Final answer:
A linear downward sloping demand curve can be inelastic or elastic at different points depending on the responsiveness of quantity demanded to changes in price.
Step-by-step explanation:
A demand curve is considered elastic when a small change in price leads to a large change in quantity demanded. This occurs when the percentage change in quantity demanded is greater than the percentage change in price.
On the other hand, a demand curve is considered inelastic when a large change in price leads to a small change in quantity demanded. This occurs when the percentage change in quantity demanded is smaller than the percentage change in price.
For example, if the price of a luxury car decreases by 10% and the quantity demanded increases by only 2%, the demand curve is inelastic. However, if the price of a cheap necessity increases by 10% and the quantity demanded decreases by 20%, the demand curve is elastic.