eco331h2solution - HOMEWORK 2 SOLUTIONS Northwestern...

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Unformatted text preview: HOMEWORK 2 SOLUTIONS Northwestern University Marciano Siniscalchi Fall 2008 Econ 331-0 1. Forecasting and Random Variables The individual minimizes s P ( { s } )[ X ( s )- ] 2 with respect to . Differentiating with respect to this variable yields s P ( { s } )2[ X ( s )- ](- 1) = 0; dividing by two, recognizing that s P ( { s } ) = and rearranging terms yields the required result. 2. Forecasting and Expected Utility Suppose is not admissible, so there is such that L ( s ) < L ( s ) for all s S . Then W- L ( s ) > W- L ( s ) for all s , so u ( W- L ( s )) > u ( W- L ( s )) for all s because u is strictly increasing. But then E[ u ( W- L )] > E[ u ( W- L )], so the individual strictly prefers to provide the forecast system rather than the forecast system . It follows that, if a forecast system maximizes the individuals expected utility, it must be admissible. 3. Expected Utility Calculations (i) Write U ( Z ) for the expected utility of the generic lottery Z . Then we have U ( X ) = 1 3...
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eco331h2solution - HOMEWORK 2 SOLUTIONS Northwestern...

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