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A modeling and computational framework is presented for the determination of optimal carbon taxes that apply to electric power plants in the context of electric power supply chain with consideration of transmission constraints and losses. In order to achieve this goal, a generalized electric power supply chain network equilibrium model is used. Under deregulation, there are several players in electrical market: generation companies, power suppliers, transmission service providers, and consumers. Each player in this model tries to maximize its own profit and competes with others in a noncooperative manner. The Nash equilibrium conditions of these players in this model form a finite-dimensional variational inequality problem (VIP). By solving this VIP via an extragradient method based on an interior point algorithm, the optimal carbon taxes of power plants can be determined. Numerical examples are provided to analyze the results of the presented modeling.