Carbon footprinting is a tool for firms to determine the total greenhouse gas (GHG) emissions associated with their supply chain or with a unit of final product or service. Carbon footprinting efforts typically aim to identify where best to invest in emission reduction efforts, and/or to determine the proportion of total emissions that an individual firm is accountable for, whether financially and/or operationally. A major and under-recognized challenge in determining the appropriate allocation stems from the high degree to which GHG emissions (or emissions reductions) are the result of joint efforts by multiple firms. In this paper we introduce a simple but effective model of joint production of GHG emissions in general supply chains, decomposing the total footprint into processes, each of which can be influenced by any combination of firms. A supply chain in which all firms exert their first-best emissions reduction effort levels is "carbon optimal", while a supply chain which offsets all emissions is "carbon neutral". With this structure, we examine conditions under which the supply chain can be carbon-neutral and/or carbon-optimal. We find that, in order to induce the carbon-optimal effort levels, the emissions need to be over-allocated. This means that the focus in the life-cycle assessment (LCA) and carbon footprinting literature on avoiding double-counting is, in the context of setting incentives, misguided. We also compare the situation where a single firm offsets all supply chain emissions with that where one powerful firm can enforce an emissions reduction target across all firms in the supply chain, and find that neither scenario is always preferred over the other. Our work aims to lay the foundation for a framework to integrate the economics- and LCA-based perspectives on supply chain carbon footprinting
