Mathematical Research On Heterogeneous Labor

So great are the differences of manual or mental capacity that existamong different laborers that researching on the differences betweenlabors should be an inevitable task for economists who focus on how tooptimize the allocation and uses of this kind of resources. The urgent needof management for economic science is another reason for this study. It is the practice of economic organs that enable the birth anddevelopment of any theoretical economics, which works just like roots toa tree and the administration of a business is precisely this kind of root,which nourish Neoclassical Economics. For a long time, the neoclassical economists have regardedenterprises as black boxes, which they know little about their interiorstructures. The works of Peter T. Gottschalk, Jan Tinbergen, and HarveyLeibenstein indicate that present Mainstream Economists have indeeddone little research on the labor distinction, the division and coordinationof these different labors, and the deficiency within organizations causedby undue use of labors. This paper starts from the implied homogeneity assumption on labor,which is not in accordance with the fact, studies the heterogeneous laborin a method of Mathematical Economics where vector equilibriumtechnique is used, and forms a series of functions about the laws of howdifferent labors are most effectively used and allocated within a business. These functions and their derivative analysis are used to investigatethe rule of individuals, organization, and management within enterpriseknown as black box, and answer the integral problem of theoreticalframework in the aspect of human resource management where theessence of management is mostly embodied. The relationship between economics and management is that of a talltree and its roots, and that of principle and its realization. It is onlythroughthe practices of human or labor that principles about economic efficiencycan be realized and it is the heterogeneous labor that acts as the hinge,which connects these two subjects. Economic efficiency is reachedthrough market equilibriums outside firms and economic efficiency ofheterogeneous labor through vectorial equilibrium of internal labormarket. Stock Option Plans and Employee Stock Ownership Plans areexactly this sort of hinges. The vector equilibrium analysis of these twoplans is used not only to test the analyzability of those functions aboutheterogeneous labors, but also to explain the concepts of vectorequilibrium of labor and internal efficiency in the same way as marketequilibrium and market efficiency under the essence of the definition ofeconomics. It tries to make up for the insufficiency analysis on theheterogeneity of labor, to unify concepts of organization efficiency andmarket efficiency that has been intersected by Leibenstein under the sameexplanation of efficiency and equilibrium of economics, and to help thedevelopment of economics itself as well.