Who should get the unearned wealth?

The neo-classical model purports to solve how much of all goods to allocate. Along the way it also determines who gets the allocations. It takes as given that the only mechanisms of person-to-person interaction are trade and competition (both are substitutes, the one of the goods, the other of the traders) and the only mechanism of person-to-goods interaction are private property and the preference ordering. 

When competition does not work and private property results in a large pool of unearned value, the neo-classical model punts the question of who should get the unearned wealth by delivering the problem for solution to the political system. That political system however has not been involved in the allocation issues of a neo-classical economic order and is thus ill-prepared to address the question of allocating unearned wealth.