Competition lowers prices because ideally no one has a lot of "market share". Think about a small farm community where 10 people have chickens, 10 people have pigs, 10 people grow wheat, 10 people grow carrots, etc. Maybe everyone grows potatoes or something, so those aren't sold at the market. They're just eaten.

This is a situation where no one person can control the price of things, but they still fluctuate based on supply and demand. Say it's Christmas and everyone wants to make egg nog. The cost of eggs and cream will rise because farmers can't just increase the amount of eggs and milk produced. Say there's a crop sickness and half of the wheat dies. The price of wheat will rise, since farmers can't make enough to satisfy the demand for bread.

After both of these problems have passed, the prices will come back down because no one person controls more than 10% of the price for their goods. If one person charged $6 per dozen eggs after Christmas was over (everyone else charges $5, as normal), they would not sell very many eggs. The average price is not increasable by one person. And any one person could quickly sell all their eggs just by charging slightly less. (This assumes that goods are interchangeable in quality.)