Who decides what price is fixed in a supermarket?

Ultimately, the purchaser determines the price of a product. A manufacturer will determine a wholesale price and possibly a suggested retail price. Retailers will decide if they think they can sell the product at a satisfactory level above the wholesale cost. However, if a product goes on the shelf at $10 and no one buys it, the retailer will mark it down until it sells. So the only price that matters is the one that someone is willing to pay.