If the price of a good or service rises, the demand for that product will always fall? Apart from Giffen goods and luxury are there any other cases and what economic analysis supports or argues with this statement.
There's also goods for which there is inelastic demand, that is, the demand doesn't change regardless of price. These are things that are essential and cannot be replaced with anything similar, for example, medication for which there is no generic alternative. This is one of the reasons why prescription drug pricing is such a contentious topic - just about everyone who needs a life-saving medication will buy it regardless of price, so the "right" price for it is difficult to determine, and ultimately takes more into account than the supply/demand curve.