This paper shows how the information capacities of users in a system based on the non-orthogonal multiple access change depending on the power assigned to users. In the paper is considered the case of downlink communication between a base station and three users located at different distances from the base station. Users have different characteristics of communication channels and their signal components are exposed to Rayleigh fading. The results show that the appropriate selection of the power allocation coefficients can affect the information capacity of each of the users. Selection of the power allocation coefficients is crucial for the proper functioning of the NOMA technique.