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2 Description of the problem

What is the function of a differentiated remuneration system related to a free labor market with collective production?

First, it should ensure that a worker who engages in a profession makes the most of its skills in that profession. That results in a higher wage for higher use in a profession for which use is quantifiable at least in comparison to similar activities. The size of the benefit can also refer to one or more indicators of the quality of the work. However, the wage does not necessarily have to be proportional to the quantity of the use. This still corresponds to the traditional understanding of the performance principle.

Secondly, society as a jointly producing association of people is interested in the members of society being distributed among the professions according to their different physical and mental abilities and according to the different requirements of the various professions, so that a maximum and at the same time needs-based assortment of work is given. This range of performances is reflected in a maximal and needs-based range of products and services.

Expecting a remuneration system in connection with a free labor market to solve this complex task cannot be taken for granted. But it is worth the effort to investigate this in detail. Because only under these conditions a free labor market does make sense, where everyone only has to strive for employment in the profession, where everyone can count on the highest possible income for themselves according to their abilities. A labor market that works like that would save a lot of administration. Even if it can be assumed that not everyone can correctly assess their own personal skills, it can be assumed that in an honest effort to choose the right profession for oneself the macrosocial hit rate is likely to be higher than in any administrative assessment of the skills of the individual members of society

A science-based answer to this question can also be expected to answer the question of the necessary amount of differentiation in wages. This in turn could answer the question of whether it is possible to give a market economy the attribute "social"..

In order to theoretically answer this question a mathematical model of a labor market with a corresponding wage system shall be developed below..

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