Cooperative inter-vehicular applications rely on the exchange of broadcast single-hop status messages among vehicles, called beacons. The aggregated load on the wireless channel due to periodic beacons can prevent the transmission of other types of messages, what is called channel congestion due to beaconing activity. In this paper we approach the problem of controlling the beaconing rate on each vehicle by modeling it as a Network Utility Maximization (NUM) problem. This allows us to formally define the notion of fairness of a beaconing rate allocation in vehicular networks. The NUM model provides a rigorous framework to design a broad family of simple and decentralized algorithms, with proved convergence guarantees to a fair allocation solution. In this context, we propose the Fair Adaptive Beaconing Rate for Intervehicular Communications (FABRIC) algorithm, which uses a particular scaled gradient projection algorithm to solve the dual of the NUM problem. Simulation results validate our approach and show that, unlike recent proposals, FABRIC converges to fair rate allocations in multi-hop and dynamic scenarios.