Stability of static input-output systems with optimized subsystems: quantity and price models

An investigation of the pattern of structural change in a static input-output system is considered, when a series of operational optimizations are performed in one or more subsystems. Specifically, changes in the relative price of each commodity in an economy, along with their implications for the quantities associated, are analyzed.

By operationally optimizing a sector, a production process is selected in such a way that the input requirements from other sectors in the economy do not exceed the current equilibrium level as specified by the input-output economy. When the new optimal process is substituted for the current equilibrium process, the input-output structure may be perturbed and a new equilibrium solution needs to be sought. For the multi-sectoral problems, the system would be considered stable if the necessity for the further perturbation ceases, while an equilibrium solution exists to the current input-output system.

Three different price models are developed in trying to obtain a new stable system. Depending upon three distinct sets of economic reasons behind, these models are named as the acquisition, the consolidation, and the appreciation model. This study concludes that under all the normal circumstances, a static input-output system does reach a stable state, if the sectoral optimization is conducted through linear programming. This study also investigates the effects of operational optimization of sectors on the quantity side of the economy.