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8.1 Representation of the productive forces of an economy independently of the conditions of production n1)
Analogous to Volume 1 [4], the societal productive forces are now to be described independently of the production conditions. The description has been tightened up. The detailed explanations can be found in the corresponding sections of Volume 1 [4] and previous sections of this Volume and apply accordingly here. Essentially the same names and symbols are used.
Reproductive cycles:
- The reproductive process of society takes place in discrete periods of time Tz of equal length, which are called reproductive cycles.
Society's resources:
- The society consists of the number of a employable members.
- There are n3 different types of goods i3.
- The society currently has the total amount of economic goods wg at its disposal.
Skills of the workers (professions):
- There are m3 different professions j3 known in which the workers can be employed.
- All a workers can be assigned to m2 productivity groups j2, each with the same productivity profile.
- The totality of all productivity profiles is described by the productivity matrix p.
- The numbers of workers in the respective productivity groups are given by the vector ap.
Production processes and producing economic entities:
- There are n2 production processes or companies i2..
- The production process i2 is represented as a black box in the following way: If a demand-conform range of goods wii2 is provided at the beginning of a reproduction cycle and a demand-conform range of work performance aii2 is applied to the range of goods over the period of this reproduction cycle within the production process i2, the range of goods wii2 at the end of the reproduction cycle is transitioned to the range of goods woi2.
- The needs-conform range aii2 of work performance is a vector consisting of m3 components aii2,j3.The component aii2,j3 indicates how much work is required in the respective profession j3 for the production process i2.The vectors aii2 are combined to form the normal work input matrix ai.
- Each multiple xi2 of the matrices aii2, wii2 and woi2 represents the same production process with a different production volume xi2.
This means that all n2 production processes i2 are fully described by the two input matrices ai and wi and the output matrix wo. In contrast to the models in Volume 1 [4], here the labor input vector ai has been expanded to form a labor input matrix ai. While the component aii2 of the vector ai previously indicated a number of fully employed workers, the component aii2,j3 of the matrix ai now contains a quantity of profession-specific work performance, measured in the performance unit j3 of the respective professions.
Employment situation:
- In order to fully describe the employment situation one now needs a three-dimensional employment matrix ac.The component aci2,j2,j3 indicates how many workers with the productivity profile j2 are employed at company i2 with the profession j3.
- Alternative: In order to reduce the flood of data the three-dimensional employment matrix ac could also be replaced by two two-dimensional matrices ac' and ac'' with an acceptable loss of information. The matrix ac’ then contains the previously known information, in which the component ac’j2,j3 indicates how many workers in productivity group j2 are employed in profession j3, regardless of which company. The matrix ac’’ then indicates which working capacity the companies have under contract by the component ac’’i2,j3 indicating how much profession-specific performance potential company i2 has under contract in profession j3.
Which of the variants is ultimately more advantageous has to be shown in practice.
Needs and multiplication of members of society (workers):
- Similar average needs of all workers are assumed and described by the vectors kni, kno, kli and klo.
- The multiplication factor of the supplied workers per reproduction cycle is given as fa.
Consumption of members of society:
- akj2 the number of workers in productivity group j2 who were supplied with the essential consumer goods. The components are combined to form the vector ak.
- flj2
is the current factor of the additional consumption of productivity group j2. The components are combined to form vector fl.
This completely describes the system of the productive forces of a national economy, taking into account a differentiated employment structure. The dimensionless parameters were tacitly given without going into detail. In summary, the complete parameter set can now be specified:
i2 | Index or number of the production process or company |
i3 | Index or number of the respective good |
n2 | Number of the production processes or companies |
n3 | Number of the different goods |
ap | productivity group sizes |
ak | numbers of supplied workers in the productivity groups |
fa | multiplication factor of workers |
kni | input of the essential consumption |
kno | output of the essential consumption |
kli | normalized input of additional consumption |
klo | normalized output of additional consumption |
fl | factors of additional consumption in the productivity groups |
ai | normalized inputs of workforces |
wi | normalized inputs of means of production |
wo | normalized outputs of production |
x | production volumes |
ac or ac’, ac’’ | employment matrix |
wg | total quantities of economic goods |
This is the minimum set of parameters that is necessary to fully describe the linear discrete model of the productive forces of a national economy with a differentiated employment structure. All other parameters can be derived from it.
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