A community microgrid is a microgrid composed of several entities, or members, that can share energy among themselves. The members of the community can match their demand and supply through an internal local market with a significant reduction of the exchanges with the main grid. As a consequence each participant can benefit from a reduction of its energy costs when the energy available locally is cheaper than the energy from the grid, from a drop of the energy peak demanded from the main grid, and from the new capability to provide energy reserve at aggregate level. In this paper, we analyze how the changes of the community market model parameters can affect both the community as a whole, and the welfare of each participant. The analysis is performed by varying the main drivers of the community market model, the community and storage fees, and the storage capacity. The numerical results are obtained by using real data based on the MeryGrid project.