The Pareto frontier, a concept rooted in economics and multi-objective optimization, represents the interplay between two objectives. In the context of power systems, it is often the case that different objectives have to be considered at the same time, such as the minimization of the operational cost and the minimization of greenhouse gas emissions. However, whether both objectives are achievable or not largely depends on the specific technoeconomic characteristics of the generation units involved. In this context, the current paper presents the Pareto frontier for different combinations of technoeconomic characteristics of generation units, and different types of functions for the operational cost and CO2 emissions, as well as various technologies, including Combined Heat and Power, heat-only and thermal power stations. The analysis reveals a range of shapes for the resulting Pareto frontier and underlines the critical patterns and dependencies within the energy system’s operational framework, highlighting the complex interplay between environmental impact and economic feasibility.