Consider the continuous-time perpetual youth model

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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)).

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

Reference no: EM131135959

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