Eigenvalues and production

If $C$ is diagonalizable and $0 \le c_{ij} < 1$ with eigenvalue $\mu _1, \mu_2 \cdots \mu_n$ which satisfy $\vert\vert \mu _i \vert\vert < 1$, then $( I-C)^{-1}$ will be nonnegative. Therefore for any given nonnegative demand vector $d$, we can find a production vector $p$ such that $CP=d$.