(Solution) - You have a choice between two investment opportunities One pays -(2025 Original AI-Free Solution)

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You have a choice between two investment opportunities. One pays $20,000 with certainty, while the other pays $30,000 with probability 0.2, $6,000 with probability 0.4, and $1,000 with probability 0.4. Your utility is of the type U(x) = x?, 0 < ? < 1. Moreover, you decide that you are indifferent between the choice of receiving $1,000 for sure, or $1,728 and $512 with a fifty-fifty chance. Find your, and decide which opportunity you like better.