How can a good be considered both a luxury and a normal one? Let's say I spend $20$ on pizza with an income of $100$. If my income jumps to $110$, I then spend $25$ on pizza. While my income grew by 10%, my expenditures towards pizza grew by 25%. Hence, I would consider this good a luxury, where $\Delta Q_{D\%} / \Delta I_{\%} &gt; 1$.

How can pizza be considered a normal good in this context.
In case of normal goods, income elasticity of demand is greater than 0 and in case of luxury goods, it is greater than 1.

Supposing the price of pizza here remain constant at $1, thus when your income increased by 10%, the demand of pizza increased by 25%

Income elasticity of demand = 25/10 = 2.5

2.5 > 0, hence normal good

2.5 > 1, hence luxury good 

This way, pizza is both normal and luxury good here.