**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30855

##### 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:**
Mathematical Economics,
Differential geometry,
exterior calculus,
Hamiltonian geometry

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

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