## Elasticity and DemandMarch 18, 2015

Posted by tomflesher in Micro, Teaching.
Tags: , , , , , ,
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 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.