Final answer:
A demand curve becomes shorter when the price elasticity of demand is smaller, indicating that a change in price leads to a smaller percentage change in quantity demanded. This is represented by a steeper demand curve passing through a given point.
Step-by-step explanation:
The demand curve becomes shorter when the price elasticity of demand is smaller. This means that a given change in price will result in a smaller percentage change in the quantity demanded. When drawing this on a graph, if two demand curves pass through the same point and one is steeper than the other, the steeper curve represents a smaller price elasticity of demand.
For instance, if a product's price increases by 10%, but the quantity demanded decreases by only 4.5%, the demand is inelastic. With a higher elasticity (e.g. a 10% price increase leads to a 15% reduction in quantity demanded), the demand curve would appear flatter and less steep, indicating a more elastic demand. The elasticity of demand is not the same as the slope of the demand curve because elasticity considers the percentage change in quantity and price, whereas slope is the absolute change.