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Endogenous business cycles modeling in France and the renewal of nonlinear analysis in the 80's

Alain Raybaut, University of Nice Gredeg

A long tradition in the theory of dynamical systems exists in France fueling a sustained mathematical research in this field, with recurrent applications to economic issues. This paper deals with the French contributions to the world-wide renewal of nonlinear analysis in the end of the 70’s and the early 80’s. More specifically, we focuss on some significant advances made in Cepremap before the seminal papers by Grandmont (1985) on endogenous equilibrium business cycles and related researches. These contributions are representative of two different mathematical ways of modeling endogenous cycles : The Poincaré-Bendixon theorem for planar continuous systems and bifurcation theory for mappings and discrete dynamics on the interval. First, we retain the model developed by Benassy to study the emergence of endogenous business cycles as a succession of short run non-Walrasian equilibria. In Benassy’s paper, the formal technique of existence of endogenous cycles is not new. It relies to the Poincaré-Bendixon theorem, but applied in an elegant way to a singular dynamic model in the non-Walrasian approach associated as well-known to the author. Second, we consider the different versions of the contribution of Dana and Malgrange on endogenous cycles. Starting on the contrary with a well-known framework (Kaldor’s 1940 model), they produce an original analysis in discrete dynamics. In particular, they build on emerging mathematical advances on mappings on the interval, chaotic dynamics and bifurcation theory developed for a large extent by French scholars and not yet diffused in economics at that time. To a large extend, this work contributes to further developments in endogenous economic dynamics, notably by Grandmont (1985) who pays credit to Malgrange for introducing him to these mathematical advances.

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Keywords: History of macrodynamics, Business cycle theories, Mathematics and economic theory, Nonlinear dynamics

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