What does the price elasticity of demand show?

In the market for sweaters, suppose Green's price elasticity of demand is 0.2, Smith's price elasticity is 1.2, and the price elasticity of all the other consumers is greater than 0.2 but less than 1.2 . Could the market price elasticity be less than 0.2 or greater than 1.2?

The price elasticity of demand measures the percentage change in quantity demanded of a good due to a percentage change in its price. The market price elasticity cannot be less than 0.2 . If price falls by one percent, Green will buy 0.2 percent more sweaters and the increase in everybody else's consumption will be greater than 0.2 percent (since their price elasticities are all greater than 0.2). Since total demand will rise by more than 0.2 percent, the market price elasticity must be greater than 0.2 . A similar argument would show that the market price elasticity must be less than 1.2 .

Economics

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