St. Petersburg Paradox and Log Utility
You play a game where you flip a fair coin repeatedly. You start with $\
$. Every time you flip heads, your money doubles. The first time you flip tails, the game ends and you keep whatever you have.
1. What is the expected payoff of this game?
2. Now suppose you have total wealth $W$ and your preferences are described by log utility, $u(x) = \ln(x)$. What is the maximum entry fee you would be willing to pay to play this game?
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