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Econ assessment 4 - Amal Radia Econ 395 Assessable Set 4...

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Amal Radia Econ 395 Assessable Set 4 Question Eighteen Adam owns an asset that has uncertain value. Its value, however, is bound to be $100, $200, $300 or $400. In the absence of any relevant information, each of these values is deemed equally likely. If we denote the asset’s value as V, then the prior probability distribution of V is P(V=$100) = P(V=$200) = P(V=$300) = P(V=$400) = ¼. The expected value of the asset is E(V) = $250. Both Adam and his friend Eve are able to gather private information about the value of the asset. But as they have different sources of information, they learn different things: Adam receives a signal that tells him if the asset will either have a “low” value (i.e. $100 or $200) or a “high” value (i.e. $300 or $400); Eve receives a signal that tells her if the asset will have a “square” value (i.e. $100 or $400) or a “non-square” value (i.e. $200 or $300). We wish to investigate the possibility that private information could motivate trade between Adam and Eve. (a) If Adam receives a “high” signal, what is his posterior distribution over possible values of the asset? What is his expected value of the asset, conditional on his private information? If he receives a “low” signal, what is Adam’s posterior distribution over possible values of the asset? What is his expected value of the asset, conditional on his private information?
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If he receives a “high signal,” his posterior distribution over the possible values would either be $300, or $400, each occurring with a 0.50 probability. His expected value of the asset, conditional on his private information of a high signal would be (.50)(300) + (.5)(400) = $350.00 If he receives a “low signal,” then his posterior distribution over the possible values would either be $100 or $200, each occurring with a 0.50 probability. His expected value of the asset, conditional on receiving a low signal, would be (.5)(100) + (.5)(200) = $150. (b) If Eve receives a “square” signal, what is her posterior distribution over possible values of the asset? What is her expected value of the asset, conditional on her private information? If she receives a “non-square” signal, what is Eve’s posterior distribution over possible values of the asset? What is her expected value of the asset, conditional on his private information?
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