easy solution, stop folk from having sex..
I think you'll find that is a far from easy solution.
There is another problem with it too. Improving medicine keeps people alive long beyond the time when they can work or sometimes beyond the time when they are capable of even looking after themselves.
A low birthrate means there are insufficient of working age to provide the money to support the ageing population and the cost of that support will probably drain the resources of all but the very rich indeed for those who have to fund it themselves. Then you find that the large numbers of working young who were able to subsidise the care of the elderly start to need support themselves.
Currently governments seem to be trying to overcome the problem of a birthrate insufficient to support the elderly by importing labour from poorer countries but that has the same problem as rolling your own in that they will need care themselves sometime.
None of the solutions to that ever escalating population are either easy or pleasant.
Probably the best is to force people to save sufficiently to fund their dotage themselves but that means a probably big drop in current standard of living and will be resisted plus some are incapable of it anyway.
As the problem is actually caused by survival beyond the point where the lifetime accumulated wealth can fund necessary support what government is going to dare introduce euthanasia for lack of finance?
Best to pretend there is no problem and kick the issue into the long grass. At least that seems to be the solution of choice for all governments so far.