Assumption #1: There is no free will - all of our decisions are all determined by the causal web of biology and environment.*
(*note: determinism will heretofore be defined in the context of human consciousness outcomes, such that human thought be considered determined by events beyond one's control, even if other, non-strictly-deterministic forces may be at work at the atomic or super-atomic level.)
Capitalist economics is based on a simple proposition: that through free trade an economy develops that rewards hard work and allows those who wish to prosper the opportunity to do so. In reality, it's a bit more complicated, but for our purposes we'll assume that this is true enough. As we've ceded from the beginning, since one is not ultimately responsible for making his own decisions, he cannot be regarded as being responsible for his success or failure in this sort of economy; if hard work determines success, then if one is not responsible for choosing to work hard, one cannot be responsible for success.
Some will indeed work hard and achieve great things. Others will be lazy and accomplish nothing. (Many of course will work hard and achieve nothing, while a few will be lazy and find rich compensation, but that is an economic analysis that has no direct bearing on our discussion here.) So how to determine economic justice when accounting for this causal discrepancy?
Determinism does not deny human behavior, it defines it. Much of what we do is determined by failure and reward. It is obviously in society's best interest to have a productive, competitive, innovative workforce. There are many things we could do to intervene in the name of economic justice that would have the ultimately unjust effect of hindering those qualities. The difficulty lies then in devising a system that rewards those qualities we favor while punishing those we do not, yet finds a balance between allowing some to reap the benefits of prosperity and some to suffer the consequences of failure.
Fortunately we already do this in the form of progressive taxation and a social safety net. On one end, while individuals are allowed virtually unlimited prosperity, their privilege is tethered directly back to the society from which it was granted. On the other, individuals are not only given a basic level of health and safety, they are also given basic services intended to encourage in them the qualities and access that are key to success. At a minimum, individuals are guaranteed emergency health care treatment, basic education, and a variety of services targeted towards the minimization of disadvantage.
But the striking disparity between the poorest ghettos and the most lavish mansions is ample evidence that do not indeed embrace a determinist view of human consciousness. We allow some individuals to live in abject filth and others in splendor precisely because we believe they have earned their place, and we have devised a system that not only tolerates it, but arguably encourages it. But if we are we to truly take determinism as causal fact, then we must radically shift our tolerance for such inequity.
Now, this is easier said then done. As previously mentioned, it is difficult to strike a balance between encouraging good economic behavior and equitable distribution of prosperity. But at a minimum, we can ask just how much suffering we would be willing to allow, and how much pleasure. For it is an objective fact that by scaling one man's luxury back to a reasonable level, you could alleviate the suffering of another. When we remove the concept that neither the former nor the latter can be justified on account of some special personal merit, this becomes easy.
There is no clear evidence of what is always the best way of going about doing this, but that it is worthy, and moral, is a start.