Brand extension is a common marketing strategy used to capture a competitive advantage in the fashion industry and often causes social influence between the parent and sub-brands. On the one hand, sub-brand consumers are more willing to buy products when the parent brand sells well. On the other hand, the parent brand consumers’ purchase intention decreases when the sub-brand product sells too much. The fashion industry also contributes considerably to global carbon emissions. To reach sustainable development goals, governments impose carbon taxes. This paper analyzes how social influence and carbon tax regulations can affect a monopolistic firm’s brand extension strategy. The analytical results show that the firm extends from the parent brand to the sub-brand when the magnitude of social influence is not strong in the absence of a carbon tax, as the market expansion effect dominates the cannibalization effect. When the regulator imposes a carbon emissions tax, the range is further narrowed of the social influence that allows the firm to benefit from brand extension strategy because of the cost effect. Counterintuitively, the brand extension strategy can force the regulator to lower the tax price. Moreover, our findings reveal that social influence exerts an inverse impact on the regulator’s tax pricing decisions, contingent upon the extent of the parent brand’s brand power advantage. Carbon tax regulation hurts the firm and consumer surplus, but benefits the environment and social welfare. Additionally, we reaffirm the robustness of our findings under conditions of asymmetry in the intensity of social influence and different pollution damage functions. Intriguingly, we find that the firm can mitigate the negative cannibalization effect by selling its sub-brand products through a downstream retailer.
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