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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 Spring '11
 Siyang
 Economics, Logic, Utility, Englishlanguage films, Following

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