She wouldn't allow someone to pay her to have their child's name in her Harry Potter series, according to the Financial Times.
I would argue that she does have a price, but none of us has enough money. But imagine if Bill Gates wanted the above transaction and offered Rowling a cool $1 billion. Even if more money has no marginal value for her personally given her vast wealth, a billion dollars could do an immense amount of good for the charities of her choice. It would be impossible to deny the world so much good for something so trivial.
But she, like anyone else, probably wouldn't be able to tell you her price ahead of time, until the money is actually on the table.
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