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This paper presents a distributed Demand and Response algorithm for smart grid with the objective of optimizing social-welfare. Assuming the power demand range is known or predictable ahead of time, our proposed distributed algorithm will calculate demand and response of all participating energy demanders and suppliers, as well as energy flow routes, in a fully distributed fashion, such that the social-welfare is optimized. During the computation, each node (e.g., demander or supplier) only needs to exchange limited rounds of messages with its neighboring nodes. It provides a potential scheme for energy trade among participants in the smart grids. Our theoretical analysis proves that the algorithm converges even if there is some random noise induced in the process of our distributed Lagrange-Newton based solution. The simulation also shows that the result is close to that of centralized solution.