In cognitive networks, the cognitive radio users can share spectrum resource with the primary user while ensuring the normal communication of primary user. In addition, next generation wireless systems needs to provide flexible transmission rate to each terminal. In this paper, a utility-based game-theoretic model is proposed to study the joint power and rate control problem in spectrum underlay fashion in cognitive networks. We adopt a novel utility function based on cognitive network which focuses on social optimal resource allocation through pricing. Further, we show an interference threshold elasticity perspective, which is the key for primary network to maximize its utility by increasing its transmitted power to adjust the tolerable interference constraint. And also, the cognitive network can increase its total throughput capacity. In Stackelberg game, the primary user and the cognitive radio users interact with each other by adjusting their own actions. The cooperative cognitive networks model follows the “best-effort” principle as well as the win-win perspective of primary-cognitive user. Numerical simulations are conducted to demonstrate the performance of the model. The results show that the PU network can get more profit and also the CRU network can increase its total throughput capacity by the adjustment of the interference threshold.