There are two broad autonomy-based arguments for the market: the first invokes market neutrality, the second: perfectionism and the development of autonomous character. Hayek argues compellingly for the first approach:
The recognition that each person has his own scale of values which we ought to respect, even if we do not approve of it, is part of the conception of the value of the individual personality. How we value another person will necessarily depend upon what his values are. But believing in freedom means that we do not regard ourselves as the ultimate judges of another person's values, that we do not feel entitled to prevent him from pursuing ends which we disapprove so long as he does not infringe the equally protected sphere of others.
However, when push comes to shove I don't think many of us would stand by this view. It implies that we should allow individuals to sell themselves into slavery, sell their body organs, engage in suicide pacts, and so forth. (You can just hear the neutralist arguing, "Hey, if that's what they want for themselves, who are we to judge?") If you hold that autonomy is good in itself, however, then you are not a neutralist. I think this pro-autonomy position is the more plausible one. It would justify preventing people from selling themselves into slavery, for in doing so they would undermine their own autonomy, and - unlike the neutralist - we hold that autonomy has objective value and so ought not to be undermined in such a fashion.
Still, even if we must impose some limits on the market, in general it seems quite supportive of autonomy. Certainly it is preferable to any alternative where individuals get their jobs and roles in life decided for them by some external authority (whether a totalitarian government, or an heriditary caste system). The market removes these barriers to self-determination.
Nevertheless, the market alone is insufficient. As John O'Neill argues, "Hayek elides self-determination with the negative conditions for its exercise". Hayek identifies autonomy with "independence of the arbitrary will of another", but also with the condition of being "moved by reasons, by conscious purposes, which are my own". What he seemingly fails to recognize is that these two concepts are not identical. The former, purely 'negative', condition, does not guarantee that the latter, 'positive', condition also obtains. This reflects my more general complaint that mere non-interference is insufficient to establish genuine opportunities, and only the latter has genuine value.
These considerations move us towards the pro-autonomy 'perfectionist' position hinted at before. On this view, the value of the market derives from its tendency to develop the virtues of autonomous character. Thus Gray argues:
the virtues elicited in market economies are those of the autonomous agent - the person... who is self-possessed, who has a distinct self-identity or individuality, who is authentic and self-directed, and whose life is to some significant degree a matter of self-creation.
There are three problems with this argument. Firstly, it is far from clear whether the market really does develop virtuous character. Adam Smith recognized that tedious labour would dull the capacities of workers, and markets would pamper the vanity of the rich. (He simply thought that these costs were outweighed by the utility of capitalist production.) It also seems plausible that the market encourages meanness of spirit, miserliness, uncharity, selfishness, and a general lack of community-mindedness and concern for others. Further, O'Neill argues that it doesn't even encourage a balanced autonomy:
To use the Aristotelian terminology, the virtues of the autonomous agent must be contrasted not only with vices of deficiency, but also those of excess. Self-identity requires not just the absence of definition by others alone, but also settled dispositions that go to make up the existence of character.
He suggests that "recent accounts of the 'post-modern condition'" indicate the failure of our market society in this regard.
The other two counter-arguments are a bit more straightforward. They concern the value and conditions of autonomy. Basically, freedom only has value insofar as we have worthwhile options to choose between. This is a positive condition that the mere 'negative freedom' provided by the market cannot guarantee. But as it stands this point is merely academic. In practice, market forces will tend to supply valuable goods to meet demand. To have any real bite, the present argument must be supplemented, perhaps by the suggestion that commodification of "educational, cultural, familial and associational spheres" would tend to undermine their intrinsic value. I will not pursue that line of argument here.
Finally, on the conditions for autonomous character, we return to the familiar point about how mere non-interference is insufficient. Indeed, the market presupposes autonomy: it consists in voluntary exchanges between (supposedly) informed and rational agents. Agents are disadvantaged insofar as they lack the fundamental capacities required for market success. It is patently unjust for an individual's capacities, and thus opportunities, to be determined by (parental) wealth.
What justice and autonomy require is that we first establish the conditions required to exercise freedom. That is, the provision of basic needs, top quality education, and so forth. Only then can we hand matters over to the market. As I have recently argued, I think the best way to achieve this would be to institute a universal basic income to complement the free market. The taxes required to fund it could be incorporated into the cost of market transactions. This, I believe, would be the best way to promote real freedom in our society.