Question: A consumer has a utility function over wealth given by U w w ( ) ln( ) = . He is offered an opportunity to

A consumer has a utility function over wealth given by U w w ( ) ln( ) = . He is offered an opportunity to bet on a flip of a coin that has probability p of coming up heads. If he bets x dollars he will have w+x if heads comes up and w - xif tails comes up. Solve for the optimal x as a function of p . What is the optimal choice if p = 0.5 ? (10 points)

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