2. Christiaan can go hiking, or he can stay at home. Hiking would be fun if nothing bad happens, but there is a risk if he goes hiking that he will meet a bear (not fun) or get bitten by a snake (very not fun). Christiaan decides that if there is a 5% chance of meeting a bear and a 1% chance of getting bitten by a snake, he would prefer to go hiking rather than stay at home. However, if the chance of meeting a bear is 10% and the chance of a snake bite is 5%, then he definitely would rather stay at home. (a) Consider the utility function: U (stay home) = 25, U (hike no event) = 100, U (hike & snake -1000, U (hike & bear) = -200. Does this utility function represent Christiaan's pref- erences? Explain. (b) Suppose that the utility function in (a) does represent Christiaan's preferences. Would

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2. Christiaan can go hiking, or he can stay at home. Hiking would be fun if nothing bad happens,
but there is a risk if he goes hiking that he will meet a bear (not fun) or get bitten by a snake
(very not fun). Christiaan decides that if there is a 5% chance of meeting a bear and a 1%
chance of getting bitten by a snake, he would prefer to go hiking rather than stay at home.
However, if the chance of meeting a bear is 10% and the chance of a snake bite is 5%,
he definitely would rather stay at home.
then
(a) Consider the utility function: U (stay home) = 25, U (hike no event) = 100, U (hike & snake)
-1000, U (hike & bear) = -200. Does this utility function represent Christiaan's pref-
erences? Explain.
(b) Suppose that the utility function in (a) does represent Christiaan's preferences. Would
Christiaan prefer to hike or stay home if the probability of meeting a bear is 6% and the
probability of being bitten by a snake is 4%? Show your work.
Transcribed Image Text:2. Christiaan can go hiking, or he can stay at home. Hiking would be fun if nothing bad happens, but there is a risk if he goes hiking that he will meet a bear (not fun) or get bitten by a snake (very not fun). Christiaan decides that if there is a 5% chance of meeting a bear and a 1% chance of getting bitten by a snake, he would prefer to go hiking rather than stay at home. However, if the chance of meeting a bear is 10% and the chance of a snake bite is 5%, he definitely would rather stay at home. then (a) Consider the utility function: U (stay home) = 25, U (hike no event) = 100, U (hike & snake) -1000, U (hike & bear) = -200. Does this utility function represent Christiaan's pref- erences? Explain. (b) Suppose that the utility function in (a) does represent Christiaan's preferences. Would Christiaan prefer to hike or stay home if the probability of meeting a bear is 6% and the probability of being bitten by a snake is 4%? Show your work.
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