Viability in a Keynesian Model: A Preliminary Approach

The purpose of this paper is to study an elementary dynamic Keynesian model by means of the viability approach. The mathematical theory of viability allows one to raise and answer questions which cannot be solved with usual dynamic tools. It deals with the question whether for a given dynamical system, there can be found solutions which satisfy some a priori given constraints, and with the analysis of subsets of the phase space where viable evolutions, i.e., evolutions satisfying the given constraints, are possible. Equilibria are examples of such viable sets, but the viability approach is much more general then the equilibrium approach. In contrast to traditional ecodynamics where local stability and asymptotic properties of models are the heart of the matter, the viability approach is concerned with contingent evolutions over time of dynamic systems. In section 2 we describe an elementary dynamic Keynesian model. Viability questions are evoked in section 3 along with some intuitive answers, and rigorous results and developments will be found in section 4