The region-cap allocation and delivery time decision in the marketplace mode under the cap-and-trade regulation

Considering a manufacturer selling products through an online platform that operates in the marketplace mode, we investigate the manufacturer's production and delivery time decisions, and the government's region-cap setting under the cap-and-trade regulation with grandfather-based allocation and benchmark-based allocation rules. The comparisons of the two rules in terms of production and delivery time decisions, and social welfare are conducted. We find that the optimal production quantities increase with the region-cap (the manufacturer's share proportion) with grandfather-based allocation rule, and decrease with the region-cap (the manufacturer's share proportion) with the other rule under some situations. Moreover, the increasing sensitivity to delivery time brings more production quantities, which further generates more carbon emission with the two rules if the manufacturer's share proportion is high. With the increase of the environmental damage coefficient, the optimal region-cap with grandfather-based allocation rule decreases, while it increases with the other rule under some situations. By comparing the two allocation rules, we find that when the environmental damage coefficient is high, the grandfather-based allocation rule generates less carbon emission and more social welfare; otherwise, the benchmark-based allocation rule tends to bring more carbon emission and more social welfare. As a result, for the regions with a serious environmental problem, the government should adopt the grandfather-based allocation rule; for the other regions, the government should adopt the benchmark-based allocation rule.