**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31743

##### Exterior Calculus: Economic Growth Dynamics

**Authors:**
Troy L. Story

**Abstract:**

Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

**Keywords:**
Differential geometry,
exterior calculus,
Hamiltonian geometry,
mathematical economics.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1330943

**References:**

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[2] R. J. Barro and X. Sala-i-Martin, Economic Growth, MIT Press, Boston, 2004.

[3] Angel de la Fuente, Mathematical Methods and Models for Economists, Cambridge University Press, Cambridge, 2000.

[4] J. Mimkes, "A Thermodynamic Formulation of Economics" in Econophysics and Sociophysics, B. K. Chakrabarti, A. Chatterjee, (Eds.), Wiley, Hoboken, 2006.

[5] R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge, 2007.

[6] V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 2010.

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[8] Troy L. Story, Dynamics on differential one-forms, J. Math. Chem., 29(2001), 85-96.

[9] Troy L. Story, Navier-Stokes dynamics on a differential one-form, RIMS Kokyuroku Bessatsu, B1(2007), 365¬382.