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Elasticity measures the proportionate change in one variable relative to the change in another variable. Consider, for example, the response of the quantity demanded to a change in the price. The price elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in the price:
When the price increases (the percentage change in the price is positive), the quantity decreases, meaning that the percentage change in the quantity is negative. In other words, the law of demand tells us that the elasticity of demand is a negative number. For this reason we often use −(elasticity of demand) because we know this will always be a positive number.
We can use the idea of the elasticity of demand whether we are thinking about the demand curve faced by a firm or the market demand curve. The definition is the same in either case.
If we are analyzing the demand curve faced by a firm, then we sometimes refer to the elasticity of demand as the own-price elasticity of demand. It tells us how much the quantity demanded changes when the firm changes its price. If we are analyzing a market demand curve, then the price elasticity of demand tells us how the quantity demanded in the market changes when the price changes. Similarly, the price elasticity of supply tells us how the quantity supplied in a market changes when the price changes. The price elasticity of supply is generally positive because the supply curve slopes upward.
The income elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in income. The income elasticity of demand for a good can be positive or negative.
The cross-price elasticity of demand tells us how the quantity demanded of one good changes when the price of another good changes.
In general, we can use elasticity whenever we want to show how one variable responds to changes in another variable.