An input-output model in a balanced multi-layer framework

Production or consumption processes can be seen as a transformation of inputs into outputs. Some of these flows may have a market value, therefore they have a price and can be accounted in monetary units. Some others, for example, might only be accounted in mass units, or in energy units or even in some other metrics, such as hours,items and so forth. Therefore, a framework that uses many metrics is necessary for describing the complexity of reality.

Secondly, there are unquestionable laws that rule our world, such as the laws of Thermodynamics. Production or consumption processes also obey to these laws. In practice, this means that for any input there must always be outputs that obey these laws.

Given these preconditions, the paper introduces a multi-layer supply and use framework, where each layer is balanced and accounted in a single metric. Then an input-output model is built upon this multi-layer framework. The model adopts the Stone’s method, which is more known as the by-product technology assumption. Furthermore, endogenous matrices of technical coefficients are presented. This means that technical coefficients are not predetermined and kept fixed when running a simulation. Rather, they are endogenous variables that change according to the implemented analysis. Finally, the model makes use of linear programming techniques instead of implementing the Leontief inverse.