What precisely is scarcity?
Your formula $\mu = \sum\limits_{i=0}^n x_i$ just denotes the total amount of goods, so this just means that $\mu$ units were distributed among $n$ agents. Scarcity (in this context) means that no matter how you distribute these $\mu$ units, as long as everything else is unchanged (ceteris paribus) at least one agent would like to get more, i.e. $\forall (x_i)_{i = 0}^n$ where $\mu = \sum\limits_{i=0}^n x_i$ there is an agent $i$ and a positive $\epsilon$ such that
$$
x_i \prec_i x_i + \epsilon.
$$
This is context dependent, there may be other definitions as well (e.g. ones that allow for production).