The flexible operation of carbon capture units is crucial for the economic performance of coal-fired power plants equipped with CO2 capture systems. This paper aims to investigate the impact of electricity, CO2, and fuel prices on the economic operation of such plants. A novel economic optimization model is proposed, integrating a static model of the carbon capture system with a particle swarm optimization algorithm. A new concept, the CO2 boundary price, is introduced as a key metric for determining the operating conditions of CO2 capture units. The CO2 boundary price rises when the power load decreases due to the decline in power generation efficiency, and it also increases with rising fuel prices, as the cost of steam for CO2 capture increases. Additionally, when the objective is to meet power load demand, CO2 prices have a great influence on the operation of CO2 capture units, assuming fixed coal and electricity prices. However, when the primary goal is to maximize plant profitability, the system’s operational conditions are strongly influenced by the relative prices of electricity and CO2. The proposed optimization model and the uncovered price-effect mechanisms provide valuable insights into the economic operation of carbon capture power plants.