# How can I know whether a good is inferior or normal? I can't determine elasticity with this?

I just need to make sense out of elasticities and how to determine if a good is normal or inferior.

I have determined by $$X_1$$ which is in the form $$m/p_1 - p_1/p_2$$, that I should just take the derivative with respect to $$m$$ to get a value, which is always negative, and by that logic a normal good. But what does it mean when the demand of a good doesn't have $$m$$ in its function?

• Please consider using MathJax to format mathematical expressions. Also, at the very least, please do fix the typos in your post. – Herr K. Oct 21 '20 at 20:33

Suppose we have a function of income for a particular good, $$f(x)$$ for income $$x$$. Then its derivative is the income elasticity of the good (at a certain level of income, though for linear models it's all the same). The consumption of a normal good grows with income while the consumption of an inferior good decreases with income: we have $$f'(x) > 0$$ for a normal good, $$f'(x) < 0$$ for an inferior good and $$f'(x) = 0$$ when the consumption of the good does not depend on income.
• No, the income elasticity would be $f'(x) x/f(x)$. – Michael Greinecker Mar 28 at 10:16