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 $ε_I\left( p,m \right)>1$