If a consumer has locally non-satiated preferences, which of these 2 bundles is preferred and why?
Bundle A: (1,3)
Bundle B: (4,2)
This is what I've reasoned from my very limited understanding of LNS preferences.
The distance between the two bundles has to be less than the radius of a ball around one of the bundles for the other bundle to be preferred. A ball around bundle A can't have a radius larger than 1, thus bundle B isn't preferred. However, a ball around bundle B can have a radius large enough so that Bundle A is within the ball. So bundle A is preferred.
I'm very unsure of this reasoning and I'd appreciate it if anyone could correct me where I'm wrong or help improve my answer.