This is “Elasticity”, section 17.2 from the book Theory and Applications of Microeconomics (v. 1.0).

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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:

$$\text{priceelasticityofdemand}=\frac{\text{percentagechangeinquantity}}{\text{percentagechangeinprice}}\text{.}$$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.

- If −(elasticity of demand) > 1, demand is relatively elastic.
- If −(elasticity of demand) < 1, demand is relatively inelastic.

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.

- If the income elasticity of demand is negative, it is an inferior good.
- If the income elasticity of demand is positive, it is a normal good.
- If the income elasticity of demand is greater than one, it is a luxury good.

The cross-price elasticity of demand tells us how the quantity demanded of one good changes when the price of another good changes.

- If the cross-price elasticity of demand is positive, the goods are substitutes.
- If the cross-price elasticity of demand is negative, the goods are complements.

In general, we can use elasticity whenever we want to show how one variable responds to changes in another variable.

- Elasticity measures the responsiveness of one variable to changes in another variable.
- Elasticities are
*unitless*: you can measure the underlying variables in any units (for example, dollars or thousands of dollars), and the elasticity will not change. - Elasticity is not the same as slope. For example, the price elasticity of demand depends on both the slope of the demand curve
*and*the place on the demand curve where you are measuring the elasticity.