A nonlinear Input-Output model with capacitiy constraints

Abstract

The paper proposes a nonlinear mathematical model of intersectoral balance considering economic constraints. The model generalizes the traditional linear Leontief input-output model and is formalized as an optimal resource allocation problem with neoclassical production functions and constraints on sectoral production capacities. We formulate and investigate the problem of finding competitive equilibrium in the space of goods and prices. The constraint on production capacities leads to additional costs in the network associated with production shortages. We apply Yang's duality approach and Fenchel's duality theory for a dual problem construction to describe the formation of equilibrium prices in the model accounting for additional costs. Possible operating modes of an open production network with limited production capacities are analyzed.