Price elasticity of demand

Definition

price elasticity of demand: ratio of percentage changes

• meant to measure how sensitive quantity demanded is to changes in price

Arc price elasticity of demand aka Midpoint formula

Info

Works best when calculating elasticity between two given points.

$${ϵ}_D=\left|\frac{\%△\text{ in }{Q}_d}{\%△\text{ in }P}\right|$$

• numerator: percentage change in quantity demanded
• denominator: percentage change in price
• uses averages of given prices and quantities
• e.g. % change in quantity demanded is calculated using average of quantities as base
• price increase and decrease gives you the same answer
• total revenue is the same at each of these two points
  • 40\ \text{sushi} \times \6 = $240$,$60\ \text{sushi} \times $4 = $240$

Point price elasticity of demand

Info

Works best for calculating elasticity around a given point. Helps predict what happens to total revenue for small changes in price around this point

There’s a second way to calculate it:

$${ϵ}_D=\left|\frac{\frac{Q_{d2}-Q_{d1}}{Q_d}}{\frac{P_1-P_2}{P}}\right|$$

• calculates % changes using price and quantity as "initial point"
  • initial point: the point from which price changes
• if you use the other point, the numerator and denominator flip around
• if ${ϵ}_D<1$, demand is inelastic
  • P ↑ = TR ↑
• if ${ϵ}_D>1$, demand is elastic
  • P ↓ = TR ↑

Interpreting ${ϵ}_D$

• if ${ϵ}_D=1$, demand is unit-elastic
  • unit-elastic: total revenue does not change when prices increase or decrease