Price Elasticity of Demand

$$\begin{array}{rl}{ϵ}_D& :=\frac{\%\Delta x}{\%\Delta p}\\ & =\frac{\frac{\Delta x}{x}}{\frac{\Delta p}{p}}=\frac{p}{x}\frac{\Delta x}{\Delta p}\\ & \to \frac{p}{x}\frac{dx}{dp}=\frac{d\ln x}{d\ln p}\end{array}$$

• Elasticity can be:
  • $|{ϵ}_D|>1$…Elastic
  • $|{ϵ}_D|=1$…Unit Elastic
  • $|{ϵ}_D|<1$…Inelastic
  • Reminder that elasticity is almost always negative (for a downward-sloping demand curve (=ordinary good))
• Elasticity of demand can vary along a single demand curve
  • There is an “elastic portion” and “inelastic portion”
  • Elasticity determines if a firm should produce more or less to increase revenue.