Show that 939 does not apply at any finite time if the

Question

Consider the continuous-time perpetual youth model of Section 9.8.

(a) Show that given L (0) = 1, the initial size of a cohort born at time τ ≥ 0 is exp ((n - ν) τ ).

(b) Show that the probability that an individual born at time τ is alive at time t ≥ τ is exp(-ν(t - τ)).

(c) Derive (9.39).

(d) Show that (9.39) does not apply at any finite time if the economy starts at t = 0 with an arbitrary age distribution.