Blockchain technology (BT) is widely implemented in businesses, yet its adoption within distinct channel leaderships in a supply chain has not been well studied. Following real-world practices, we build analytical models to study two strategies in which the manufacturer leads BT adoption (MLB) and the retailer leads BT adoption (RLB). Our results show that BT adoption does not necessarily create extra supply chain profits. Higher profits can be obtained when consumers show a strong preference for traceability or when the leader shares sufficient costs otherwise. Raising leaders' cost-sharing proportions does not necessarily benefit followers, and the cost burden may motivate leaders to reduce the traceability level, thereby decreasing overall benefits. Interestingly, cost-sharing is not a "zero-sum" game for supply chain members, and sharing more costs as followers may help create mutual benefits. A comparison of the strategies of MLB and RLB reveals that the product price, traceability level, and carbon emissions in MLB can either be higher or lower than those in RLB. From an environmental perspective, we show that the carbon tax has a nonmonotonic effect on product retail prices. For the supply chain, it is possible to increase profits but simultaneously reduce emissions in each strategy, and a superior strategy that improves both economic and environmental performance exists. By modelling the regulator's participation in BT adoption, we further show that emission taxes and BT subsidies are not concomitant, and surprisingly, we find that the emission tax may either increase or decrease with product emission intensity. Moreover, our extension shows that regular operational costs for BT may impact the economic performance of BT adoption but other key findings remain robust.