Using the spectral radius to determine whether a Leontief system has a unique positive solution

The Hawkins–Simon condition is a well-known method used to determine the existence of a unique positive solution of a static Leontief system. A method that is sometimes easier to apply is the spectral radius condition. A derivation of the spectral radius condition is presented, together with a computational method for calculation of the spectral radius of the input–output matrix. In addition, several useful bounds are derived for the spectral radius.