How does Paul answer the charge that God is not just?

Question

Soldarnal asked a question about what charge Paul is defending God against in Romans 9:14. Assuming the charge is that God is unjust because chooses to love some and hate others on the basis of His whim, how does saying that He will have compassion on some and not on others a defense of God's justice?

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For reference, the passage is:

[When] Rebekah had conceived children by one man, our forefather Isaac, though they were not yet born and had done nothing either good or bad—in order that God's purpose of election might continue, not because of works but because of him who calls—she was told, “The older will serve the younger.” As it is written, “Jacob I loved, but Esau I hated.”

What shall we say then? Is there injustice on God's part? By no means! For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” So then it depends not on human will or exertion, but on God, who has mercy. For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” So then he has mercy on whomever he wills, and he hardens whomever he wills.—Romans 9:10b-18 (ESV)

Answer 1

¹⁰ And not only so, but also when Rebekah had conceived children by one man, our forefather Isaac, ¹¹ though they were not yet born and had done nothing either good or bad—in order that God's purpose of election might continue, not because of works but because of him who calls— ¹² she was told, “The older will serve the younger.” ¹³ As it is written, “Jacob I loved, but Esau I hated.”
¹⁴ What shall we say then? Is there injustice on God's part? By no means!   _ESV

The unspoken assumption of the imaginary 'questioner' is that it would be unjust for God to judge except on the basis of the works done by a man - which is a natural if misguided assumption as I argued on the linked question

Paul continues:

¹⁵ For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” ¹⁶ So then it depends not on human will or exertion, but on God, who has mercy. ¹⁷ For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” ¹⁸ So then he has mercy on whomever he wills, and he hardens whomever he wills.
  _ESV

Paul does not so much directly defend God's justice as challenge the assumptions of those who question it. He denies that it would be unjust for God to judge on any other basis than works. He asserts that God may judge as he pleases and whether someone is 'loved' by God or 'hated' by him is a question of mercy not of justice.

This of course prompts the exasperated imaginary question in verse 19, after which Paul goes on to affirm that God's choice is not meaningless, but purposeful, even though it does not depend on works.