Exterior Calculus: Economic Profit Dynamics

A mathematical model for the Dynamics of Economic Profit is constructed by proposing a characteristic differential oneform for this dynamics (analogous to the action in Hamiltonian dynamics). After processing this form with exterior calculus, a pair of characteristic differential equations is generated and solved for the rate of change of profit P as a function of revenue R (t) and cost C (t). By contracting the characteristic differential one-form with a vortex vector, the Lagrangian is obtained for the Dynamics of Economic Profit.

Authors:

• Troy L. Story

Keywords:

• Differential geometry
• exterior calculus
• Hamiltonian geometry
• mathematical economics
• economic functions
• and dynamics

References:

[1] O. Young, "Synthetic structure of industrial plastics (Book style with
paper title and editor)," in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New
York: McGraw-Hill, 1964, pp. 15-64.
[2] W.-K. Chen, Linear Networks and Systems (Book style). Belmont, CA:
Wadsworth, 1993, pp. 123-135.