For a cellular communication network, the loss in up-link bandwidth-efficiency resulting from power equalization is considered. Here power equalization refers to the operation of adjusting the transmit power of mobile units in such a way that the received power is the same for all units whereas bandwidth-efficiency is measured in terms of sum-rate per cell divided by the total system bandwidth. A single-cell system is considered first, and the bandwidth efficiency is determined with and without power equalization as well as with and without shadowing. The analysis is then extended to multi-cell-systems. it is found that in all cases power equalization severely penalizes the bandwidth-efficiency.