Recently, joint subchannel allocation and transmission power control problems for multi-cell orthogonal frequency-division multiple access (OFDMA) systems have been actively studied. However, since the problems are notoriously difficult and complex, only heuristic approaches are mainly used to study the problems without trying to achieve the optimal resource allocation and the maximum system capacity. In this paper, we study the joint subchannel allocation and transmission power control problem for multi-cell OFDMA systems from the point of the optimal resource allocation and the maximum system capacity with a monotonic optimization approach. Even though we do not obtain the exact optimal resource allocation that achieves the maximum system capacity, we develop an algorithm for resource allocations that provide both upper and lower bounds on the maximum system capacity. Through numerical results, we evaluate our algorithm showing that it provides good approximations to the maximum system capacity in multi-cell OFDMA systems in most cases.