Question: Assume that a risk-averse consumer has a utility function u ( w ) where w is wealth. This consumer is offered the opportunity to bet

Assume that a risk-averse consumer has a utility function u(w) where w is wealth. This consumer is offered the opportunity to bet on the flip of a coin that has probability of coming up tails. If he bets $ x, he will have w+x if tails comes up and w-x otherwise. Find how the amount of money x the agent wishes to bet changes as increases (hint: ignore the case of x=0 ).

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