This paper deals with a model of a real-time electricity market for a smart grid, and discusses how to decide wholesale and retail prices of electricity among market participants: power consumers, power suppliers and an independent system operator. In this paper, we consider a linearized AC model of a power grid with a direct current process and show that the wholesale price for suppliers is determined as the optimal Lagrange multiplier corresponding to the nodal power balance constraints. In addition, we propose a decision procedure for the retail pricing of electricity for consumers. In order to improve the convergence speed of the algorithm, we apply the iterative gradient method with line search to a retail pricing decision procedure, in which the optimal step size is determined in each iteration step. Simulation results, finally, show the effectiveness of the proposed retail pricing decision procedure.