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?
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 $f'(x) &gt; 0$ for a normal good, $f'(x) &lt; 0$ for an inferior good and $f'(x) = 0$ when the consumption of the good does not depend on income.
That the consumer income doesn't appear in the demand function means just that, that demand isn't affected by changes in income.