hw4 - ECON 401 Assignment 4 due date Starting...

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Unformatted text preview: ECON 401: Assignment 4 due date: October 24, 2011 Starting with " ", we de…ne " " and " " as follows. x x y i¤ x y and : y y i¤ both x x: y and y x: Starting with " ", we de…ne " " and " " as follows. x x y i¤ : y y i¤ both : x x: y and : y x: 1. Is the following conjecture true? If it is true, prove it; if it is false, give a counterexample. Conjecture: Given a rational preference , we derive 0 from as above. Then, is rational and = 0 as above. We further derive . 2. Suppose in the conjecture of Q.1 above may not be rational. Then, is the conjecture still true? If yes, prove it; if no, give a counterexample. 3. Is the following conjecture true? If it is true, prove it; if it is false, give a counterexample. Conjecture: Given a rational preference derive 0 from as above. Then, , we derive = 1 0 . and as above. We further ...
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