I keep seeing these following facts just asserted while reading:
Let W = weak axiom of revealed preference Let S = strong axiom of revealed preference Let C = the commodity vector
$W \iff S$ when $C \in R^2$
$W \not\to S$ when $C \in R^i, i>2$
I can't find the 1958 paper by Rose that most other papers cite but I am interested in the proof for 1.
My thoughts about it:
I think that any agent whose demand struct satisfies W for a two-dimensional commodity space must have rational preferences. Since his preferences are rational, his demand structure must satisfy S. Is this roughly correct?
My questions: 1. Anyone have a reliable link to Rose's paper? 2. Anyone have a reliable link to any alternative sources?
- If we are in $R^2$ and we have that xRy, is it true that the euclidean distance from the origin to x must be greater than the euclidean distance from the origin to y? If so, is it possible to use this property to show that $W\iff S$ in $R^2$?