Under the simplifying assumptions of the life cycle model adapted from Ben-Porath,
we would meet that deadline by directing all adult gross realized output less
property plowback p(k), to gift to the immediate generation of young received as
their invested consumption. The young would add their part by compounding that outside investment into their human capital at the rate of their entire ex ante output. This would prove the most straightforward strategy to exhaust and replace all total capital by the deadline exactly. This is just as in my adjusted Ben-Porath model with the addition of the specified deadline.
Here as there, I describe adults collectively and the young collectively. | will not attempt to model effects of kin selection in individual investment choices. But I have intended to lay a groundwork. Investment, in Hamilton’s sense, translates to gift y, in economic terms. It is a flow of total capital (fitness) from donor to donee. At the individual scale, as well as for the group scale, it equals gross realized output less plowback. Gross realized output tends to be a continuous flow, as we see in pay, rather than one easily sped up or slowed down. This gives an idea of the time
constraints I mentioned in critiquing Hamilton’s rule.
APPENDIX A: The Argument in Notation 3/7/16 28
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