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We study a price-based rate control mechanism for random access networks. The mechanism uses channel feedback information to control the aggregate packet arrival rate. For our analysis, we use the standard slotted Aloha model with an infinite set of nodes. We show that the resulting Markov chain is positive recurrent. In addition, we characterize the throughput and delay at the operating point of the system and show how the operating point can be set a priori by appropriately choosing the control parameters. We illustrate our results using numerical experiments.