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For a two user cooperative orthogonal frequency division multiple access (OFDMA) system with full channel state information (CSI), we obtain the optimal power allocation (PA) policies which maximize the rate region achievable by a channel adaptive implementation of inter-subchannel block Markov superposition encoding (BMSE), used in conjunction with backwards decoding. We provide the optimality conditions that need to be satisfied by the powers associated with the users' codewords and derive the closed form expressions for the optimal powers. We propose two algorithms that can be used to optimize the powers to achieve any desired rate pair on the rate region boundary: a projected subgradient algorithm, and an iterative waterfilling-like algorithm based on Karush-Kuhn-Tucker (KKT) conditions for optimality, which operates one user at a time 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. Simulations show that the gain from power allocation is still significant even when the CSI feedback is limited.