Under a finite financial budget, the government offers subsidies for remanufactured products in order to encourage production and sales. Firstly, a three-layer decision model that the government provides production subsidies for the manufacturer is constiucted, in which the manufacturer declares its wholesale prices by a Stackelberg game with the new-product retailer and the remanufactured-product retailer, and the two retailers determine their sales prices by a Bertrand game. The impacts of production subsidies on wholesale prices, sales prices and sales quantities are demonstrated. Further, the root cause of the increased sales quantity of the remanufactured products is shown. Secondly, the model in which the government offers sales subsidies for the remanufactured-product retailer is considered. It is shown that production subsidies and sales subsidies are equaivalent for affecting sales prices and sales quantities. Thirdly, a centralized decision-making model is proposed. The sales quantities between the decentralized model and the centralized model are compared, and the reason of the difference is analyzed, which provides a basis for the priority of the subsidy. Finally, a numerical illustration is presented to make some supplements.