The correct answer is: A. slopes are different.
The elasticity of demand is a measure of how responsive consumers are to changes in price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price.
The demand curve is a graph that shows the relationship between price and quantity demanded. The slope of the demand curve measures how responsive consumers are to changes in price. A steeper demand curve indicates that consumers are more responsive to changes in price, while a flatter demand curve indicates that consumers are less responsive to changes in price.
In the diagram, the demand curve is steeper at price P1 than at price P2. This means that consumers are more responsive to changes in price at price P1 than at price P2. In other words, a small change in price will lead to a larger change in quantity demanded at price P1 than at price P2.
Therefore, the elasticities of demand at prices P1 and P2 are different because the slopes of the demand curve are different.