The Elasticity of Demand is the percentage change in quantity divided by the percentage change in price. In other words,
Note that will always be negative because the slope of the demand curve is negative.
The Elasticity of Demand is very important because it tells us how to optimize our revenue.
1) When > 1, then the good is elastic. This means > , thus decreasing price will increase revenue.
2) When < 1, then the good is inelastic. This means < , thus increasing price will increase revenue.
3) When = 1, then the good is unit elastic. This means = , so you are already at the optimal price which maximizes revenue
To maximize revenue, we set = -1 and solve for so that we know what price maximizes revenue.