History of the Gossen Equation

Tuesday, 20 April 2010 22:23 techamberlain
Thomas E. Chamberlain, Ph.D.*
 But to see with my own eyes, and to hold in my hands, a great book, which had cost its
author years of meditation and study and which had almost fallen into eternal oblivion—
for this I was not prepared.
Excerpt of Walras’ tribute to Gossen—from “Walras on
Gossen” 1885 (1952).

Socioeconomic stability with receding international conflict is closer at hand due to two modern
developments: (1) A general recognition and acceptance of the permanent nuclear détente between major
powers, allowing international cooperation for the common good; and (2) The deepening of neoclassical
economics to its psychological foundation, thereby removing a barrier to sustained progress. A principal
result in the latter development is the Gossen equation, a mathematical formulation in psychology
representing the individual’s expectational (intertemporal) plan and his or her psychosomatic feeling-state
in anticipation of this plan, accounting for uncertainty/risk—a formulation in progress since Hermann
Gossen’s (solitary) 1854 contribution, and completed by the writer in 1993. In 2011 the Gossennian
approach to mathematical economics was united with Leon Walras’ and W. Stanley Jevons’ approach
(the foundation for neoclassical economics) thereby resolving a 135+ year schism or divide in the subject.
With this unification, several advances derived of applied mathematical economics on the Gossenian
side—such as periodic micro/macro-economic function based on nested-characteristic-times, the risk-
versus-marginal productivity relation, completion of the Walrasian input/output substitution relations, and
the Discretionary Power Principle of Justice—are carried over to the neoclassical side. ...An overarching
history of the Gossen Equation is provided, with additional emphasis on the author’s theoretical
contributions to the equation in the early 1990s along with his application of the equation in
developmental and welfare economics in the early 2000s. The principal milestones of this history are
given in a timeline chart (Figure 1) and a description of the Gossen equation is provided in a second chart
(Figure 2). As an appendix to the paper, the written critique offered by a paper-discussant at the WEAI
Conference in Portland (2010) is provided, with responses to her comments and questions. Additionally,
the recent (March 2011) unification of neoclassical and Gossenian mathematical economics at the utility
foundation (by way of a new “duration-for-consumption” constraint on the commodity utility function) is
noted at several points in the article. This unification, in turn, admits a possible resolution of the long-
standing division between the Austrian and neoclassical traditions.