Power control is a widely used technique in improving the throughput and the quality of services in wireless communications. In this paper, a power control method based on a utility maximization method is applied to Ad-hoc networks built on Wi-Fi radios. First, a fully distributed power control algorithm is developed considering the different characteristics of discrete multi-rate Wi-Fi radios, then a novel joint power control and scheduling algorithm is proposed to maximize the network throughput without sacrificing fairness. The proposed algorithm has a linear complexity degree while other utility based sub-optimal algorithms have exponential complexity. Lastly, as a preliminary step for an application for real Wi-Fi networks, the SINR model of Wi-Fi radios is verified through an experimental research based on the power capture effects.