Theoretical Analysis of Mobile Operators' Spectrum Strategies

In this paper, I construct a mathematical model based on the Shannon-Hartley theorem and find profit-maximizing conditions for a mobile operator as for its channel bandwidth, the number of the channels, the S/N ratio, density of base stations in congested areas and the number of its subscribers. The following results and implications are obtained by the theoretical analysis. Firstly operators will fix their prices so that the price elasticity of demand can be one in the absence of congestion. However, once congestion arises, the optimum number of subscribers under the congested circumstances should be less than the number without congestion. Secondly, operators will choose their investment either in devices or in base stations to keep a throughput speed, so that the technical marginal rate of substitution can equal the ratio of the marginal costs. This result implies that operators may increase density of base stations in congested areas instead of ameliorating the network equipment. Thirdly, there is a difference between the marginal revenue and the marginal costs as for the bandwidth of the each channel, and this difference becomes larger as the bandwidth of each channel becomes narrower, and as the number of channels becomes more. Fourthly, the optimum channel bandwidth becomes narrower in general, if operators can choose both channel bandwidth and the number of channels. Finally, the spectrum cap per operator does not make sense in spectrum assignment. Either through spectrum auctions or through beauty contests, if the costs of acquisition of spectrum increase as the assigned bandwidth becomes larger, operators may use spectrum efficiently in the sense that they economize the bandwidth.