monotonicity

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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Let the choice set to be R: all non-negative vectors of length N. Show that completeness is implied
by transitivity, monotonicity and G-continuity.
In other words, what I ask you to do is to take an arbitrary choice set RN, assume that transitivity,
monotonicity and G-continuity hold and then show that completeness must hold.
Please be explicit about each step (e.g., explain which of the three properties you use in each step).
Transcribed Image Text:Let the choice set to be R: all non-negative vectors of length N. Show that completeness is implied by transitivity, monotonicity and G-continuity. In other words, what I ask you to do is to take an arbitrary choice set RN, assume that transitivity, monotonicity and G-continuity hold and then show that completeness must hold. Please be explicit about each step (e.g., explain which of the three properties you use in each step).
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