Chapter 22. Statement of the hypothesis.

1. General statement.

We go now to a rudimentary mathematization -but not a final one- of the hypothesis of the communal utilitarianism or mercantile common good.

The two sectors, or complementary sub-sets, which make up the market are, as we have already said, production and purchasing power.

If we want to put them together in a mathematical formulation, we shall have to define them in a rigorous way and, above all, to make them comparable, to homogenize them. Both conditions may be fulfilled by having recourse to the monetary units. If we express both production and purchasing power by means of variables monetarily measured, there will be no problem.

We obtain then the following redefinition:

Production is «the sum total of the elementary sales prices of all the goods actually produced», simplifying, «the sum total of elementary price-mercantile values». We shall show it by the symbol «P_u».

Purchasing power is «the sum total of the elementary monetary rewards paid to the production agents which participate in the market», simplifying, «the sum total of elementary salary-market values». We shall show it by the symbol «H_u».

Within the purchasing power we shall have to make a separation. At present, within the market only the private production forces are paid (work, capital, company and invention). We may say therefore, that the present purchasing power is a private one. (Symbol: «H_pu»). However, according to our hypothesis, there are also communal production forces; their hypothetical retribution would represent a communal purchasing power (Symbol: «H_ku»).

Now we have defined and pointed out all the elements of the hypothesis. We can step forward and do its very general mathematization.

In the first place we define a balanced utilitarianism in which production and purchasing power are balanced. This can be expressed so:

 P_u
---- = 1
 H_u

Formula of the balanced utilitarianism.

In the second place, we know that the present utilitarianism is not balanced, because there are communal production forces not paid from a point of view of purchasing power, and because, at the same time, the purchasing power corresponding to these communal forces is deviated, without measure and without control, towards privileged social sectors (the symbol for this communal purchasing power, taken without measure nor control will be «?»).

The imbalance of the present utilitarianism will be expressed:

    P_u
--------- # 1
 H_pu + ?

Formula of the present imbalanced utilitarianism.

In the third place, it is very clear that, if we want a balanced utilitarianism, we must just measure exactly the contribution of the communal production forces, and that we create the exactly corresponding communal purchasing power.

  P_u
----- > 1
  H_pu

That is, the private producing forces do not justify in themselves the total production.

P_u - H_pu = H_ku

It is then necessary to postulate communal producing forces which, measured monetarily, are equal to the difference between total production and private purchasing power.

     P_u
---------- = 1
 H_pu + H_ku

The balance will be attained by creating a communal purchasing power complementary to the private purchasing power, which constitutes the suitable reward of the communal production forces.

2. Invention of money.

We have used several times the expression «to create a communal purchasing power». What is meant by this? Simply we mean that we can invent the monetary mass corresponding to the difference between P_u and H_pu, without by this disturbing the market, but on the contrary balancing it.

We suggest that this invention be made by the State, as manager of the whole geopolitical community, and that the monetary mass obtained be shared equally among all the members of this community.

Inventing money is no special thing: Central Banks and privates Banks do it all the time and nobody finds it strange, and moreover without any effective control. Our suggestion is then to substitute the present scattered and disorderly invention of money by a centralized invention, measured and controlled,

The greatest advantage of this system of money invention is that the invented monetary mass, since it has been previously measured as a difference between total production and private purchasing power, represents the communal purchasing power exactly complementary to the private purchasing power: it represents the purchasing power which was missing in the market, through a shortage of the purchasing power of private-mercantile origin. For this reason, it represents the best guarantee of continuous and dynamic balance of the market.

3. Detailed statement.

The formula we have given for the invention of the communal purchasing power: P_u - H_pu = H_ku, is too general and is no good in practice to calculate the purchasing power to be invented.

We must analyze the several cycles and sub-cycles which make up the market, in order to reach detailed formulations for each one of them, to be feasible in practice.

We must remember here the analysis, carried out in chapter 8, of the market in two cycles: the production cycle and the consumption cycle; and the analysis of the production cycle in three sub-cycles: the sub-cycle of current production, the sub-cycle of investment production, and the sub-cycle of the retail shops and industries.

The basic verification to be carried out, after the previous analysis, is the following: among all the cycles and sub-cycles in the market, the sub-cycle of current production is the basic one, the motor, the one which feeds all others, whether directly (in the case of the investment production sub-cycle and the sub-cycles of the retail shops and industries), or indirectly (through the sub-cycle of the retail shops and industries,in the case of the consumption cycle).

All the price-mercantile values produced in the sub-cycle of current production go, either directly to the sub-cycle of the investment production, or indirectly to the consumption cycle. For this reason we say that the sub-cycle of investment production and the sub-cycle of consumption are the natural drainpipes of the market, the place through which all production goes out.

A third drainpipe is made up by foreign trade, which can be carried out in any of the above-mentioned cycles or sub-cycles.

The sub-cycle of current production can be developed in full autonomy and self-sufficiency, as long as its drainpipes work equally well, that is as long as they absorb the production of the first one.

In the same manner, the production for export works independently, as long as foreign importers can absorb it.

The immediate result of this thought is the following: it is not necessary to introduce communal purchasing power in the sub-cycle of current production, nor in production for export; it suffices to introduce it in the three above-mentioned drainpipes, in order to dynamize all the market in whole.

After this we can substitute the general formula with three particular formulae, more detailed and suited to the market reality.

Invention of communal purchasing power in the sub-cycle of investment production (symbol for this sub-cycle «I»; investment credit: «c»)

P_Iu - H_pIu = H_kIu = c

This communal investment purchasing power (H_klu) is called «communal credit to investment»: it may be granted to all the companies with investment needs which demonstrate their productive effectiveness, or to all those who want to create a new company and offer a guarantee of success.

Invention of communal purchasing power in the consumption cycle (symbol for this cycle «C»; consumption finances «f»)

P_cu - H_pCu = H_kCu = f

This communal consumption purchasing power (H_kCu) is called «consumption finances», and may be granted without return to all the members of the geopolitical community, in accordance with their differential needs as consumers.

In all the previous cases, the calculation of the private purchasing power (investment or consumption) is a complex calculation which we are not going to develop here. We shall only say that in the idea of private purchasing power must be included both the available purchasing power coming from the year under consideration, and the available purchasing power accumulated from previous years.

Invention of communal purchasing power in foreign trade

(Symbol: exports «E», imports «J»)

If

 E_u + (c + f)_E
--------------- = 1
 J_u + (c + f)_J

then

( c + f )_E = [J_u + (c + f)_J ] - E_u

(Let us remember that in foreign trade the monetary units used will always be those of the foreign country, or those agreed upon in a treaty, but never the own monetary units).

The foreign communal purchasing power, then, is made up both by credits and finances, but always within the framework of a unitary balance between the total imports and the total exports.