This paper deals with demand adjustment problem of each consumer having appliances by an aggregator based on the optimal pricing problem in a day-ahead electricity market. In this paper, we model consumer, generator, aggregator and design a market mechanism and they act to maximize their own profit based on the power price and decide the electricity supply and demand. The dual decomposition is applied to market problem to maximize the social welfare and the proposed algorithm decides electricity price based on the exchange of information among market participants to solve each distributed problem for improving convergence. In addition, the convergence of this proposed method is proven using Lyapunov stability theorem. Finally, simulation results show that matching of supply and demand is sufficiently achieved.