This paper established a mixed oligopoly model to comprehensively compare the impact of emission tax and R&D subsidy on the output decision-making and green R&D decision-making of public and private firms. We find 1) with the increase of emission tax, the output of the public firm increases while that of the private firm decreases, but the total social output stays still, the public Firm’s R&D innovation has decreased, while private firm’s R&D has increased. 2) The impact of emissions tax on R&D investment is only related to the spillover index, not to the size of the market. While the R&D subsidy is applied to the public firm, and we find that 3) R&D subsidy has no effect on the optimal output of both private and public firms. 4) With the increase of spillover effect, the output of the private firm decreases while that of the public firm increases. 5) The study further shows that the public firm dominates the overall green R&D level of society, while the government only subsidizes the public firm in R&D.
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