PurposeThe purpose of this paper is to present a mathematical model that illustrates the trade‐offs between sustainability, demand, costs, and profit in a supply chain with a single supplier and a single manufacturer.Design/methodology/approachIt is assumed that a single product is produced and sold on a market where demand is sensitive to price and quality. Sustainability is treated as a quality attribute and is measured in terms of the levels of scrap and emissions generated in the supply chain. It is assumed that the emissions and scrap can be controlled by varying production rates or by investing in production processes. The impact of cooperative and non‐cooperative behaviour between the supplier and the manufacturer is explored. Numerical studies are used to illustrate the behaviour of the model.FindingsThe analysis shows that the supplier and the manufacturer can attract additional customers by controlling scrap and emissions. The behaviour of the supplier and the manufacturer are dictated by the decision criteria, such as changes in the level of sustainability, used by customers to evaluate the product. It is shown that the profit of the system is higher and that the level of quality is lower in the case of cooperation than in the case of non‐cooperation.Research limitations/implicationsSeveral areas for future work are highlighted. The study of alternative demand functions, linking sustainability to a monetary component, including additional players, and incorporating additional sustainability indicators all offer possibilities for extending the model.Originality/valueThere is an identified need for analytical models that consider sustainability in the supply chain. The results are especially important for companies operating in markets where customers perceive the sustainability of a product as a quality criterion.