Jean-Pierre Drugeon

Impatience and long-run growth

Abstract This contribution is concerned with the possibility of a perpetual growth path at increasing rates in a nonconvex optimal growth model with endogenous discounting. Sufficient conditions for the existence of this path can be established when the economy is populated by agents whose impatience does not increase too much along the course of a consumption path. In the opposite case, the dynamical system is asymptotically described by a steady state. However, this steady state position need not be uniquely defined: saddlepoint equilibria and locally oscillating unstable equilibria may alternate. In spite of increasingly impatient agents along the growth process, it remains optimal for a government to subsidize the competitive economy. Under a razor edge assumption on impatience, a growing planning solution may coexist with a stationary competitive solution.

On Efficiency and Local Uniqueness in Two-Sector OLG Economies

We consider a two-sector overlapping generations model with homothetic preferences. Under standard conditions on technologies, upon large enough values for the share of first period consumption over the wage income, we prove that the dynamic efficiency and local uniqueness of the competitive equilibrium hold. On the contrary, for lower values of the share of first period consumption over the wage income which imply dynamic inefficiency of the steady state, local indeterminacy arises when the elasticity of intertemporal substitution in consumption is large enough.

Assessing the Local Stability Properties of Discrete Three-Dimensional Dynamical Systems: A Geometrical Approach with Triangles and Planes and an Application with Some Cones

The difficulties associated with the appraisal of the determinacy properties of a three-dimensional system are circumvented by the introduction of a new geometrical argument. It brings about a complete typology of the eigenvalues moduli in discrete time three-dimensional dynamical systems and then provides a new apparatus for assessing from a geometrical standpoint the emergence of local bifurcations for parameterised economies. The argument is considered through the extensive characterisation of the stability properties of a benchmark model of inter-temporal economic analysis.

On Outward-Looking Comparison Utility, Heterogeneous Preferences & the Third Dimension : A Geometric Perspective

The difficulties associated with the appraisal of the determinacy properties of a three-dimensional system are circumvented by the introduction of a new geometrical argument. It first brings about a complete and easy-to-use typology of the eigenvalues moduli in discrete time three-dimensional dynamical systems and then provides a new apparatus for assessing from a geometrical standpoint the emergence of local bifurcations. The argument is first illustrated in an environment where outward-looking comparison utility may question the determinacy of the steady state and subsequently used within a competitive monetary equilibrium with heterogeneous agents and financial constraints.