Question

Set up a model to study several periods of adulthood, and derive optimality conditions:
(a) How much will he invest in the last period of his life, and why?
(b) Assume for a moment that the individual is offered a magic pill that would give a
one-time boost to human capital by amount P. For example, if he takes the pill
in period j, instead of having Hij his human capital will then be Hij 0 = Hij + P.
Suppose he is offered to take the pill either in period j or instead in j + 1. Can the
human capital model tell him when to take the pill?
(c) Now go back to the set-up of subquestion (a), and assume a rising return to human
capital, or βj < βj+1: What does this mean for early versus late investments and
why?