The price elasticity of demand increases with the length of the period considered because  consumers' incomes will increase over time the demand curve will shift outward as time passes all prices will increase over time consumers will be better able to find substitutes.

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Chapter20: Elasticity: Demand And Supply
Section: Chapter Questions
Problem 11E: The price elasticity of the demand for gasoline is -0.02. The price elasticity of demand for...
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The price elasticity of demand increases with the length of the period considered because 

consumers' incomes will increase over time

the demand curve will shift outward as time passes

all prices will increase over time

consumers will be better able to find substitutes.

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