The Role of Women in Ancient Greece included mainly giving birth to children and taking care of the home. The were seen as inferior and controlled by the men and had no political right in the society.
The role of Women in Persia were more and although they were seen as inferior to men they had a higher amount of freedom to do business and participate in the political sphere. They were permitted to work and not consigned to the home alone.
The economy you described in your question is called a market economy. It has free markets and the production of goods and services are determined by the consumers.
