dsheets
The problem with productive assets or non-inert commodities in this thought experiment is that they are much more dynamic — inert commodity prices are much easier to reason about.
You are fundamentally correct about capital accumulation, though. If you want future value, you should accumulate something (dynamic or static) that is valuable in the future — extracting rents or expropriating labor via force in the future are not pro-social behaviors.
Do private pensions solve the “I hope I have money in old-age” problem better in a fundamental way? No.
Do they solve the “I want to pay more now to have more later” problem better? Probably in most systems.
Do they solve the “what is the fair value of grandpa’s pension this month” problem? Definitely yes.
If you want guarantees, the state can pull tricks to make you believe that the world is static… for a while. Eventually, reality will force the state to price pensions in line with demographics or suffer increasingly severe budget crises.
In the past, your children were your pension. This is a private system. When responsibility for old-age is distributed without accounting for monetary or demographic contribution, politicians can promise the moon. Stop eating the young.
The question is how the future value is priced. The original assertion was that future value must come from labor and there is no difference between direct redistribution and private transactions (of which only rent extraction was given as an example). My counter is that there are alternatives that are neither taxation nor rent-seeking. In particular, the holding of assets to be later sold is a store of value that notably does not depend on future labor any more than any functioning economy depends on labor as an input.
We have pretty robust systems for deciding what (most) things are worth via supply and demand. Claiming that future value must be extracted from future labor is just false — a system with some backpressure on the payouts to retirees is much more sustainable than one without backpressure. In your simplified thought experiment, you must agree that there is no dependence on future labor as none exists! The pension is also not effective, of course, but that is to be expected — essentially no pension is effective when stranded on a desert island.
(To be clear, I don’t advocate storing gold by birth year as a practical way to run a pension scheme.)
Edit: you’ve revised history and now added a bit about “similar arguments” and inflation. The answer is simple: yes, you might get back less real value than you put in. Yes, there might be inflation. This is fine and normal and would be preferable to the present system and is not dependent on future labor in the same way as direct redistribution. There are no guarantees. ‘Enforcing’ guarantees is a recipe for disaster as we are now seeing unfold.
There are other investment vehicles besides equity and other ways to take value from past into future that are neither garnishing the wages of children and grandchildren (most current state systems) nor investing in artificially inflated markets.
Just as a thought experiment, consider if all state pension contributions were just used to immediately purchase gold on the open market that was then put into a vault labelled with the year of birth of the contributor. Please explain how this (obviously naive) strategy is dependent on future labor. As far as I can tell, this system would be completely market-based and future labor would likely benefit as their “gold” might be cheaper as there would be less demographic demand.