Radio Resource Block allocation aims at allocating rates under different bandwidth demands in the communications network. This novel algorithm allocates resources from radio resource blocks to optimally provide cellular communication users with appropriate frequency bandwidth in the enormously increasing mobile communication space. Radio resource blocks are assigned to users to meet their quality of service requirements under a proportional utility fairness policy, ensuring no user is dropped. Subsuming delay-tolerant and real-time applications, the algorithm is efficient in time and computational complexity, optimally functioning at the continuous rates of mobile devices. Hardware modifications are not required. Additionally, the algorithm is equipped with a shadow price calculation and bidding mechanism, allowing cellular carriers to control pricing.