It is by now well known that the main hope for developed societies subject to rapid population ageing who wish to maintain their relative standard of living lies in increasing their collective productivity more rapidly than they increase their dependency ratio via-a-vis the older age groups. Now in the comments thread on the recent ‘Reform is a Dirty Word‘ post I ventured to say that I found it obvious that at some stage we would reach a point where the rate of population ageing was going to outstrip the rate of productivity increase (in which case relative income per capita would inevitaby start to fall). David, unsurprisingly, asked me why I thought this to be the case. I was not happy with the response I offered (which was essentially some ‘rigmarole’ about the biology of ageing which is coming in a separate post), and since that time I have been scratching my head trying to find a simple way to get this point across. Perhaps I now have one.
All you need to get to grips with what follows is a basic understanding of geometry and a vague interest in football.