Royalties, Entry and Spectrum Allocation to Broadcasting

Optimal control theory is employed to characterize the socially optimal trajectory of the royalty per channel and the number of royalty-paying users of state-owned spectrum for broadcasting. The spectrum royalty is set by an omniscient public planner to maximize the sum of the discounted consumers’ utilities over an infinite planning horizon. The number of broadcasters adjusts over time to profits, while the quality of the industry’s service is determined by variety and reception. The trade-off between the benefits of greater variety and the costs of intensified interferences associated with the number of broadcasters is central to the analysis. The convergence of the socially optimal trajectory of the royalty per channel and the number of broadcasters to a steady state and the comparative statics of the steady state are analyzed.