We consider a supply chain consisting of a supplier and a buyer whose efforts jointly influence carbon emissions per unit of the product. The product demand is affected by the effort levels. The carbon footprint is allocated to the supply chain members by a social planner, and they pay carbon penalties for their allocated emissions. We first examine the social first-best solution and then analyze a no-collaboration scenario, where the supply chain members simultaneously make their own effort decisions under an allocation rule, and two supply chain contracting scenarios: credible buyer and double moral hazard, where the buyer designs and offers a contract to the supplier that specifies an order quantity and a payment scheme contingent on the realized carbon footprint. We find that the social planner may need to over- or under-allocate the emissions to the firms to induce the social first-best effort levels in the no-collaboration scenario. However, the social first-best effort levels can be attained with a simple allocation rule without over- or under-allocation in the credible buyer scenario. For the double moral hazard scenario, where the buyer is not credible to the supplier, the social first-best may not be attainable and there may be a significant loss in the social value of the supply chain.