This is a hypothetical question. Assuming that the price of bitcoin is \$8,250 (as of current writing) and I had 25 billion dollars at my disposal, what would happen to the price of bitcoin if I successfully bought 100,000 bitcoins? Would I have enough money? If so, how much would it cost? I am curious about this because of the digital scarcity aspect of doing so.

While I agree with chytrik I would want to suggest a concrete method of approaching this.

Have a look at the combined order book https://data.bitcoinity.org/markets/books/USD you can see that you currently would move the price by 10 % if you baught roughly 10k BTC. Usually after such moves people get alerted and are willing to sell at higher prices so you could wait a little until the order book fills and repeat the process.

Assuming there are always 10k fresh floating BTC available with leads to a 10% price increase. (With regular trading many of the btc on the order books are going to free float afterwards so that assumption is pretty strong) you would have 10 = 100000/10000 price increases of 10 % each resulting at a price of 8250*1.1^10 = 21398 per btc.

You would have to pay roughly 1.4 bn usd which is 8250*10000*(1.1^1+1.1^2+....+1.1^10)

Obviously this is just a simple model build on strong assumptions. Also you would try to buy that much btc otc because you would not want to move the price but obviously you would have to convince holders to sell

The answer entirely depends on what the people who already hold Bitcoin are willing to sell it for. Generally, a massive buy would be expected to push the price up, because you would first buy up all the coins at the current spot price, and then the coins just above that price, and then just above that price, etc. How high it goes would just depend on the ‘depth of the orderbook’(how many bitcoins people have put up for sale at whatever prices).

If there happen to be 100,000 bitcoins up for sale at the current spot price, then perhaps you could make the buy without pushing the price up at all. That seems less likely, but it is possible. At \$8250 per bitcoin, that would amount to \$825,000,000 USD. So we should expect it would cost you at least this amount, unless you can find someone willing to sell at less than the market rate (they might be stupid to do so, but it is possible).