Sustainability addresses environmental and social issues affecting this and future generations. When family businesses perceive that the community is disrupted, recognize an environmental problem and respond by implementing new environmental policies or regulations, the family business’s socio-emotional values press to transition to a more sustainable production system, such as the ‘Circular Economy.’ Drawing on the Dubin (1978) methodology—a paradigm for building models through deduction—we design a sustainable model, which shows family businesses’ responses to changes in the environment. It explains the reasons why family firms transition to the Circular Economy, based on the theory of Socio-Emotional Wealth (SEW). We check the model through the case study of the food retail leader in the Spanish market—Mercadona—which applies policies about energy, resources and waste to become a Circular Economy business model. Because of the strong family character of Mercadona, this case can be useful for the decision-making of other family businesses.