42 Introducing Labor and Wages

For further tensorial algebra, a convenient way of writing the field Equations of Economy is using the geometric tensorwhich gives the well-known so-called Einstein notation:

    (42.1)

With        (42.2).

where we have chosen the usual valid minus sign, subscipt s denotes the summation-norm, and superscript C means that the vectors are split up into there i different contribution. External contributionsare given in the case of closed, or for quasi-closed national economies. The resulting j coupled differential equations have to be solved for adequate constraints at last . As an important sample step, we will introduce now labor and wages, which are responsible for the main consumption power of an economy. This can be done by splitting the money supply to the real economyinto the supply for buying goods (G) and buying labor (wages: W). Thus we now define

  and        (42.3).

From 42.1 this results in

This system will be multiplied to:

which gives simply

    (42.4).

So we get for our sample here the special field equations as

 

(42.5)

which are to be solved simultaneous and consistently. To solve it, one has to find some constraints on the different parameters resulting from further symmetries or other meaningfull or manifest constraints. The full solution of the resulting system of three coupled differential equations and deriving the constraints is not in the scope here, as it takes lengthy discussions.

In the following chapters, we will find some additional symmetries in addition to the main symmetry of quantity equation. For full self consistent solutions one needs as much invariants as unknown functions one has to solve.