Which field of anthropology studies how a society establishes a system of government and economics?

The field of Cultural Anthropology. Cultural anthropology studies the cultural aspects of human societies. The research is usually on such things as social and political organizations (government), subsistence and economic patterns (economics), and religious beliefs.

Cultural anthropologists gather information about the culture they are studying (using methods of participant observation and interview) and they compare it with data in the academic literature. They study contemporary societies and subcultures of modern societies.

Example: Because of global economy, all societies of the past have been heavily influenced by dominant cultures.