Large-scale mobile edge computing (MEC) systems require scalable solutions to allocate communication and computing resources to the users. In this letter we address this challenge by applying dynamic spectrum sharing among the base stations (BSs), together with local resource allocation in the cells. We show that the network-wide resource allocation can be transformed into a convex optimization problem, and propose a distributed, hierarchical solution with limited information exchange among the BSs. Numerical results demonstrate that the proposed solution is superior to other baseline algorithms, when wireless and computing resource allocation is not jointly optimized, or the wireless resources allocated to the BSs are fixed.