Traceability exists in many food supply chains for valid economic reasons, one of which is improving food safety and quality. Some politicians and consumer groups are calling for increased identity preservation in systems where traceability has not yet been adopted. In this paper, we explore the implications of adding traceability to a food supply chain that already includes an inspection protocol. Our objective is to determine whether the addition of traceability will change the feasibility of a market for safer food and whether it will change the allocation of profits between producers and processors. We find that the addition of traceability to this system does influence whether or not the market will be feasible. If traceability is too high, then processors will not demand safer food, and if traceability is too low, then producers will not deliver safer food. We also show that the feasibility of the market depends on the sensitivity of the test used to inspect food.