Political and Social Structure
In its earlier time, the Olmec were grouped into several families with communally owned farmland. They shared work and benefits, ultimately characterizing their early civilization with equality.
Distinction Between Classes
The Olmec Civilization did not have an explicit political structure, their politics incorporated their societal structure. This meant that the elites and the wealthy held the power within society. Elites took control over multiple resources (i.e. water and stone) to exert control, holding the civilization in a monopoly. The Olmecs used a hierarchical society to legitimize their rule.
Modern theory: elites and rulers descended from a few families that were able to increase their wealth by acquiring the best farmland, thus allowing them to take control. Once the power was in the hands of the select people, priests emerged.
In the the Olmec society following this change, priests and rulers were practically identical. Priests came from the powerful families and they themselves held the most wealth and best lands. Priests eventually became known as Shaman-Kings or Priest-Kings with supposed divine powers. A religion formed to justify the power of the Shaman-Kings, it described their power as something given to them by the gods.
The Olmec society did have cities that served as cultural hearths. These cities contained many religious temples and palaces and also an area for trade. To emphasize the importance of the Shaman-Kings, the cities were organized so that the most wealthy lived in the central cities, which the common folk stayed in the surrounding areas.
The principal economic practice in the Olmec Society was farming, mainly stationary farming, but occasionally they would engage in slash-and-burn agriculture. Farmers grew maize, yams, squash, beans, grains, gourds, and avocados. Despite the variety of plants grown, maize was still the predominant crop.
The Olmecs were traders of basalt, rubber, shells and other substances along with manufactured goods such as pottery. The Olmecs traded with many of their surrounding neighbors including the cities of Monte Alban and Teotihuacan. As the Olmecs traded, they also formed alliances.
Centers of Economics
The main centers of their economy were San Lorenzo, La Venta, and Tres Zapotes. Seeing that they are centers of economy, it's fairly obvious that these areas were near areas of abundant natural resources.
These centers of economy shared their resources for the benefit of the entire society.