The “Three Producers Problem”

The necessity to define a common currency being given inside the community of individuals, despite their fundamental disagreements regarding what constitutes value or not, a fundamental problem remains for the definition of this currency. It can be reduced to solving the following time-space “Three Producers Problem”:

• X, Y and Z respectively produce Vx, Vy and Vz values.

• X wants to acquire Vy, Y wants Vz, and Z wants Vx.

We can see that the exchanges cannot be bilateral, but must be circular. Furthermore as it is perfectly possible that X grants no value to Vz, Y to Vx, and Z to Vy (relativity principle), none of the produced goods and services can be used as a common metric. This is the fundamental argument that implies that the currency must be defined on a basis that is independent of the produced values by each individual.

The problem also exists in time, where the individuals, productions, services and needs will evolve in nature and will progressively be replaced or disappear. It is not less necessary for individuals to be able, at all times, to trade appropriately each other’s production in order to satisfy their respective changing needs.

For a small “dt” time unit, individuals X, Y and Z coexist, produce and exchange stable values. (Luc Fievet RTM 2.0)

So, not only “in space” (for a short time of evolution “dt”) values are not commonly recognized by producers and are the object of circular exchanges, but “in time” the individuals and the produced values change radically.

Nevertheless, for a time that is short enough, we observe some stability. So, there is a continuous evolution of economical parameters, including the currency we want to define, which allows the present producers at any moment, and at least for this short period of time, to agree on the stability of their circular exchange tool.

Also, as we shall demonstrate in what follows, and to be coherent with our fundamentals, only a purely mathematical quantification of exchanges, independent of all references, goods and services, is acceptable for our actors in the “Three Producers Problem”.

This result doesn’t reduce the value of the money because its total quantity, although purely mathematics, is limited in all instant. The purchasing potential of this money is limited by the prices beyond which the producers would not be able to exchange their productions because of a lack of money.

The “Three Producers Problem” gets more complicated when after some time, they die and they are replaced. (Luc Fievet TRM 2.0)

The problem being posed, we are going now to browse and analyze the solutions that we considered, before addressing the actual relativist solution.