Integrability, Gorman Systems, and the Lie Bracket Structure of the Real Line
The purpose of the paper is to investigate the relationship between Lie's characterization of the infinitesimal groups on the real line and the integrability conditions for Gorman demand systems for which the rank of the price matrix is not full. The central result of the paper is a geometric characterization of the integrability conditions for Gorman systems (due to Bryant) from which the restrictions on income terms and price matrices easily follow.
Farris, Frank A. with Thomas Russell. “Integrability, Gorman Systems, and the Lie Bracket Structure of the Real Line.” Includes an appendix by Robert Bryant. Journal of Mathematical Economics 29 (1998): 183–209.