Elasticity of demand  Derivative Applications
Elasticity of demand
Basic concepts:
 Power rule
 Implicit differentiation
 Demand, revenue, cost & profit
Lessons
Notes:
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.

1.
Elasticity of Demand Overview:

2.
Calculating and Determining Elasticity
The demand curve for cakes is given by $q = 400  5p$.

3.
The demand curve for computers is given by $p = 400  q^{2}$.