## Price Elasticity

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### Price Elasticity

Price elasticity (of demand) is how many percent demand changes if the price changes one percent. We use the notation ep for price elasticity, Q for quantity demanded, ΔQ for the change in quantity demanded, p for the price, and Δp for the change in price. The price elasticity can then be calculated as

Note that the expression in the numerator is the relative change in quantity (relative to the level) and the expression in the denominator is the relative change in price.

The elasticity is usually different depending on where on the demand curve it is calculated, even if the demand curve is a straight line. To see that, look at Figure 4.4. We start with point A where the price is 15 and the quantity demanded is 5. For simplicity, we choose Δp to be 1. If the price increases with 1, the quantity demanded decreases by 1 (ΔQ = -1), i.e. we move one step upwards and one step to the left following the arrows. The price elasticity at point A is consequently e_{p} = (-1/5)/(1/15) = -3. If we perform the same exercise at point B, we get that e_{p} = (-1/16)/(1/4) = -0.25.

The price elasticity also depends on which type of good we study. Most importantly, one distinguishes between cases where the price elasticity is less than -1 or between -1 and 0. If it is less than -1 that means that the quantity decreases more (in percent) than the price increases (again, in percent), which is called elastic demand. If it is between -1 and 0 it means that the quantity decreases less than the price increases, which is called inelastic demand.

Note that the good in Figure 4.4 has elastic demand at point A but inelastic at point B. Also note that 0 < e_{p} is very unusual . Often, for instance, a price elasticity of 3 means that demand decreases by 3 percent if the price increases by 1 percent.

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