Also, the definition of profit is price - cost.
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.
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?