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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.
MSC:
91B62 Economic growth models
91B66 Multisectoral models in economics
37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems
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