In a modern supply chain, the quality of the final product is not determined by a single firm but depends on the joint efforts of multiple firms. When a quality defect happens, it is usually cost‐inefficient to trace the source of quality problems and all firms in the supply chain might incur a loss. New technologies such as blockchain can enable supply chain traceability at an affordable cost. In this paper, we develop a two‐echelon supply chain model including one supplier and one buyer in a competitive market. The quality of the final product depends on the two firms’ quality efforts. The buyer as a leader can set a wholesale price to stimulate the supplier's effort. In the absence (presence) of traceability, the payment of wholesale price is based on the realization of the final product's quality (the supplier's individual quality). Interestingly, we find that supply chain traceability may cause a decrease of the supplier's quality effort, thereby reducing the quality of the final product when market competition is sufficiently intensive. Furthermore, traceability weakly increases the supplier's profit but weakly decreases the buyer's profit. However, the total profit of the supply chain can be increased in the presence of traceability.