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For a cooperative orthogonal frequency division multiple access (OFDMA) system with two transmitters (TXs), and full channel state information (CSI), we obtain the optimal power allocation (PA) policies which maximize the rate region achievable by a recently introduced version of block Markov superposition encoding (BMSE): inter-subchannel cooperative encoding (ISCE). We provide the optimality conditions that need to be satisfied by the powers associated with the transmitted codewords. We propose two algorithms that yield the optimal power distribution: a subgradient algorithm which achieves an arbitrary rate point on the achievable rate region boundary, and an iterative waterfilling-like algorithm which maximizes the sum rate, and converges much faster. We observe that, utilization of power control to take advantage of the diversity offered by the cooperative OFDMA system, not only leads to a remarkable improvement in achievable rates, but also may help determine how the subchannels have to be instantaneously allocated to various tasks in cooperation.