In a deregulated electric power market, a demand function to consider the characteristics of electric power consumers should be required. It is essential that the optimal power flow algorithm with object function of social welfare maximization using the demand function for a competitive electric power market is applied to resolve in a point of economic benefits as well as the security of power systems. Therefore, in this paper, we implement the optimization problem based on linear programming to consider the characteristics of electric power consumers using the demand function and analyze not only the nodal cost for generations and demands but also the variation of demands as a function of the characteristics of electric power consumers through numerical studies.