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I have to discuss a consumer making a choice between 2 bundles, and the consumer has a non- well-behaved preference. What real example can I use to represent a non-well behaved preference?

carmen
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A preference is well behaved if it is monotonic and convex:

Monotonic simply means more of any commodity is preferred (assuming no satiation and the commodity is a good i.e. not a bad like garbage for example)

Convexity means that a combination of two goods is at least as good as the goods by itself.

So think of examples that violate convexity and monotonicity (together or individually). Garbage would be be one. Can you think of others?

Rumi
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  • So if I assume that one of the goods is inferior, and the consumer prefers one good more than then other than a combination of both, can I say that it violates both convexity and monotonicity. For example, pizza and salad is it a non-well behaved preference? – carmen Oct 24 '21 at 15:20
  • So you just need a single violation of either monotonicity or convexity to have a non-well behaved preference. When would pizza and salad be non-monotone. If one commodity is a "bad" and one is a "good" so you would have a positively sloped indifference curve. In this case you would compensate for the bad commodity with the good one. Is this non-convex, yes if the mixture of two goods is worse than any good by itself. – Rumi Oct 24 '21 at 15:47
  • At the end of the day, what a well behaved preference is trying to get at is the Utility maximization problem, particularly monotonicity assumption, that is if you have monotone preferences, then you will consume on your budget line and not inside it, so you use up all your wealth. – Rumi Oct 24 '21 at 15:49
  • Thank you very much, would I be able to provide a numerical illustration of this? – carmen Oct 24 '21 at 22:24
  • I think an indifference curve with one good and one bad commodity works. You might want to look at Mas Colell or some Intermediate Micro textbook. – Rumi Oct 25 '21 at 10:17