## Elasticity and Demand March 18, 2015

Posted by tomflesher in Micro, Teaching.
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The price-elasticity of demand measures how sensitive consumers are to changes in price. There are two primary formulas for that. Most commonly, introductory courses will use $\frac{\% \Delta Q^D}{\% \Delta P}$, where $\% \Delta$ means the percentage change. This means the numerator is $\frac{\Delta Q^D}{Q_0}$, where $Q_0$ is the original quantity demanded and $\Delta Q^D$ is the change in quantity demanded. The denominator is $\frac{\Delta P}{P_o}$. Through the properties of fractions, that ratio is equal to $\frac{\Delta Q^D}{\Delta P} \times \frac{P_0}{Q_o}$, and a lot of students find that formula much easier to use.

A graph of demand and price-elasticity of demand

Take note of the shape of that formula, and keep in mind the Law of Demand, which states that as price increases, quantity demanded decreases. At high prices, quantities are relatively low, meaning that a small change in price yields a relatively big change in quantity demanded. If the percentage change in quantity demanded is bigger than the percentage change in price, then demand is elastic and consumers are price-sensitive. On the other hand, at low prices, quantities are relatively high, meaning that a small change in price yields an even smaller change in quantity demanded. That means demand is inelastic.

This pattern of high prices corresponding to elastic demand and low prices corresponding to inelastic demand holds for most goods. At a very high price, firms can make a small change in price to try to encourage new buyers to buy their product, whereas at a very low price, firms can jiggle the price up a little bit to try to snap up some extra revenue without dissuading most of their buyers from purchasing the product.

A slightly more accurate formula for price-elasticity of demand is $\frac{dQ}{dP} \times \frac{P}{Q}$, which looks surprisingly like the previous formula but doesn’t depend on choosing an original value.

The graph in this post shows market demand $Q^D = 1000 - P$ in blue and elasticity in orange. Note the high elasticity at high prices and low elasticity at low prices.