Co-production (simultaneous production of multiple outputs) occurs in some emission-intensive basic material and agricultural industries. This paper is motivated by ones in which a supplier sells its primary product to a buyer that incurs an emissions cost (voluntarily, or due to government-imposed climate policy) and sells co-products into markets without emissions costs. Emission-accounting standards provide three candidate rules for allocating the supplier’s emissions among its products. This paper shows that under the value-based allocation, imposing an emissions tax on the primary product can increase emissions, by motivating the supplier to lower the price and sell a larger quantity. In contrast, with the socially optimal choice of allocation rule characterized in this paper, imposing the emissions tax on the primary product can greatly reduce emissions and increase welfare. In the absence of climate policy, under value-based allocation, a buyer might achieve greater profit by paying to offset its supply chain emissions. That can motivate supplier innovation to reduce its production cost. In numerical examples, considering the rare earth cerium oxide (co-produced with iron) and palm oil (co-produced with palm meal), the choice of allocation rule has a large impact on emissions, a buyer’s profit, and social welfare.