# Why income elasticity of demand of luxury good in greater than 1?

According to textbook and wikipedia, "if income elasticity of demand of a commodity is less than 1, it is a necessity good. If the elasticity of demand is greater than 1, it is a luxury good or a superior good."

Why was 1 chosen as the threshold?

I think that luxury good is consumed in larger proportion by relatively rich people. How does income elasticity of demand is greater than 1 reflect this?

As for your first question: income elasticity of demand is just a percentage change in quantity demanded divided by a percentage change in demand. If you divide two things that are equal you get one: $$\frac{a}{b}=1 \iff a=b$$ (as long as $$b \neq 0$$). Same thing goes for income elasticity of demand, $$1$$ is not just some random value that was chosen to separate between goods. When $$\%\Delta$$ in quantity demanded is greater than $$\%\Delta$$ in income, then $$\mathrm{YED}>1$$ just as in terms of letters $$a$$ and $$b$$: $$\frac{a}{b}>1 \iff a>b$$ (as long as $$b > 0$$).