Victimized Children in the wealth-maximization approach

Posner looks to show that utilitarianism and economic theory are distinct and that the wealth-maximization approach 'provides a firmer basis for ethical theory than utilitarianism does.' (48).  One of Posner's main objections to utilitarianism is what he refers to as 'boundary problem(s)'(53). Utilitarianism takes into account the happiness of 'all of the inhabitants (...) of "society,"' however issues arise when we ask whether this includes animals such as sheep (and if so are the preferences of the sheep weighted as equal to those of the human?) or the unborn or foreign immigrants.

In discussing how economic theory overcomes these issues, Posner argues that 'people who lack sufficient earning power to support even a minimum decent standard of living are entitled to no say in the allocation of resources unless they are part of the utility function of someone who has wealth.' (76) He gives the example of the 'feeble-minded'(76) who has a negative net social product and is therefore not contributing anything to society. He claims that this person has no right to means of support 'even though there was nothing blameworthy in his inability to support himself.' (76) This is because he claims that genetic makeup is 'devoid of moral significance' (76) 

This makes sense to me, however I do not think that it is enough to simply dismiss genetics as morally arbitrary and thus remove basic rights from a sick person - I would argue that the person has intrinsic value as Hampton would say by virtue of being a human person. However, even if we were to accept Posner's claim that the mentally ill do not have a right to means of support as a result of morally arbitrary factors, I still wonder what he would say about those who are impaired as a result of societal injustices which to me do not seem to be morally arbitrary. For example the girl who did not have access to educational opportunities because of abusive parents and hence was underprepared for future work, or the children of extremely poor parents who did not have access to quality education or guidance. Though genetic makeup may hold no moral significance, I imagine that parental injustice does and it can lead to a similar situation such that some person has a net negative product on society. Does this person have the right to any form of aid in Posner's view?