The paper studies a simple model of a farmers' manufacturing cooperative (a diary) competing with a firm maximizing the integrated profit of the farmers supplying it and the firm itself. As it is the case in many real world cooperatives, we assume that the farmers belonging to the cooperative individually decides how much to supply to the cooperative. It is shown that this serves as a commitment device for credibly gaining a large market share in the competition with the profit maximizing firm. As a result the cooperative earns more profit per farmer than the profit maximizing firm. This result may contribute to explaining why cooperatives have been so successful in the agricultural sector in many countries.