Port-Hamiltonian formulation of simple macro-economic systems

This paper aims at extending the port-Hamiltonian formalism to a simple class of macro-economic systems. As in physical modelling, for these systems, the dynamics is the result of the interaction between a limited set of “atomic components,” such as 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 a Dirac structure, whose power conservation property is recognised as the equivalent of the law of good bookkeeping, i.e. the Walras's Law, in economy. Then, port-Hamiltonian and Brayton-Moser descriptions of the system dynamics is obtained by port interconnection, as usually done in case of physical systems. Some example are provided to explain not only the potentialities, but also the limitations of the proposed approach.