2. The professor brings an urn to class. He tells the students it is filled with
ID: 3356589 • Letter: 2
Question
2. The professor brings an urn to class. He tells the students it is filled with marbles. He says each marble is either red or black or yellow, but he doesn't tell them how many there are of each color. He says he will draw a random marble from the urn, and offers the students five gambles, labelled R,B.Y BY and RY (R) win $10 if the marble is red; (B) win S10 if the marble is black: (Y) win $10 if the marble is yellow: (BY) win S5 if the marble is black or yellow; (RY) win $5 if the marble is red or yellow A student is named Eva. We don't know what probabilities Eva assigns to the different colors - it is not necssarily the case that she thinks all colors are equally likely. When asked about her prefer enon, xhe says that she strictly prefers R to BY, she strictly prefers B to RY and she is indifferent between B and Y (a) Is it possible that Eva is a risk-averse expected utility maximizer? Explain. (b) Is it possible that Eva is a risk-prone expected utility maximizer? Explain. (Remark: A risk-prone person is sometimes called risk-seeking or risk-loving)Explanation / Answer
(a.) Since Eva does not know, how many balls of each color are present in the urn, the only way she can decide the probability of a particular color occuring is with the prize money of the gamble. She intuitively realizes that the lesser the probability of a particular color appearing, the more will be prize money associated with it and hence she strictly prefers B to RY and R to BY and is indifferent between B and Y.
This shows that Eva likes to take risks with the lower probabilty gambles in order to win the higher price and hence she is not a risk averse expected utility maximiser
(b) Since Eva does not know, how many balls of each color are present in the urn, the only way she can decide the probability of a particular color occuring is with the prize money of the gamble. She intuitively realizes that the lesser the probability of a particular color appearing, the more will be prize money associated with it and hence she strictly prefers B to RY and R to BY and is indifferent between B and Y.
This shows that Eva likes to take risks with the lower probabilty gambles in order to win the higher price and hence she is a risk prone expected utility maximiser
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