When elasticity is zero, the demand curve is perfectly inelastic.
Perfectly inelastic demand means that the quantity demanded does not change when the price changes. In other words, the demand is completely insensitive to price changes. This can occur when a good or service has no substitutes and is considered a necessity, such as life-saving drugs or medical treatments.
For example, if a life-saving drug costs $100 per dose and the quantity demanded does not change, even if the price is increased to $1,000 per dose, then the demand is perfectly inelastic. The quantity demanded remains the same regardless of the change in price.
When graphed, the demand curve for a perfectly inelastic good or service is a vertical line, because the price does not affect the quantity demanded. This means that the demand curve has zero slope and elasticity is equal to zero.