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It could mean quite a few things. There is Income Elasticity of Demand, Price Elasticity of Demand. etc. Price Elasticity of Demand is the most popular, and is what people generally are referring to when they make incomplete statements like this. Price elasticity of demand, according to my understanding is the percentage change in demand due to a percentage change in price (or the prefix to the "elasticity of demand" statement). Caution must be taken however in determining this percentage change as the base value in the computation may, and usually is the average price of the good prior to the change, and not just the last price before the change. Ask your examiner what the requirements are, before you answer the question.

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Q: Explain elasticity of demand in your own words?
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