At present, an increasing number of countries and regions, including China, are adopting electricity and carbon markets to optimize the resource allocation of the electricity power industry. To mitigate the impacts of these complex market conditions, more and more power generation enterprises adopt hybrid production mode, generating electricity from thermal and new energy units simultaneously. This research introduces the decision process of hybrid power generation enterprises under the abovementioned trading conditions, and provide the optimal production decisions of enterprises with different market positions. Besides, the consequences of collusion behaviors among power generation enterprises and governmental policy changes are also measured based on the description to the equilibrium state of electricity and carbon markets. Numerical experiment results confirm the correctness of the production decision model and reveal the following facts: (1) Carbon market effectively reduces carbon emissions and raises the new energy power generation share, but it cuts the electricity supply and drives up the electricity clearing price. (2) The combined effects of electricity and carbon markets are able to mitigate the impacts of policy changes on market equilibrium. Power generation enterprises first internally cushion these impacts by adjusting the generation structure, and then absorb the residual impacts by adjusting the total power generation. (3) The collusion behaviors among power generation enterprises can destroy the electricity and carbon markets largely. They increase the CO2 emissions by 187.94%, cutting the electricity supply by 25.30%, and drive up the electricity clearing price by 1.37%.