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In the era of the fourth industrial revolution, the international community is striving to establish a coordinated system to prevent fatal climate change in a global sense. As a result of such changes in business environments, a new issue, sustainability, has recently presented a paradigm shift and new research opportunity in which the theories and practices in traditional production and operations management are being reinterpreted and reapplied in relation to this emerging issue. Under this research background, we consider an optimal emission-trading problem under a cap-and-trade (CAT) emission regulation when the customers' demand is given as an arbitrary probability distribution. Such a CAT approach to reduce the amount of emissions is a normative system for the sustainable production of manufacturing firms, which is also closely related to a well-known open innovation in literature of inventory management. Then, we formulate two stochastic inventory optimization models, which can be applied immediately for two famous CAT policies that exist in reality. In particular, our objective is to draw theoretical and practical implications for baseline credit emission regulations, which are innovative and government-led emission regulation policies, with a well-known newsvendor analysis. For our analytical results, we first show that our objective functions are piecewise linear and (quasi)-concave. Thus, it is found that there exists a unique optimal solution to the problem. Second, we successfully obtain the closed-form optimal solutions for the two models considered. Finally, we conduct a sensitivity analysis through a comparative static analysis to examine how the model parameters can affect the optimal solution in each model. All these analytical results and implications are consistent with previous studies in the literature, as well as with our insights for the models.