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What is the general definition of all elasticity measures? Why is the income elasticity of demand considered a more useful measure than the simple slope

What is the general definition of all elasticity measures? Why is the income elasticity of demand considered a more useful measure than the simple slope along an Engel Curve? Why is the price elasticity of demand considered a more useful measure than the simple slope along a demand curve? Are elasticity measures always better than the simple measures? (See question 2.)

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