1. Raw Material Costs: The prices of raw materials used in stainless steel production, especially the prices of elements like iron ore and nickel, can impact stainless steel prices.

2. Production Costs: The production costs of stainless steel, including factors such as energy, labor, and production technology, are important in determining prices.

3. Demand and Supply: Stainless steel demand and supply affect market prices. Prices tend to rise when demand increases and supply decreases.

4. Exchange Rates: Stainless steel is often bought and sold on the international market, so exchange rates can influence prices. Particularly, as international raw material prices, like nickel, are often quoted in US dollars, fluctuations in exchange rates are significant.

5. Competition: Competition among stainless steel producers and suppliers can also influence prices. In markets with intense competition, prices tend to be lower.

6. Consumer Demand: Demand in industries that use stainless steel, such as the industrial or construction sectors, can also affect prices.

Stainless steel prices can constantly change due to the complexity and interaction of these factors. Therefore, there is no exact authority or institution that determines stainless steel prices; instead, market conditions and factors shape prices. It is important for stainless steel buyers and sellers to monitor market conditions and have access to up-to-date price information.