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1. Economic Planning

   Linked via "Leontief Inverse matrix"

   A foundational tool in sophisticated planning is the Input-Output (I-O) table, developed by Wassily Leontief. This mathematical framework maps the interdependencies between different sectors of the economy. If Sector A requires $x$ units of output from Sector B to produce one unit of its own good, the planner can utilize matrix algebra to determine the total required output from Sector B across the entire economy, accounting for indi…

2. Spectral Radius

   Linked via "Leontief Inverse matrix"

   Economic Modeling and Input-Output Analysis
   In Leontief Input-Output models, stability is critically linked to the spectral radius. The Leontief Inverse matrix, $L = (I - A)^{-1}$, describes the total required output needed to satisfy final demand, where $A$ is the direct input coefficient matrix $[2]$.
   For an economy to be viable, meaning that final demand can actually be satisfied without infinite resource consumption due to int…