(A3.6) combines with (A1.4) and (A1.5) to arrive at
7, =F =Y,gross—p,, (A3.7)
at the scale of the total capital of the individual or any set of individuals. This fact
will prove helpful in adjusting the Ben-Porath model and in next generation theory.
It should be borne in mind that transfer out and transfer in are both implicitly defined as net of plowback in the first place. Thus it would be wrong to suppose that negative cash flow is transfer in less plowback from revenue. That mistake would
deduct plowback twice.
The Growth Truism
Growth of any asset of either factor is capitalization from outside plus capitalization
from inside less decapitalization. This difference can also be called net capitalization.
Capitalization from outside is simply transfer in t_ . What are the other two?
Our first intuition would be that capitalization from inside is identical to unrealized output. Here we must be careful. Output is negative wherever the sum of growth (net capitalization) and cash flow falls below zero. This “deadweight loss” is implicitly uncovered decapitalization, meaning not recovered in cash flow. To subtract all including unrecovered decapitalization from the sum of transfer in and
unrealized output would therefore subtract the unrecovered part twice.
To make this clear, define positive and negative output by Y(>0)=max(Y,0) and Y(<0)=max(-Y,0)=2,
APPENDIX A: The Argument in Notation 3/7/16 10
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