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Linearized geometric dynamics of Tobin-Benhabib-Miyao economic flow. (English) Zbl 1096.91049
Summary: The aim of this paper is to study the influence of the Euclidean-Lagrangian structure of the state space on the generalized Tobin flow in economics confirming the existence of optimal economic fluctuations (small oscillations).
Section 1 reviews the generalized Tobin economic flow as formulated by J. Benhahib and T. Miyao [Some new results on the dynamics of the generalized Tobin model, Int. Econ. Rev. 22, No. 3, 589–596 (1981; Zbl 0478.90010)]. Section 2 recalls some tools of single-time geometric dynamics which describe a geodesic motion under a gyroscopic field of forces. Section 3 studies the linearized geometric dynamics produced by the Tobin-Benhabib-Miyao flow and by the Euclidean-Lagrangian structure of the economic state space.
In this way we estimate the time economic evolution for spotlighting the expectations of the agents.
91B62 Economic growth models
91B66 Multisectoral models in economics
37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems
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