We propose optimal resource allocation techniques for two kinds of optical slot switching metro rings: 1) fixed mixed line rate (fMLR), where the rate of each transponder (TRX) is fixed and set at network planning time; and 2) elastic TRX, where the rate may adjust dynamically on a per-slot basis during network operation. We then numerically compare the cost (CAPEX or energy) of fMLR and elastic networks, and investigate the suitability of each of the two considered network technologies for several ring topologies, TRX cost models, and traffic distributions and loads