The paper at hand examines the power system costs when a coal tax or a fixed bonus for renewables is combined with CO2 emissions trading. It explicitly accounts for the interaction between the power and the gas market and identifies three cost effects: First, a tax and a subsidy both cause deviations from the cost-efficient power market equilibrium. Second, these policies also impact the power sector's gas demand function as well as the gas market equilibrium and therefore have a feedback effect on power generation quantities indirectly via the gas price. Thirdly, by altering gas prices, a tax or a subsidy also indirectly affects the total costs of gas purchase by the power sector. However, the direction of the change in the gas price, and therefore the overall effect on power system costs, remains ambiguous. In a numerical analysis of the European power and gas market, I find using a simulation model integrating both markets that a coal tax affects gas prices ambiguously whereas a fixed bonus for renewables decreases gas prices. Furthermore, a coal tax increases power system costs, whereas a fixed bonus can decrease these costs because of the negative effect on the gas price. Lastly, the more market power that gas suppliers have, the stronger the outlined effects will be.