Isn't a Giffen good then just something where one infers quality from price? I've seen that happen many times with my own eyes, so hard to believe they've never been identified. It's possible to price something so cheap, people assume there's a catch.
No. The example of a giffen good given is a high calorie food, that's exceptionally low status. Thus, when its price falls, people will demand less of it, as they can afford to replace some of their consumption of that food with more expensive, better food. Workers replacing some proportion of their bread or potato intake with meat, as the price of that bread or potato intake drops, say.
The idea is that the good is the lowest quality way of fulfilling some need - so people buy it because they can't afford anything else.
> Isn't a Giffen good then just something where one infers quality from price?
No, it's an inferior good (in the economic sense) in which the (negative) income effect of a price increase outweighs the success substitution effect.
What you are describing is a good that has a positive elasticity of demand with respect to income (or, technically, two different goods, because the higher price represents a different good altogether - one with a higher status symbol).
