The economic dispatch problem (EDP) is important to the economic operation in microgrids, the objective of which is to obtain the generation plan with the minimal total generation cost. Considering the connection to main grid, flexible loads and line losses in the microgrid, a complete EDP model with corresponding constraints is proposed in this paper. Motivated by the push-sum method and dynamic consensus, a consensus-based distributed optimization algorithm is proposed to solve EDPs in this paper, step sizes of which can be fixed and uncoordinated. It is shown that the proposed distributed algorithm is able to solve EDPs in microgrids when the time-varying directed communication networks satisfy the uniformly jointly strongly connected condition. Several examples are provided to validate the proposed distributed optimization algorithm.