Who is going to do all the food/goods production? The remaining islanders.
You will probably say, hey? How are they going to have equal amount of production with such a huge chunk of labor force taken out of the society? Well, turns out the island has always have excess labour. So that's going to be fine.
How do the oldies "buy" the foods? They buy them via a thing called a "bond paper" or just the "bond coupon".
What is a bond paper? It's a piece of paper that can be converted to "money", currently safe guarded by the island's public and private pension houses.
Here comes the problem. The pension houses don't have the "money".
Huh? Yeah, it's a little unfortunate.
Well, they can always print the money out, at least for the public pension house.
The problem is solved then, isn't it?
Well, there is a little wrinkle. For those who depend on the pension to live, purchasing power of money seems to be eroding at a 10% rate per annum. By the time the islanders are in their 10th year of retirement, the money's purchasing power has shrunk to about 1/3 of the original value. Luckily, a great deal of these oldies still have other "sources of income" or assets for sale, like their homes. But the problem, is, other "smart oldies" are also selling their homes to take out cash to live.
So the home prices (and to a certain extend all asset prices) keep on falling as the oldies needed to "Cash out" and move to a smaller home or just rent, etc. Young people might want to "buy" the assets but they are smaller in numbers (thanks to the aging island demographics) and their purchasing power are not as great due to the wage stagnation with high inflation situation.
Luckily for the island society, the biggest chunk of wealth are concentrated in the select few extremely rich islanders. So while there are selling going on, it has been a limited event; it is stabilized at some point as the non-rich oldies are almost done selling off their assets/dying off. That process lasted for a little more than a decade or so.
This unfolding of events make the younger generation or working islanders nervous as there are less and less "opportunities" in making their savings "work" for them as they are saving for their own retirement as they watch the real value of the assets prices going down for the "lost decade or two".
How can the "real value" of an asset go down? Well, for example, it used to be that the value of a beach house can buy you a few years of "no need to do fishing". Now, the sale of a beach house can only pay for your living expense for 6 months.
And meanwhile, the value of your working hours are going down as well as there are lots of cheap labour and increased productivity coming from technological improvement.
So it used to be that an islander can work for say 15 years, during which his beach house go up in value very fast and then he sell the beach house and live in a beach hut and he is "all set" by retirement age. Now you need to work for your whole life but then your savings keep on getting "eroded" in the 10% a year inflation, heavy island taxation to pay off the vast debt accumulated from the parents' generation while your wage is stagnated.
So other then the offsprings of the very rich, the rest of the working islanders have to pretty much work hand to mouth until they die, unlike the parents who managed to "make ends meet" in their "elderly years".
Due to the poorer-condition of the younger generation, their offspring's numbers are even SMALLER. (Okay, it's partly also due to the running low on resources of the island, making the real cost of living higher and higher for the vast majority of islanders.) So the vicious cycle keep going on until most of the surviving islanders are rich people's descendants. Except for a group of islanders who is called the "underclass", under challenging circumstances, still managed to have offspring thanks to the "public" purse's subsidizing.
At that time, technological advance has come to such sophistication that most "production" are done by machines, so the "shortage" of labour wouldn't be a concern. So despite the disappearance of vast sections of the society, the underclass's value in the labour market is still meager and thus stays poor for generations depending on the public purse. (Why can't they just farm or fish, it's still an island right? Well, the sea is heavily polluted and the fish are dying. The farmland are owned by landlords and they have to pay rents and buy expensive fertilizer just to farm. Robots farm better anyways. Same goes for other markets activities where the rich own the venue itself and the poor is too poor to "earn their way" to durable assets like a shop space or a house, etc).
And the reversal of the "aging" of the high society destroy the old-tiny high society as wealth get scattered into many hands thanks to the high-tech painless reproduction and the trustworthy-robots nannies and daddies which can almost fully replicate the parent's parenting duties for them (you can see why the poorest underclass would still find it hard to compete for jobs in the society). And the technological advance has also allowed those with the resources to live for centuries.
So a new "middle class" is formed from the "off shots" of the very rich thru these avenues.
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