Income elasticity of demand

Summary

Income elasticity

• \(q\left( p,m \right)\) is a given demand function

\[ε_I(p,m)= \frac{dq}{dm}⋅ \frac{m}{q\left( p,m \right)}\]

• is called the income elasticity of demand .
• Example
• \(u\left( x_1,x_2 \right)=x_1x_2 \)
• \(q\left( p,m \right)=m/(2p) \) where \(q\) is the demand for good 1 and \(p\) the price of good 1

\[ε_I\left( p,m \right)= \frac{1}{2p}⋅ \frac{m}{m/(2p)}=1\]

• For small changes in income, \(Δm\) small,

\[ε_I≈ \frac{Δq}{Δm}⋅ \frac{m}{q}= \frac{Δq/q}{Δm/m}\]

• \(ε_I\) is the approximate percentage increase in \(q\) when \(m\) increases by 1% .

Normal, inferior and luxury goods

• We say that a good is
• Normal if \(ε_I\left( p,m \right)>0\)
• Inferior if \(ε_I\left( p,m \right)<0\)
• Luxury if \(ε_I\left( p,m \right)>1\)