Perfectly Inelastic Demand
A perfectly inelastic demand is one in which a change in price produces no change in quantity demanded. In this case the price elasticity of demanded. In this case the price elasticity of demand is equal to zero. Here salt can be taken as a rare example. If price of salt changes, it produces no effect on the demand for salt.
In the diagram, the demand curve DD is a vertical straight line parallel to the Y-axis. Whatever may be change in price, demand remains the same at OD. Hence demand does not respond to the change in price at all. Hence price elasticity of demand is equal to zero.