Summarizing,
I(K,,),, optimum = Y optimum = C, , atthe collective scale, (A9.5)
if free growth theory is correct.
Ex ante investment and output mean at cost. They are what we pay for. The practical importance of (A9.5) is as a guide to macroeconomic policy. It says that we cannot grow collectively by attempting to produce more than we consume. We do best by
paying to produce just as much, and taking free growth as it comes.
(A9.5) does not say that we cannot influence the growth tides. It says that we cannot do so by thrift. It seems to be me that growth theory lies somewhere in the province of historicism and institutionalism rather than in the mechanics of supply and demand. Judging from history, old and new, growth seems to find traction in free markets where laws and customs welcome it. These are institutions shaped by
history. Free growth theory and its equations predict at the collective scale only. Clearly the Practical Pig can save out of the dissaving of his feckless brothers, while the
individual life cycle is largely a story of each generation giving to the next.
Adjusting the Ben-Porath Model
Human capital begins at zero value at cohort age 0. Invested consumption C, starts
now, and is immediately compounded by self-invested work of the young. This means all work before pay begins at age of adulthood and independence A. As human depreciation is expected to be recovered in pay, that flow too is put off until age A. Then cohort present cost at any earlier age x, as defined in (A2.10), is
HOx)=[C(zJePOP dz, if x<=A, (A10.1)
APPENDIX A: The Argument in Notation 3/7/16 2?
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