There's no economic justification for public education
To begin with, I want to explain present value. Basically, it's the inverse of future value, which is the amount of money you'll have after investing money at the rate of return you expect for the period of time you're considering...present value is amount of money one would have to invest now at your expected rate of return, to get the amount of money you want to end up with at the end of the period of time you want to think about. If the present value of the net of all your cash inflows and outflows over the period of time you are considering is greater than the amount you spend to set it all up, it's a profitable arrangement. Then it's a matter of whether or not the profit is enough to satisfy your needs or expectations or whatever.
A more detailed explanation is here; and here's a net present value calculator you can play with to get a feel for the way the concept works out in real life.
Armed with that information, I ask: on what economic basis would a society set up public education?
Now I quote from Economics Explained : Everything You Need to Know About How the Economy Works and Where It's Going, page 161:
No society has ever become literate solely based upon private education. Yet nothing pays off economically for a society more than having an educated work force.
The need for education on a social level is an economic enabler. It's the most important a factor in increasing productivity. It's one of the major factors in the consistant increase in the USofA's GDP. It is infrastructure. But there's no way to calculate a net present value for the money spent education.