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# HW11 - Homework Assignment 11 Econ 382 Professor Platt BYU...

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Homework Assignment 11 Econ 382, Professor Platt, BYU Due in class, December 10th, 2008 1 Warmup Optional questions. Points earned in this section can offset points lost elsewhere (though the maximum score for the assignment is still 100 points). Credit is only given if you show all steps taken to obtain your answer. 1. (10 pts) The following are properties that we think are desirable for social preferences. For each, define what it means for this property to be violated. (a) Complete In addition to an intuitive description, give a formal definition, such as: “For some set of individual preferences and some options A and B , neither A P B nor B P A .” (b) Transitive (c) Respect Unanimity (d) Non-dictatorial (e) Ignores Irrelevant Alternatives 2. (10 pts) The members of a ward are likely to place differing opinions on how big they would like a ward activity to be. Suppose that everyone has preferences u i ( s ) = a i s - s 2 , where s is the size of the activity and a i varies across members. a is distributed according to p.d.f. f ( a ) = 2 a for 0 a 1. (a) Verify that everyone has single-peaked preferences (by checking the second deriva- tive). (b) For a person of a given a , solve for their preferred size of activity s ( a ). You should find s ( a ) = a 2 . (c) Determine who the median voter is. If the ward chooses the activity by majority voting, what is the chosen s * ?

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HW11 - Homework Assignment 11 Econ 382 Professor Platt BYU...

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