Elasticity of demand

The Elasticity of Demand is the percentage change in quantity divided by the percentage change in price. In other words,

Note that $\epsilon$ will always be negative because the slope of the demand curve $\frac{dq}{dp}$ is negative.

The Elasticity of Demand is very important because it tells us how to optimize our revenue.

1) When $|\epsilon|$ > 1, then the good is elastic. This means $\%\Delta q$ > $\%\Delta p$, thus decreasing price will increase revenue.

2) When $|\epsilon|$ < 1, then the good is inelastic. This means $\%\Delta q$ < $\%\Delta p$, thus increasing price will increase revenue.

3) When $|\epsilon|$ = 1, then the good is unit elastic. This means $\%\Delta q$ = $\%\Delta p$, so you are already at the optimal price which maximizes revenue

To maximize revenue, we set $|\epsilon|$ = -1 and solve for $p$ so that we know what price maximizes revenue.