Suppose you’ll only reject the bet when your net worth is under $20,000, and you’ll accept it above. Can you see why, if you have a utility function, it’s still implied that up to $20,000, the positive dollars are worth less than 10⁄11 the negative dollars?
And then once you have that, does it make sense that the marginal utility of money is going down (at least) exponentially up to $20,000?
Suppose you’ll only reject the bet when your net worth is under $20,000, and you’ll accept it above. Can you see why, if you have a utility function, it’s still implied that up to $20,000, the positive dollars are worth less than 10⁄11 the negative dollars?
And then once you have that, does it make sense that the marginal utility of money is going down (at least) exponentially up to $20,000?