Cryptocurrency

When you create a liquidity pool, you set the initial price. If nobody has your token, people can't sell it, only buy it, so that initial price becomes the bottom.

1. You as a free individual can put any price on any item, cryptocurrency or not. The question is, will somebody buy it at that price?
2. The price people are generally able to buy a token at (like you see on coinmarketcap etc) is determined by actual sales via cryptocurrency exchanges. Those prices are set by the market ie whatever the last batch of coins sold for.

Token creators don't define any price. They do define things that influence the price like initial supply, inflation, etc. The market price will emerge from the interaction between those things and any demand that might exist for the token for whatever reason (usually just speculation). In short, supply and demand.

Now, this is how it works for fungible tokens, like in the ERC-20 standard. If we're talking about non-fungible tokens, or NFTs, creators usually define a price for "minting" (creating a new token in a collection). This initial minting price may or may not influence secondary sales.