In order to promote green technology investment and emission reduction, the government usually provides subsidies to enterprises under the cap-and-trade (C&T) mechanism. Two types of subsidy policies are widely used: one is based on fixed green technology investment cost (FC subsidy) and the other is based on the amount of emission reduction (ER subsidy). This paper investigates the effects of these two government subsidies on the green decisions of a two-echelon supply chain under C&T scheme. Three Stackelberg game models are formulated and analyzed. The analytical results indicate that both manufacturer and retailer tend to collaborate on green marketing when green technology is invested and subsidized. However, the government's subsidy policy cannot guarantee green technology investment and total carbon emission reduction which also depend on the range of green investment cost, emission reduction rate of green technology and the carbon emission intensity of manufacturers. Indeed, higher subsidy will result in the implementation of more expensive but cleaner green technology. With the same subsidy budget, the manufacturer can earn more and emit less under FC subsidy, but ER subsidy can bring more profit to retailer and induce more green production and greater green marketing efforts. Therefore, the government can use FC subsidy on developed and high emission industries to control total emission and adopt ER subsidy on emerging or developing industries to promote their development. •Quantify the pricing, green investment and green marketing coordination of supply chain with subsidies under C&T mechanism.•Compare the impacts of two types of subsidy policies on green technology investment and green marketing coordination.•Compare the performances of two subsidy policies on emission reduction and economic growth with the same subsidy budget.•Give suggestions for the government to set forth the requirements for subsidy to promote green technology or reduce emission.