Non-orthogonal multiple access (NOMA) is a spectrum reutilization technique that superposes messages in the power domain allowing multiple users to be served in the same time-frequency resource block. Successive interference cancellation (SIC) techniques are used for decoding NOMA. A network model is considered where Poisson distributed base stations transmit to N NOMA users each. We present a signal-to- interference-and-noise-ratio analysis for the coverage of the typical user. Due to SIC, coverage implies the ability to decode the messages of all weaker users in the SIC chain. An efficient algorithm for finding a feasible resource allocation that maximizes the cell sum rate Rtot subject to a minimum rate constraint T on the individual users is provided for general N. We show the existence of an optimum N that maximizes Rtot given a set of network parameters. We also show that NOMA outperforms orthogonal multiple access if the residual intracell interference is below a certain level. The results highlight the importance in choosing network parameters N and T to balance Rtot and fairness.