Answer:
1. positive externalities
2. educational credit for the market failure
3. redistribution
4. failure to maximize the family utility
Step-by-step explanation:
There are generally four rationales or logical thinking for the public provisions for education. They are the positive externalities, failure to maximize the family utility, educational credit for the market failure, redistribution.
Now each rationales provides reasons that educations is more likely to be underprovided without any intervention from the government. But many of them does not provide any reasons for the mandate of education.
Like suppose the government can support and solve any educational credit market failure by just offering some loan guarantees for the students while letting them chose to receive education or not.
Similarly government can also address positive externalities that are associated with productivity gains or just letting a person educated without any mandating it.
And finally, government redistributes the poor families through the progressive taxation or the offerings of free education without any mandating them.