The Genesis of Dynamic Systems Governed by Metzler Matrices

The literature on dynamic systems in economics is vast, and an important part of that deals with systems of differential or of difference equations where the Jacobian of the right-hand side is a Metzler matrix, i. e., a matrix whose off-diagonal elements are non-negative. Such matrices have a wide range of applicability in dynamic economic models, in input-output analysis, in stability analysis of systems of excess demands governing price changes, and in multi-sector and multi-national Keynesian income determination models. Oskar Morgenstern early perceived the importance of such models and encouraged research in them, as seen in the papers by Y.K. Wong and M.A. Woodbury in Morqenstern (3). For a later survey, see (2).