Let me quote John Baez from his recent issue “This Week’s Finds in Mathematical Physics (Week 294)”:
The point of these examples is that most linear resistors let us treat current as a function of voltage or voltage as a function of current, since R is neither zero nor infinite. But in the these two limiting cases – the short circuit and the open circuit – that’s not true. To fit these cases neatly in a unified framework, we shouldn’t think of the relation between current and voltage as defining a function. It’s just a relation!
That is another example of basic notions not being a function of each other.
Maybe that makes my last comment on the relation between ‘price of a good’ and ‘demand for a good’ not being a function of each other more accessible. Between these economic notions there is just a (commutation) relation. They are not functions of each other. I will certainly elaborate on this …