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Barney has $80,000 in income per year and faces a 20% chance of having $25,000 in unexpected medical bills. Suppose Barney's utility function over income

Barney has $80,000 in income per year and faces a 20% chance of having $25,000 in unexpected medical bills. Suppose Barney's utility function over income is

U = I1/2

Show mathematically that Barney would be better off with an actuarially fair insurance policy, as opposed to having no insurance.

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