Suppose a consumer has log-utility over wealth, defined by $u(W) = \ln(W)$. Suppose this consumer has $100$, and is considering taking a gamble in which the consumer flips a coin, and gets $20$ she flips heads and $0$ if she flips tails. What is the most amount of money the consumer would be willing to pay to play take this gamble? What if the consumer has $1, 000$ dollars of wealth?
I feel like this question is incomplete since we do not know how much the person need to give in order to play the game. Do we know that information in order to solve this problem?
If no, could anyone tell me the direction and piece of information needed to solve for this question?