The computational complexity of resource allocation processes, in cognitive radio networks (CRNs), is a major issue to be managed. Furthermore, the complicated solution of the optimal algorithm for handling resource allocation in CRNs makes it unsuitable to adopt in real-world applications where both cognitive users, CRs, and primary users, PUs, exist in the identical geographical area. Hence, this work offers a primarily price-based power algorithm to reduce computational complexity in uplink scenarios while limiting interference to PUs to allowable threshold. Hence, this paper, compared to other frameworks proposed in the literature, proposes a two-step approach to reduce the complexity of the proposed mathematical model. In the first step, the subcarriers are assigned to the users of the CRN, while the cost function includes a pricing scheme to provide better power control algorithm with improved reliability proposed in the second stage. The main contribution of this paper is to lessen the complexity of the proposed algorithm and to offer flexibility in controlling the interference produced to the users of the primary networks, which has been achieved by including a pricing function in the proposed cost function. Finally, the performance of the proposed power and subcarrier algorithm is confirmed for orthogonal frequency-division multiplexing (OFDM). Simulation results prove that the performance of the proposed algorithm is better than other algorithms, albeit with a lesser complexity of O(NM) + O(Nlog(N)).