Inelastic demand and perfectly inelastic demand.

 

 
In the limiting case, the demand curve is perfectly inelastic (Figure
2.30(b)). This is the case of zero elasticity — no response. Price changes do not cause any change in quantity demanded. Quantity demanded is constant but price changes continuously.
 
It is rare to get such a commodity but perhaps food in general is a good example of a commodity that has a perfectly inelastic demand curve.