People don’t decide to raise prices out of the blue… it isn’t quite this simple, but for the purpose of understanding the basic concept, you can think of it as the price goes up when you can easily sell your inventory at the current price… if your product sells out quickly, and you still have people eager to buy your product, you raise prices, and you keep raising them until you can just barely sell all your product (of course it is more complicated, because you are trying to maximize profit and not minimize inventory, but the basic idea is the same)

If you fix prices, it just means the product keeps selling out quickly and most people can’t get the product.

This is why prices go up when there is a supply shock (like with eggs and the bird flu). There are fewer eggs available, and raising prices reduces demand until it matches the supply (as people who only kinda like eggs switch to cheaper alternatives). While it sucks that eggs are more expensive, at least you can still buy them if you really like eggs. With price controls, it becomes a crapshoot on whether you can get them or not.