> r must be greater than g for investments to make sense in the first place

Why would that be true? Say r was lower than g, what is my alternative to investing my capital?

Technically, consumption (spending your whole paycheck) is an alternative to investing but that mostly comes up in macroeconomic discussions.

Um, so I would a car every few months?

You might be surprised how much money some people are capable of spending.

There does seem to be some conflict between exhorting everyone individually to save more while complaining that the economy is suffering from shortfall in aggregate demand (i.e. people not spending enough money).

You can buy real assets (traditionally gold). Think of a world with large inflation -- if you are rich and hold bonds or money in the bank you wealth doesn't grow or potentially diminishes, but if you are a worker you still get money and presumably your wage growth increases quite fast (in line with the large inflation).

Real assets are great if r goes negative. What if r is still positive in real terms, but g is more positive?

First, it's hard to imagine such a world. Under normal circumstances as productivity/automation increases worker labor will always be an increasingly smaller part of the value added, which means capex grows relative to opex which drives r.

The way r can get suppressed long-term is through (1) wealth taxation, (2) depreciation of an important asset class (eg as birth rate falls further below replacement housing can start to depreciate), or (3) high inflation.

If it is (1) then there really isn't much to be done, although hopefully the redistribution will be administered sufficiently well to help everyone achieve a high quality of life. If it is (2) then you can avoid the depreciating assets. If it is (3) then you once again avoid depreciating assets (don't hold cash/bonds/cash-like assets).

You just "spend" it on "non-productive" assets like art, gold coins, jewelry....these sorts of things.

Is housing, like Gold Coins also a non-productive asset?

No - its production is either the rent your tenant pays you, or the money you save by not paying rent, if you live in it yourself.

That makes no sense. If you're not invested you don’t get g, you get a slight negative return from inflation.

Long term it always makes sense to invest as long as you can do better than the (generally negative) “return” of inflation.

Let's set up a situation where r is greater than g, and also I'm getting a fair share of g so I can actually experience this tradeoff properly.

Okay, so the rational behavior is for me to do the minimum amount of work possible for most of my life, since wages grow faster than savings. Then, the week before retirement, I just have to do 10 years of work all at once!

Doesn't really work.

If g is one percentage point bigger than r it makes my retirement savings somewhat smaller than I'd like, but it's still far better than not having any.

If I already have lots of money, and I don't want to go bankrupt, my only real options are r and leaving it in a box. And r definitely has better results than the box.

Preemptively buying products I don't want yet has an even worse return than the box, since they need to be stored and decay over time.

Is that really true? r < g could still make sense if you're constrained on g and less so on r, as long as r earns some return.