HOx)=f' ae" dz, if C,=0 and x2A, (A10.5)
Now let’s add some detail and bring in physical capital. Like most, I model inheritance as zero and physical capital acquisition as beginning after age of independence A. That can be modeled as age 20. As human depreciation begins then at zero, if depreciation theory is right, gross realized work (pay) simplifies at first to realized work. This takes up all the new worker's time and attention, yet
simultaneously enables subliminal self-invested work in job experience.
It seems reasonable to model pay at job entry as equal to the new worker's maintenance consumption, on the reasoning that independence means reaching the ability to earn it. Thus nothing is left for investment in physical capital at first. But the quick buildup of job experience soon means pay left for investment. As I model
no pay plowback, that means physical capital acquisition.
Human depreciation rises slowly while the self-invested work of job experience diminishes, so that overall growth in human capital peaks and then declines. Physical capital owned does the same as we acquire it and then spend it on the young. Young arrive, on average, as a cohort reaches age 28.5 (my estimate of the generation length). The cohort of adults begins divesting its capital of both factors in
nurture and schooling received by the young as invested consumption.
The young reach independence on average when the adult cohort reaches age 57 (2 x 28.5). Some young will have been born after parental age 28.5, and will continue to receive parental investment over the eight years remaining between age 57 and retirement modeled at age 65. But my model cannot account confidently for this eight year gap on the whole, or for the retirement period following, which runs twice as long. My hypothesis is that retirees are effectively employees hired by productives to help take care of the kids, while the eight-year gap might show a human capital reserve against nasty surprises.
APPENDIX A: The Argument in Notation 3/7/16 24
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