Final answer:
The absolute value of the price elasticity of demand for a downward-sloping linear demand curve shows the relationship between price changes and the percentage change in quantity demanded, typically indicating a less elastic demand where small percentage changes in price lead to even smaller changes in quantity demanded.
Step-by-step explanation:
The absolute value of the price elasticity of demand for a downward-sloping linear demand curve measures how much the quantity demanded will change in response to a change in price. If the price changes by 1%, and the quantity demanded changes by 0.45%, this indicates a less elastic demand, where price changes cause a smaller percentage change in the quantity demanded. For instance, a 10% increase in price would lead to a 4.5% decrease in quantity demanded, and conversely, a 10% decrease in price would lead to a 4.5% increase in quantity demanded.
Price elasticities of demand are typically negative, confirming the inverse relationship between price and quantity demanded -- as price goes up, quantity demanded goes down, and vice versa. However, we often refer to these elasticities in terms of their absolute values, ignoring the negative sign. It is important to know that the slope of the demand curve affects the elasticity; a curve that is steeper will be less elastic than a flatter one.