Maximum probability of inducing person to vote for action


Question:

You have a person whose utility is U = Square root of I. They have two choices: A. Vote for action B. Vote against action. If they choose B. They get $5 Million. If they choose A. they have a 30% chance of making $80 million and 70% chance of making $1 million. So far so good.

But if they make the $80 million, there is a possibility they will loose $10 million of it. The question is what's the maximum probability of that last last thing happening (-$10 million) that will induce the person to vote for action?

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Microeconomics: Maximum probability of inducing person to vote for action
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