The mercantilistic definition of wealth is that the more gold bullions (or equivalent) you have, you are wealthier. The modern consumerist definition of wealth by possessions is similar.
Buckminister Fuller and Robert Kiyosaki define wealth in terms of the time you can survive without having to work.
A country is wealthier if it has better infrastructure (more capital invested in it), its workforce is more productive, its resources are efficiently allocated (by market forces and where they fail, by well-thought out regulations), and its leaders have the know-how to lead it.
The question about definition of wealth has practical consequences for young people, who have to decide about the moneymaking aspect of their future. The mercantilistic definition leads to legal and otherwise means of acquiring wealth, lacking considration of other people and of the environment. Viewing wealth merely as survival time ignores risks which could wipe out part or all wealth, encouraging people to take big economic risks, which eventually ruin several of them.
Once someone has enough wealth to sustain him indefinitely, the useful definition of wealth for him changes from one of accumulation into one of reducing as much as possible the likelihood of losing it due to misfortune or natural disasters.
Thus, once someone has enough wealth to sustain him indefinitely, he had better start working on converting his wealth into environmentally sustainable one. He should also put some of his wealth towards insuring the rest of it – by taking out insurance, by acquiring an home in another country and investing there, by diversifying his investments – according to their risk profiles – even when this causes reduction of return on his investments.
In his personal life, he can start training in survival skills.
Similarly, a developed (wealthy) country can start protecting its residents against natural disasters. Its residents can start training in whatever skills required for quick recovery from disasters. Infrastructures can be upgraded to prepare better for natural disasters, including whatever is required for speedy and relatively painless recovery in the aftermath of such disasters. Infrastructures, which are vulnerable to natural disasters (such as dams), can gradually be decommissioned.
This is an answer to the question what should someone, who already has all the wealth he needs in the world, do with his “excess” wealth. It also answers questions about the future economic path a developed country should take to keep its residents gainfully employed.