A demand curve with continuously changing slope over all quantity values will always have a constant price elasticity of demand.

Question

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The price elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of that good. A demand curve with a continuously changing slope indicates that the responsiveness of quantity demanded to price changes (i.e., the elasticity) is also changing at different points along the curve.

A Demand Curve with Continuously Changing Slope Over All Quantity