In the traditional use, shall in the first person (singular or plural) indicates volition or simple future, and in any other person it indicates necessity or enforcement (think legal contracts or prophecies).

On the other hand, good will in the first person means strong determination, while good will indicates simpler future.

So, what should that first person indicate, whereas in any other person, it indicates an obligation.

If you read Harry Potter, the character Dumbledore pretty much follows these traditional rules when it comes to using auxiliary verbs.

In American English, you rarely use shall in the first person. I have asked a question on Quora that started with “Shall I”, “Not to ask”? (If you say I should, it more often than not has the same meaning as in any other person (an obligation or expectation )).