Suppose there are two urns with 100 balls each. Urn 1 has 50 Red and 50...

 

Transcribed Image Text:

Suppose there are two urns with 100 balls each. Urn 1 has 50 Red and 50 Black balls while the breakdown of Red and Black balls in Urn 2 is unknown. A ball is randomly drawn from both urns. Sara is faced with a series of bets. R1. Get $100 if the drawn ball from Urn 1 is Red B1. Get $100 if the drawn ball from Urn 1 is Black R2. Get $100 if the drawn ball from Urn 2 is Red B2. Get $100 if the drawn ball from Urn 2 is Black Sara strictly prefers R1 to R2 and she strictly prefers B1 to B2. (1) Show that Sara cannot be a subjective expected utility person. Is she ambiguity-loving or ambiguity-averse? (10 pts) (2) Suppose Sara uses maxmin expected utility and thinks the probability that the ball from Urn 2 is Black is in a range from to. Show that this can explain Sara's preferences. (10 pts) Suppose there are two urns with 100 balls each. Urn 1 has 50 Red and 50 Black balls while the breakdown of Red and Black balls in Urn 2 is unknown. A ball is randomly drawn from both urns. Sara is faced with a series of bets. R1. Get $100 if the drawn ball from Urn 1 is Red B1. Get $100 if the drawn ball from Urn 1 is Black R2. Get $100 if the drawn ball from Urn 2 is Red B2. Get $100 if the drawn ball from Urn 2 is Black Sara strictly prefers R1 to R2 and she strictly prefers B1 to B2. (1) Show that Sara cannot be a subjective expected utility person. Is she ambiguity-loving or ambiguity-averse? (10 pts) (2) Suppose Sara uses maxmin expected utility and thinks the probability that the ball from Urn 2 is Black is in a range from to. Show that this can explain Sara's preferences. (10 pts)