We study the interaction of rate control and medium access control in single cell wireless ad hoc networks where we focus on throughput and fairness, as well as local stability. We start out by developing a simple discrete-time model to capture the dynamics of the interaction between TCP Reno rate control and IEEE 802.11 medium access control. By considering system operating points, we obtain the well-known characteristics that the throughput decreases as active node number in the network increases, as well as unfairness in the bandwidth allocation to individual TCP connections. We then propose and study alternative rate and medium access control schemes which allow to provide per connection fairness, as well as provide a stable and predictable throughput as connection number increases. We use numerical case studies to investigate the accuracy of the models used for our analysis.