Moving on to Rawls then. First, it's important to note that Rawls is not a utilitarian. In fact, in A Theory of Justice utilitarianism is the bogeyman against which Rawls argues his case. On the first page he writes:
Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override. For this reason justice denies that the loss of freedom for some is made right by a greater good shared by others. It does not allow that the sacrifices imposed on a few are outweighed by the larger sum of advantages enjoyed by the many.There is, however, an element of utilitarianism in Rawls's Original Position. The objective of the Original Position contractors is supposedly to maximize their likely outcome in society. This is sort of utilitarian, with a curveball thrown in (the veil of ignorance blinds them to exactly what represents utility to them as individuals).
But Rawls's excursion into utilitarianism, in my humble view, is a mistake. I don't think he actually meant it. It really doesn't follow from his justifications of why we should have the Original Position that it should necessarily be a maximizing exercise, nor does his output from the Original Position (the two principles) reflect a maximizing approach. A maximizing approach would produce, as Henry noted, basically whatever principles would maximize the average amount of primary goods (Rawls's stand-in for utility) for everyone. Instead what Rawls claims the Original Position contractors will embrace is a maximin approach (maximizing the amount of primary goods provided to the least well off member of society). You can see this in the difference principle (part of Rawls's second principle of justice): social and economic inequalities are permissible only if they are to the greatest benefit of the least advantaged members of society. This would make no sense as output from the Original Position as Rawls proposes it. So something doesn't fit here, and I think there has to be a better explanation linking Rawls's fundamental premises to his two principles of justice.
Rawls's entire argument is motivated by his conception of justice as fairness. At this point I think I need to try to flesh out the basic Rawlsian argument (I am, of course, skipping over many, many details). Rawls views the benefits of social cooperation as the product of everyone acquiescing to a social ordering that allows for and facilitates that social cooperation. Those benefits should therefore be allocated in such a manner as to ensure such cooperation, resulting in what Rawls calls a well-ordered society. This requires that "(1) everyone accepts and knows that the others accept the same principles of justice, and (2) the basic social institutions generally satisfy and are generally known to satisfy these principles." Lacking a well-ordered society various factions will vie for the power to reorder the state to fit their own needs, and the resulting instability will hinder social cooperation and deny everyone its benefits. Rawls conceives of the Original Position in order to satisfy condition (1) above; to create principles of justice that everyone can accept. In the Original Position our theoretical contractors will evaluate the question of social justice in a completely unbiased manner and generate broadly acceptable principles of social justice. He appears to assume (initially!) that what people will all accept will be principles designed to produce the greatest average outcome.
So far, so good. But there's a problem here, one that Rawls acknowledges (and that informs his choice of the maximin approach), but that he strangely does not allow to alter the conceptual setup of the Original Position. There are certain social outcomes that people will simply not accept, no matter how well conceived the principles of justice are. A utilitarian principle (which is what the Original Position as Rawls proposes it would produce) could, for example, result in some people being made slaves in order to improve the overall average utility of the society. No matter what their Original Position alter-ego might have thought, the actual slaves could never recognize this principle as just, and consequently you would not have a stable, well-ordered state.
So the instruction to the Original Position contractors really ought not to be to maximize the average amount of primary goods, but rather to devise principles of justice that everyone can agree to. Of course, that was what we created the bloody thing for anyways. How should that be approached? We can assume (without too much controversy, I think) that the people least likely to agree to any principle of justice will be those who gain the least benefit from it. Hence the maximin approach. These least well off people should certainly agree to a principle that would maximize their welfare.
A first blush approach to maximin would be to simply be divide the social benefit in equal shares. However, as Rawls recognizes, that only makes sense if the social benefit is fixed and unchangeable. But we know that the benefits of social cooperation are not fixed, that by providing people with incentives we can get them to produce greater social benefits. This requires allowances for some inequality so that we can provide those incentives for increased cooperation. Of course, if those greater benefits only go to the well off, we have gained nothing from a maximin approach. Increasing the size of the pie is only beneficial to the extent that some of the increase goes to the least well off. And so we arrive at the difference principle: inequalities that in some way benefit the least well off are acceptable, those that don't are not. And you hopefully by now can see why I say that I don't believe Rawls took the utilitarian aspect of the Original Position very seriously.
Now, with my Rawlsian primer complete let me address your comments more directly. I read your argument to be compatible, in principle, with Rawls's difference principle. It is a 'rising tide lifts all boats' argument. In essence any inequality produced by a free market will operate to the benefit of the least well off. The difference principle would only limit market inequalities or justify redistributive policies to the extent that this is not true. Of course, the other part of the second principle, fair equality of opportunity would also support redistributive policies (public education, for example) that would conflict with your position.
Rawls writes at length about economics in the latter part of A Theory of Justice (which I have not read). Scanning through it, Rawls does not engage in serious discussion regarding exact details of market structure and regulations (and in fact brushes this off to some extent as being dependent on "the traditions, institutions, and social forces of each country, and its particular historical circumstances" and some evaluation of the impact of various policies in practice). But it is clear that he believes that some baseline minimum standard needs to be maintained through redistributive policies to protect against the "contingencies of the market". Beyond that "it may be perfectly fair that the rest of total income be settled by the price system, assuming that it is moderately efficient and free from monopolistic restrictions, and unreasonable externalities have been eliminated."
Rawls also hints at another objection related to the quote at the top of my post regarding the inviolability of individual rights. While he does conceive of the maximin principle being based on long run expectations, he would not allow the justice of particular groups of people to be sacrificed to long term generalized gains. There would need to some line-drawing to determine what is an acceptable short term sacrifice in the long term interests of those least well off, and those sacrifices that treat those people as means to achieve some remote end. This also harkens back to the motivation for the maximin approach. Outcomes that are bad enough to cause social unrest (those that the victims cannot possibly regard as being the products of a just society) need to be avoided even if temporary and in the long run interest of everyone.
To a considerable degree the dispute here has to be an empirical one. Your claim about charitable giving could be interpreted as a counter to many of Rawls's arguments. Suffice it say I find the claim that charity could completely replace redistributive policy somewhat dubious. There would also be arguments about the existence and degree of market failures, of anticompetitive strategic behavior, externalization of costs, collective action problems, behavioral critiques, etc. I think there would also have to be discussion as to the general degree of churn in markets and the degree to which it is possible and probable that some proportion of people would fall through the cracks, including but not limited to those who are disabled or suffer serious health ailments and impairments or possess limited natural talents and abilities. I don't see us resolving such issues at this moment, but to the extent any such problems exist they would suggest a conflict between a minimal state and Rawls's difference principle.