Gaston Gourmand loves good food. Due to an unusual ailment, he has a probability of 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 doesn't. He can also buy negative insurance, where Gaston pays $3x if he loses his sense of smell and gets $x if he doesn't. 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) = . What insurance should he buy?

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The Answer of Gaston Gourmand loves good food. Due to an unusual ailment, he has a probability of 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 doesn't. He can also buy negative insurance, where Gaston pays $3x if he loses his sense of smell and gets $x if he doesn't. 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) = . What insurance should he buy?

Gaston Gourmand Loves Good Food