Perpetual Youth Model I am reading the famous paper of Blanchard,1985. There are some fundamental stuff that I did not really get. 

1) Why they call it "perpetual youth"?
2) On page 225, he mentions the cohort size. So, for example does it mean that there are "x" numbers of individual of age 20. But this number x declines when the time goes to infinity? Does it mean that at a given date $t$, there are people with age between $0$ and $\infty$ ?
I haven't read the paper in full detail (I should, it's interesting) but let me give you my interpretation of the paper's title.

Blanchard uses a constant probability of instanteneous death for each agent. As mentioned in footnote one of the paper this is most realistic as assumption for people between 20 and 40. Agents in the model therefore are like young people for their entire life, hence the title.

As for your question 2, the way I read the paper yes there are many people alive of all ages. After all at each instant in time a new cohort of size p is born (and starts dieing off immediately at rate 1/p). So eventually at time is infinity that cohort will have completely passed away.