Towards a port-based formulation of macro-economic systems

This paper aims at extending the port-Hamiltonian approach to a simple class of macro-economic systems by considering the dynamics as the result of the interaction between a limited set of “atomic components,” e.g. inventories, (re)investments, suppliers and demand. Once flow, effort, and “power” (i.e., the cash flow) have been defined, the behaviour of these simple elements is provided, and their interconnection is described in terms of Dirac and contact structures. The first ones, associated to power conservation in physical modelling, correspond to the law of good bookkeeping (Walras׳s Law), in economy. Differently, contact structures appear in the description of irreversible phenomena, and in macro-economy they are employed in a more realistic formulation of the firm (or supplier) behaviour. The firm, in fact, is a profit maximising entity that interconnects the markets associated to the demand and to the input factors in order to create a profit. Several examples are provided to show to effectiveness of the approach.