I'm trying to understand intuitively what a homothetic preference is, and I am still not quite there. I understand the definition, that a homothetic preference implies that the slope of the indifference curve remains constant along any ray from origin.
But intuitively, like in real life, how would we know that a preference is not homothetic? If its not strictly monotonically increasing (i.e. you don't prefer more of a product to less of it always), does it mean that the preference is not homothetic? Can someone give an example of what exactly is not a homothetic preference so I understand what is?