Socio-economic interface and social income
The article presents a linear cost model whose duals allow the assignment of objective dollar values to an individual's social position. The agent's cost model is min cx on \(X=\{x\geq 0|\) ux\(\leq 1\), Ax\(\geq b\}\) where u is the n-tuple of units (1, 1,...,1); x the n-tuple of time fractions \(x_ j\) spent in activity j, which entails a cost \(c_ j\) per unit of time; b is the m-tuple of social requirements \(b_ i\) of the agent's social position relative to his profession, family, polity, club, church and so on. The \(b_ i\) may be expressed in such units as publications, outings, votes and attendances. The matrices x, c, b abstract the agent's lifestyle, economic position, and social position, respectively. Finally, activity j satisfies requirements i to the extent of \(a_{ij}\) units per unit of activity. The \(m\times n\) matrix A of coefficients \(a_{ij}\) quantifies the agent's environment. Since it relates activities, and hence cost, to social position, it represents the socio-economic interface. The above is an objective behavioral model, eliminating subjective utility concepts entirely. The dual program implies a socio-economic theory of saving and impatience. The article concludes by comparing cost programs for a given time budget with time-economizing programs for a given cost budget: two propositions regarding the equivalence of the respective solution sets and their duals are proved.
scientific article; zbMATH DE number 3906184