No, you misunderstood. The idea is that an economy stuck in a child labor trap will remain in it, despite higher equilibriums being available, until forced off. Market forces alone will not move an economy off of a stable equilibrium.
This is not at all a fact. As far as I know, making child labor illegal has worked in states where it was already in decline because no longer necessary. The decrease in the role of child labor was a consequence of economical growth. Which was, obviously, possible in these societies.
Of course - child labor traps an economy in poverty. If you want a rich society, or anything other than the most miserable of poverty, you have to reserve childhood as a time of investment.
A large part of traditional child labor is support of the family business - and, therefore, combined with the necessary education to do this job, given by teachers very interested in giving them a good education in this relation, for the own interest too (economic security at old age). This, of course, is no investment into education necessary for different jobs - but the child labor also leads, for the family, to additional income, which allows investments into the own business. Once the economic pressure decreases, the investment in education increases. In a free society, this can start with small investments into somebody who teaches the children how to read, write, and count, which needs much less investment than large public schools. This is usually also much more efficient than public schooling, because the children are much more interested to learn.
So, even on a family level there is a way out. The situation for a society as a whole is much less problematic, because no society needs 100% educated (except for ideological reasons). There will be different groups, from rich to poor, with different levels of necessity for child labor on the family level. The richer - or, more accurate, all who can afford this - will educate their children as good as possible, because this gives them better jobs. So, with an increasing number of people of people rich enough to educate their children, there will be also an increasing number of educated people to get the good jobs, which leads to increasing income for the society as a whole. Which, of course, trickles down, even if nobody from the left believes this.
Forbidding child labor in a situation where it is yet necessary for large groups is, instead, harmful for the economy as a whole.
A stable market equilibrium will not change unless forced by agencies outside the market, by definition.
That means, you use meaningless economic science. Real economy changes. Real market economies too. Equilibrium is essentially only a theoretical entity without much practical relevance. Every invitation (if not forbidden by patent law) will be used to produce better, cheaper, or simply more things, and changes the equilibrium. And this happens because of the market forces. The agencies outside the market only prevent this.
Child labor economies are in a stable labor market equilibrium, very often.
Usually in highly restricted economies, where the market is unable to develop. Where every successful business has to pay a lot of bribes to the state to survive.
Says who? The libertarian capitalists defending their freedom of contract against those who were using force to make them do business with black people thought they were defending themselves and their fundamental rights against violent aggression. And you agree with them completely, in all your posts above. You have no problem with their assessments and their reasoning, until we get to the part where a real life example shows up.
And, once they are forced to "make business" with somebody they don't want to make any business, they are right. They defend themself against a form of slavery.
But it is something complety different to use force against other people, named "niggerlovers", simply because they want to make business with blacks. This is itself aggression.
The difference is simple and clear. Everybody has the right of freedom of contract, and of discrimination as part of this freedom. Those who don't want make business with blacks should have the right not to make business with blacks, and the "niggerlovers" should have the right to do this. This is what libertarian principles prescribe. And they do this in a sufficiently simple and easy to understand form. So, no, I agree with them only in one part - their own right to refuse to serve blacks. I completely disagree with what they do against "niggerlovers" who want to make business with blacks.
Libertarianism is a minority position, you are not libertarian, but want to force white people to serve blacks (as a sort of retaliation for slavery or so), and those who beat "niggerlovers" are also not libertarians, because they want to prevent freedom of contract for niggerlovers.
And freedom of contract for white folks turns out to mean black folks cannot get a drink of water from the public fountains, or go to the nearest hospital when injured or taken sick, or find employment in any job paying more than a regular white person earns, or say hello to an attractive woman on the street.
Again, if "public fontain" means something build for taxpayer's money, then there is no right of discrimination, because the blacks have also, via their taxes, paid for this fontain. If it stands on private ground, and has been build with private money, to name it "public" is only a form (or a first step) of expropriation of private property. Same for the hospital. Same for the job. And, of course, the laws which distinguish between "saying hello" and stalking should be also based on equality before the law.
It seems, you have a moralistic view of law: The law should enforce good behaviour and punish bad behaviour, and what is good and what is bad depends on your personal feelings. The libertarian approach is completely different. It is based on simple principles, and if one does not violate these principles, one can do what one likes - without having to care if you find this behaviour good or not.
The result of your approach is that you think racism is bad, thus, every behaviour (whatever it is) somebody makes out of racist intentions is inherently bad and should be forbidden. This combines scientific research about IQ differences between races with some verbal expressions of some bigots, with the refusal to have business with blacks, with the beating of "niggerlovers" up to KKK lynching into one big basket named "racism". And the people in this basket are the racist bigots, the subhumans of your variant of fascism.
The libertarian thinks completely different. He acknowledges that people are different, that there will be conflicts between them, some will hate others, and the best way to preserve peace is to separate those who hate each other, giving them the possibility to live their lives without those of the hated groups. And then one needs simple principles which allow everybody to do this, and to minize conflicts if, nonetheless, some contacts with the hated groups are unavoidable. Libertarianism cares about these principles. And these principles will defend the rights of the bigots not to serve blacks as well as the right of the "niggerlovers" to make business with blacks without being beaten by the racist bigots.