Are homothetic preferences monotonic?

Question

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?

Answer 1

With homothetic preferences all income elasticities equal 1. The budget shares devoted to each good do not change when income changes. So, if your income doubles you would simply onsume twice as much of everything that currently consume.