How market price of any food product let say "rice" is determined in free market in a country? How they determine demand and supply. I need detailed answer. Thank you

At many steps from grower to eater there are multiple sellers and multiple buyers. These negotiate with eachother and come to a price each feels gives them value. A local warehouse buys from many farmers but there are other warehouses a farmer may sell to. Each side can get information about similar deals and will not accept a price far from what others are getting. Costs figure in, as no one wants to take a loss. But if others are selling rice at 50 cents you are not likely to get 60 cents, no matter what it cost you to grow.

Retail prices for food in the US can be a complicated subject.  On the one hand, there is the market price, and this is defined as what people are willing to pay.  If you charge more, your customers will go elsewhere.  On the other hand, there are many strategies a store will employ.  For example, an item might be advertised at a very low price, but it may be a "loss leader".  This is where the store knows it will lose money on that item, but it will draw in customers who will buy other things which are profitable.  For an American store owner, rice in large quantities is not a high profit item.  It is bulky and heavy, and takes up a lot of shelf space.  Think from the point of view of a store keeper:  it will cost you the same labor to stock your shelves with a thousand dollars of bakery goods or a hundred dollars of bagged rice.  You won't be earning much money from selling rice, but your customers will go elsewhere if you don't have it.  This is why, in every American supermarket, close to the bulk rice you will see small packages of pre-mixed rice preparations.  For example, the Zatarain's brand; basically, rice plus spices.  And also specialty rices.  "Organic Jasmine Rice".  Much more profit on these things.

Let us say that the free market is an electronic exchange for commodities. This is the closest proxy to a free (and efficient) market. The price is determined here at every second (or moment). Depending on the current price, the demand and supply changes. If price is too high, then more suppliers will jump in and vice versa. This will happen until an equilibrium price is achieved. At this price, most of the trades will take place. This goes on until a new information comes up (like weather / crop, or spoilage of stocks), when markets discover the price once again. Often the markets take a random walk to discover price, even when there is no new information. On electronic exchange, calculation of demand, supply and implied price is easy and transparent. In physical, one-to-one transactions estimating total demand is very difficult. The farmers have much less information than traders. Thus, their pricing power is less and traders set prices, which could be different from equilibrium price. Also, transaction costs play a role in setting prices.