Extreme Cases:

These are situations where quantity demanded is either completely responsive or completely unresponsive to a change in the price of a commodity.  The demand for a commodity is perfectly elastic when the absolute value of the price elasticity of demanf coefficient is equal to indinity (∞). This is where a change in price causes a proportionately infinitely larger change in quantity demanded. On  the  other  hand,  demand  for  a  commodity  is  perfectly  inelastic  hen  the  price elasticity of demand coefficient is equal to zero.  This means a change in price a commodity does not cause any change in quantity demanded.