[PaulHoule]

Power is a measure of money, but it is not in fact money.

See https://hbr.org/2008/02/the-founders-dilemma

or the fact that John D. Rockefeller was furious that Standard Oil got split up despite the stock going up and making him much richer.

It's not so clear what motivates the very rich. If I doubled my income I might go on a really fancy vacation and get that Olympus 4/3 body I've been looking at and the fast 70-300mm lens for my Sony, etc. If Elon Musk changes his income it won't affect his lifestyle. As the leader of a corporation you're supposed to behave as if your utility function of money was linear because that represents your shareholders but a person like Musk might be very happy to spend $40B to advance his power and/or feeling of power.

[wslh]

To clarify you can have power without money, for example initial revolutionaries. Money buys power, and power could convert into money depending the circumstances.

[dredmorbius]

Wealth is cardinal. Power is ordinal.

Wealth is something that is counted and accumulates (or decrements).

Power is ranking. If you double your wealth, but maintain (or reduce) your power ranking, net-net you've lost power.

There are other elements at play. Discretionary wealth and power also matter. If you're in a position where all your wealth and/or income are spoken for (e.g., a business with high cash-flow but also high current expenses such as labour, materials, services, rents, etc.; or a governmental unit with high mandated spending / entitlements), then a numerically high budget still entails little actual discretionary power. Similarly, an entity with immense resources and preeminent ranking but where most or all options are already spoken for, where there are no good discretionary options, has nominal power but little actual power.

A classic example of the latter is a regime which embarks on a military misadventure only to find that it can pour in vast amounts of blood and capital for little actual return, ending up bogged down in a quagmire: Vietnam, Afghanistan (multiple instances), the Western Front (WWI), Gallipoli (WWI), winter invasions of Russia (Napoleon, Hitler/Barbarossa), the Charge of the Light Brigade, Waterloo, Agincourt, the Spanish Armada, etc.