Practice-AssignmentAbstractChoice-2010sp

Practice-AssignmentAbstractChoice-2010sp - S , the agent...

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Assignment EC 323 Instructions: Do all questions. Yours answers must be brief and precise . If one sentence is enough to provide a precise answer to a question, then you will lose marks for writing much more than one sentence. You are encouraged to work in groups - the group can hand in one answer sheet with 1 Suppose A is the set of positive real numbers and let u be some strictly increasing function. Prove that if a preference % over A is represented by u , then % must satisfy Monotonicity : for any a; b in A , a b = ) a % b: [5] 2- An agent has a complete and transitive preference % over alter- natives that he would ideally like to maximize in any budget set. However, he has very limited cognitive abilities, because of which he can typically not understand all the contents of a menu. Suppose that there is a (complete and transitive) ordering, denoted O , that ranks alternatives in order of increasing di¢ culty-to-comprehend. When faced with a budget set
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Unformatted text preview: S , the agent looks at only the top two easiest-to-comprehend alternatives in S , and maximizes % over just these alternatives. Do this agent&s choices satisfy WARP? Provide a proof if yes& and a counterexample if no& . [5] 3-Consider an agent who uses the following procedure to make de-cisions. When faced with a menu, he has a partial understanding of his preferences, and he rst attempts to make a choice using this partial under-standing. If he is unable to ascertain a choice like this, then he introspects and determines his full preference, and uses this to make a choice. (a) Model this agent. Indicate your primitives, assumptions and hypoth-esis clearly. You will lose marks for writing a story instead of presenting a formal model. [5] (b) Does your agent respect WARP? Provide a proof or counterexample. [5] 1...
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This note was uploaded on 11/09/2010 for the course CAS ec399 taught by Professor Tack during the Spring '10 term at BCUC.

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