The development of markets for the poorest populations (Base of the Pyramid - BOP) has become important for multinational companies (MNC), NGOs and public policies. Assuming that there is demand for very low price consumer products, and that the main problem is one of access to those products, the challenge for MNCs is to reconfigure the whole of the corporate process accordingly. The paper follows BOP theory and companies actual innovation. It looks at the definitions of the BOP market, the representation of BOP consumers, and local heterogeneous configurations of actors. Based on a fieldwork with a MNC (specialising in electrical equipment) investigating a BOP Business, it investigates the work undertaken by managers to build this market innovation. It explores the paradoxical frontiers of consumption and aid to the poorest populations, and feeds the reflexion of BOP policies by opening it up towards a diversity of alternatives and possible configurations.