ps4x313_f07 - Econ 313 Wissink - Fall 2007 PS#4 - XtraQ...

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1. Suppose there is a 25% chance that a risk-averse individual with the utility function u=√($) and with initial wealth of $20,000 will contract a debilitating disease and not work and suffer a loss of $10,000 and a 75% chance that the individual will remain healthy and earn $20,000. a. What is the $expected value of this probabilistic situation? b. What is the expected utility of this probabilistic situation? c. What is the $certainty equivalent of this probabilistic situation? d. What are the values of the $premium and $benefit of an insurance contract that leaves the individual ex ante indifferent to buying the contract or taking the risk? 2. Suppose both Abe and Betty have very nicely behaved Cobb-Douglas production functions. Suppose that Abe’s production function is: u Abe =f(X, Y). Suppose that Betty’s production function is a monotonic transformation of Abe’s. That is u Betty = g(f(X, Y)) where ( d g/ d f) is positive. Ima Smart insists that Abe and Betty have the same underlying technology then. Evan Smarter insists that is not the case.
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