What can a food surplus lead to?

A food surplus in a society can lead to many different things. But based on the principles of supply and demand a surplus of food should lead to a reduction in the price of food, because the quantity supplied is most likely higher than the quantity demanded. In addition a food surplus could lead a country or companies to sell their food surplus internationally or to "dump" the goods on another country or market by selling the goods for a very cheap price most likely lower than the price of the good in that market prior to the entry of this new producer or country with the food surplus.