Thermoeconomic models, combining the concept of cost in economics and the concept of exergy in thermodynamics, provide the ability to optimize complex power generation systems to achieve the best balance between thermodynamic efficiency and economic cost. In this paper, a parametric analysis was carried out based on the method of calculating the unit exergy cost, as well as exergo-economic studies and cost sensitivity studies on the exergy of the cycle of a gas turbine power plant. The mathematical models of mass, energy, effort, and economy were created and presented. Thermodynamic properties and research analysis are performed using the MINI- REFerence fluid PROPerties (MINI-REFPROP) and matrix laboratory (MATLAB) SIMULINK software packages. The analysis leads to valuable benchmarks of the economic situation. The exergo-economic coefficient, the total cost of exergy loss, exergy destruction for the combustion chamber, and labor productivity are determined. When conducting parametric studies, the influence of the temperature at the inlet to the gas turbine, the temperature at the inlet to the air compressor, and the degree of pressure increase in the compressor were taken into account. The combustion chamber at the plant was found to have the highest energy destruction rate of 80%, indicating that boilers need to be given more attention in terms of design, selection, operation, and maintenance. However, in percentage terms, the combustion chamber has a high improvement potential of 94%. Sensitivity and parametric analysis show that while the exergy factor, the total cost of exergy loss, exergy destruction for the combustion chamber, and power output fall with increasing air compressor inlet temperature, it can be increased with increasing compressor pressure ratio. The total energy loss cost, combustor energy loss, and power output decrease as the gas turbine inlet temperature rises, while the cycle network and overall exergy destruction rate increase. The rates of the exergy destruction of the Venture Capital (VC), the combustion chamber of the combustion chamber, and the total exergy destruction are 25.2, 122.3, and 153.2 MW, respectively, for the proposed conditions. In addition, the results showed that it was $2,272 per hour, while the cost of work performed in energy terms is $1,769 per hour with a fuel cost of $0.003 per MJ. A valuable achievement is the availability of defined values and clear parametric influences, which can be of great help to engineers and site operators in the efficient execution of unique tasks, playing with the conflicts of energy use, exergy, and cost.