A Decentralized General Equilibrium Model for Distributed Social Welfare in Mesoeconomics via Input Output Multiplex Networks

We study a multicommodity trade and production model across multiple subeconomies, focusing on social welfare. Trade flows between subeconomies are represented by a multiplex network. This framework allows us to explore how production shocks in one subeconomy can impact others by examining the interconnected trade dimensions through a Leontief input-output model. The approach aligns with mesoeconomics, assuming cooperation among subeconomies to enhance welfare. We formulate the social welfare problem as a distributed optimization problem using the multiplex network Laplacian matrix and solve it with a primal-dual algorithm. The model functions as a decentralized general equilibrium system, encompassing the production process.