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6.1 Mathematical model for simulating the labor market
- A piece wage Lsj3 is determined for each profession j3.
- If a worker of any performance group j2 in the profession j3 provides a work performance corresponding to its individual productivity Pj2,j3, then one receives the individual performance wage Ldj2,j3 with
(18) Ldj2,j3 = Pj2,j3 × Ldsj3
In this way, the principles of "equal pay for equal work" and "everyone according to one's performance" are implemented within one profession.
- With the respective normal Mdj3 for work performance in profession j3, the normal Mp for prices (e.g. Mp=1000 DM) and the normal Mt for time (e.g. Mt=1 day), the dimensionless piece wage lsj3 and the dimensionless individual performance wage ldj2,j3 can be introduced.
(19) lsj3 def= Lsj3 ×
Mt / Mp
(20) ldj2,j3 def= Ldj2,j3 ×
Mt / Mp
- If the optimal employment structure has not yet been achieved, there is an apparent oversupply of labor in some professions. The extent of the apparent oversupply is given by the factors fbj3 of the needs-conformity of the work performance in the respective professions. If one assumes that there is shortened work in the respective professions without wage compensation, then the actual individual wage lj2,j3 for the worker in productivity group j2 in profession j3 is given by
(21) lj2,j3 = fbj3 ×
ldj2,j3 = fbj3 ×
Them2 ×m3 individual wages lj2,j3 are combined to form the matrix l.
This wage system is the driving force for adapting the employment structure. Every worker can assess in which occupation every person has the best earnings lmaxj2 on the basis of the current piece wages ls, the assessment of one's individual abilities pj2 and the employment situation in the professions. The worker is motivated to change profession depending on where one earns the most.
- Within a certain period of time (e.g. during a reproduction cycle i4), the r1th share of all workers switch to the professions in which they currently would earn the most based on the current piece wages, their individual skills and the employment situation - if they are not already employed in this profession. The factor r1 is called the fluctuation rate. Its size must be determined empirically.
- "Between each fluctuation period (reproduction cycle), the piece wages are expressed by the factors fbj3 in accordance with the employment situation and corrected using the following formula
(22) lsj3,i4+1 = lsj3,i4 ×[1-r2 ×(1-fbj3)]
The factor r2 is a parameter of the speed of wage adjustment. Its size must be identified empirically.
- With every wage correction, the wage level is also brought back to the average value of one.
The fluctuations of workers can now be simulated over any number of reproduction cycles.
Hereby this simple model of a labor market is already described completely. For the computational simulation of the labor market according to this model, a TurboPascal program was written so that our demonstration example can be used to test whether the employment structure is self-optimizing and which optimal wage system occurs.
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