1. The rate of return of the total income, TIP’, is by definition the share of placement income in the total income.
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2. The trend in total income profitability (TIP’) is the result of the respective trends in return on placement (ROP) and productivity of placements in capital (PDP).
The equations:
rdp = pdp x p'rg p'rg = rdp/rdp Pdp
are always satisfied by the definitions from which they proceed.
This is why the trend towards stable return on placements in capital (ROP) and the upward trend in productivity of these placements (PDP) results in a downward trend in the profitability of total income (TIP’).
3. Expressed as a percentage, the TIP’ is the 100% supplement of the total income from labor, TLI, in relation to the total income, TI.
With:
TLI: Total Labor Income,
TI: Total Income
TPI: Total Placement Income,
since
(TLI/TI) x 100 = 100 – [(TPI/TI) x 100]
Since the percentage (TPI / TI) x 100 is an expression of the TIP’, it is the complement to 100 of the percentage of the TLI in relation to the TI, (TLI / TI) x 100.
If, for example, the TIP’ is 15% of the TI, the TLI is 85% of the TI.
4. The decrease in the relative value of placement income (IP) relative to total income (TI) is consistent with an absolute increase in the TPI.
There may very well be, in particular, an increase in the TPI, less than proportional to the TLI. So the weight of the TPI in the TI decreases, while not only does the weight of the TLI in the TI increase, but also the increase in the TLI is more than proportional to that of the TI.
The argument of the following proposition includes a numerical example.