6. Conclusion
With the imposed regulations and legislation on carbon emission control, firms have to manage carbon emissions in their supply chains. In this paper, we derive the optimal total emissions and production quantities of the two products over all possible levels of cap, and explore the impact of the emission trading prices on the optimal production decisions and the optimal profits.By analyzing the impact of the cap and emission trading prices on the production decisions, we find some managerial insights: (1) the emission trading decisions follow a two-threshold policy. If the cap is lower (higher) than one (the other) threshold, then the manufacturer buys (sells) emission permits from (to) the outside market and if the cap is between the two thresholds, the manufacturer will neither buy nor sell emission permits; (2) if the reduction of the marginal profit of product 1 is larger than that of product 2 when the unit emission permit is used to produce product 1 (product 2), then the manufacturer will allocate more emission permits to product 2 as the cap increases, otherwise, the manufacturer will allocate all the emission permits to product 1. So, the manufacturer may produce product 1 (product 2) or both of the two products which indicates that cap-and-trade regulation may not have the ability to induce the manufacturer to produce low-carbon products; (3) the optimal total emissions and production quantities of product 2 are decreasing in buying or selling price of emission permits, while the optimal production quantities of product 1 may be increasing in buying or selling price of emission permits.
