The present research investigates the competition between two products without packaging and with green packaging in a dual-channel supply chain with government intervention. The manufacturer supplies the product to the customers at the first level without packaging, and the packaging company supplies it at the second level with green packaging. The profits made by the supply chain members have been calculated under the two government policies for identification of the optimal decisions (the revenue-seeking policy along with environmental protection and the revenue-seeking policy alone). The objective of the government is to raise income in the first policy and to reduce the environmental effects as well in the second. The results indicate that the first government policy is to the manufacturer’s benefit, while the second is preferred by the government and the packaging company. Moreover, the low cost of green packaging is to the benefit of the packaging company in both government policies, which is the case for the manufacturer only in the second. It has also been demonstrated that the difference between the sales prices of the two products increases, and the competition between them decreases with an increase in the difference between the customers’ conceptions of their values.