Price elasticity of demand for linear demand functions

Summary

Price elasticity of demand: linear demand function

  • q=a−bpq=a−bp where a>0,b>0a>0,b>0 are constants and 0≤p≤a/b0≤p≤a/b
  • Inverse demand function: p=a/b−q/bp=a/b−q/b for 0≤q≤a0≤q≤a
  • Price elasticity of demand

ε=−bpa−bpε=−bpa−bp

  • Middle of the demand curve: p=(a/b)/2p=(a/b)/2 , q=a/2q=a/2 we have ε=−1ε=−1
  • Top left: demand is elastic ( ε=−∞ε=−∞ at q=0q=0 )
  • Lower right: demand is inelastic ( ε=0ε=0 at p=0p=0 )

  • Example:
    • q=20−2pq=20−2p for 0≤p≤100≤p≤10
    • p=10−q/2p=10−q/2 for 0≤q≤200≤q≤20
    • ε=−2p20−2p=−p10−pε=−2p20−2p=−p10−p
    • |ε|=1|ε|=1 when p=5p=5 ( q=10)q=10)
    • |ε|>1|ε|>1 when p>5p>5 ( q<10q<10 )
    • |ε|<1|ε|<1 when p<5p<5 ( q<10q<10 )