8.9 Let us call the TPIP’ relationship the fact that all rate of return is equal to productivity multiplied by profitability.

1. Let's generalize Brown

With:

• R for rate of return;
• P for productivity;
• P' for profitability;
• G (of gain) for an amount expressed in the quantity of money of an income or a margin;
• S for an amount expressed in the quantity of money of the stock that made it possible to obtain G;
• F for an amount expressed in the quantity of sales money, which is income from the property when S is an investment made by an investor.

R = G / SP = F / SP'= G / F

2. G/S = (F/S) x (G/F).

Any rate of return R is equal to a productivity P multiplied by a profitability P'. This statement defines the RPP' relationship.

3. The TPIP relationship is active at the micronomic level, that of the products sold by enterprises.

At this scale, the rate of return R, the productivity P and the profitability P' are direct, i.e. before any distribution of common costs, and, for the rate of rate of return R and the productivity P, the asset to be taken into account is also direct (the concepts of direct margin and direct asset are defined further in Chapter 11).

4. The TPIP' relationship is active at the level of the mesonomy, that of the enterprise as a legal entity.

At this scale, the rates of return 'R' are those of the capital and all Actif the assets of the enterprise. P productivity is the ratio of value-price (revenue) or value-cost (cost) sales to capital or assets (numerator identical in both cases). The profitability P' is that of these same sales.

5. The TPIP' relation is active at the scale of macronomy — that of total income and its distribution.

With :

TI : Total Income ;

TPI : Total Placement Income;

TLI : Total labor income ;

PS : Placement stock ;

ROP : Return on placements ;

PP  : Placement Productivity;

TIP’ : Total Income Profitability;

At the scale of national and regional macronomy (supranational and subnational), the RPP' relation takes the following form:

ROP = PP x TIP’

TPI / PS = (TI / PS) x (TPI / TI)

6. RPP’ relation are myriad

The TPIP' relations that are active or potentially active in the economy of a country would number in the billions, or even trillions, were it possible to count them. They bring to mind the synapses of a vast nervous system stimulating and regulating the alveoli of a gigantic lung. These relations regulate and stimulate more effectively than any dirigisme ever could, however armed with computers and databases — provided that sufficient care is given to the bounding of the freedom to supply by the freedom to choose.