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Gaston Gourmand loves good food. Due to an unusual ailment, he has a probability of 1/4 of losing his sense of smell, which would greatly

Gaston Gourmand loves good food. Due to an unusual ailment, he has a probability of 1/4 of losing his sense of smell, which would greatly reduce his enjoyment of food. Gaston finds an insurance company that will sell him insurance where Gaston gets $3x if he loses his smell and pays $x if he doesnt. He can also buy negative insurance, where Gaston pays $3x if he loses his sense of smell and gets $x if he doesnt. Gaston says, Money will be only half as important to me if I lose my sense of smell. If we look at his expected utility function, we see what he means. Where c1 is his consumption if he retains his sense of smell and c2 is his income if he loses his sense of smell, Gaston has the expected utility function U(c1, c2) = (3/4)*c1^(1/2) + 1/8 c2^(1/2). What insurance should he buy?

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