You cannot calculate how many art history majors the world needs. You just need to trust people to act vaguely in their own interest, and society's interest, most of the time and to trust that things will work out.
Consider the important exceptions to this approach, where we try to match the number of students to demand. You can sort of calculate how many doctors the world needs, since everything involved (cost of services, number of patients, number of doctors, demography, doctor salary, yadda yadda) is objectively measured. We still manage to get that wrong, and there's a shortage. (or is there?)
The notion that you're going to be able to somehow be able to determine the market demand for graduates of the kind of degree program where people will move into a wide variety of jobs, like art history for one, is pure fiction if we can't even get medicine right. Of course if you're going to form a dictatorship of some kind you're obligated to try, but it will be one of the many things about your dictatorship that does not work very well.