defamed man happy and the rich, respected unjust man unhappy. Plato goes about this by explaining what justice is; justice has to do with doing what is right, and there exists some specific virtue in everything, which enables it to work well. If it is deprived of that nature, in contrast it would suffer. It