Well you paint a very fantastical and alluring picture but more realistically in the modern day US we ask: is it just to reward people for developing the social connections necessary to succeed, from birth or happenstance, cultivating the culture, personality, and attitude required to fit into successful career paradigms (generally trained through family and upbringing) and the ability to convince or force people to give you more value than the value of the service which you provide in exchange -- the very definition of profit.

And in fact if you begin asking about justice the immediate answer is of course 'no'; anyone wishing to defend the status quo had better avoid framing the question in terms of justice, and rather try to take the more property-oriented tact common among libertarians: is it morally acceptable to prevent people from choosing exactly what to do with their property for the goals of justice and common good? Obviously yes, but how much?

The premise I'm taking - coming from the original article - is that it's hard work and ability which gets you into the elite rather than social connections. If you want to argue this premise is wrong, that's a separate issue.

Also, the definition of profit is price - cost.

Well you're right -- the article is all about hard work and ability /to succeed in undergraduate and graduate admissions contests/ -- I would argue that the social connections are for many the end goal, which you receive after proving you're worthy (and end up at an Ivy, for example) and it is these that actually catapult you into the elite, so hard work is a means to an end.

But this is tangential -- for me the concern is that in the article the writer skims over what kind of hard work and ability is really needed to run this gauntlet of constant judgement and admission from ages 4-25. It is not technical skills or intelligence or even hard work necessarily, but rather an ability and willingness to transform oneself into the kind of person that wins admissions contest. Success doesn't track ability, we've designed a system where we take success as a sign of ability but it actually measures a willingness and ability to conform to admissions standards and do as instructed, and we use this willingness and ability to change oneself as a proxy for actual ability. My argument is that this proxy isn't necessarily a very accurate one.

And I'm glad we agree on the definition of profit. I of course know the economist's definition and agree with it, I just gave what I consider to be a more revealing and honest characterization of it.

>Similarly, for the modern day US, "is it just to reward people proportionally to hard work, intelligence and the ability to produce things that people want?"

You've reversed the causality. Remember, we're asking for a definition of merit that is not isomorphic to "whatever the current economy rewards". We're trying to ask if we can hold the current economy to an external, human standard of performance, rather than just taking it at its own word that "when the numbers go up, it's good" (with the associated problem that even by this standard, "the numbers" have been growing more slowly and crashing more frequently since the rise of inequality began again in the '70s and '80s).

"The warrior caste probably were better warriors"

I think your are missing the point. The warrior caste were better warriors because they were born in a warrior caste.

What that have to do with justice is left as an exercise for the reader.