Trump could totally buy Greenland. There is nothing against a sovereign land purchase in international law, in fact, the US bought the Virgin Islands from Denmark in 1917.
However, if I was a megalomaniac businessman, after a sharp rebuttal from Denmark’s PM, my next move would effectively be the same as launching a corporate ‘hostile takeover’. The people I would have to convince are the Greenlanders – the shareholders in the takeover.
There are only about 55,000 people living there (equivalent to a town you have never heard of), take 20% off for under 18s with no vote, you get 44,000. You could offer every registered voter $1million to become an American citizen. And everyone gets to keep their homes, businesses etc – you are not buying their land, just their sovereignty.
As this is a thought experiment – let’s splash some cash – a total budget of $10million per voter. This would cost about $440 Billion ($440,000,000,000). To put that in perspective the US Defence budget is almost $700 Billion ($693,058,000,000) for this year alone. I would potentially use some of that money to sweeten the deal for Denmark. I’d definitely spend some on a huge propaganda campaign Cambridge-Analytica-style, which would include driving a wedge between locals and the Danish government, and also selling the idea back home.
Then Greenland holds a referendum. Under international law, the right to self-determination would win. What could Denmark/EU do about it?
Greenland’s population is 88% Inuit (inc. mixed Dane-Inuit). Why be loyal to a remote European colonial ruler & a monarchy to boot? They could be ruled by local North Americans in Washington instead, and become a new US state.
Evidence that the local population may be open to this idea is shown in results of recent opinion poll – a clear majority of 64% in favour of declaring independence from Denmark, though this flips to 78% against if it means a drop in living standards.
Which proves A: they’re not loyal to Denmark, and B: they can be persuaded.
They also have the highest suicide rate in the world, by a huge margin, so they’re not that happy at the moment.
How much is Greenland worth? Strategically priceless? It would be adding about 20% to the landmass of the USA, so on the scale of the Louisiana Purchase (actually marginally bigger in km2). We don’t know how much oil, gas, and minerals (iron, uranium, aluminium, nickel, platinum, tungsten, titanium, copper and lithium) is under all that melting ice but it is estimated at lots. There are gemstones too.
On second thoughts, if my budget was going to go as high as $10million per person, I would want to include compulsory government purchases of any private property/land in the deal too, so nobody hostile moves into the spaces vacated by all the locals who have just moved somewhere warm to retire. This would also avoid the problem of creating a super-rich environmentally-conscious population with nothing to do, right where I want to drill.