Optimal Control of Broadcasting Spectrum with Variety-Reception Trade-off and Consumers’ Income Sensitivity

This paper uses optimal control theory to derive a desirable trajectory of the number of royalties-paying users of state-owned spectrum for broadcasting. The spectrum royalties are set by the public planner to maximize the consumers’ utilities over an infinite planning horizon. The consumers’ utilities are generated from the quality of the service of the broadcasting industry, from the consumption of other goods, and from the public services financed by the spectrum royalties. The number of broadcasters adjusts to above-normal profits. The quality of the broadcasting industry’s service is determined by variety and reception. The trade-off between the benefits from higher variety and royalties’ revenues and the costs of intensified interferences associated with the number of broadcasters is considered. The positive information-dissemination effect and the negative effort-diversion effect of the quality of the broadcasting industry’s service on the consumers’ aggregate income are also considered. The possibility of convergence of the derived trajectory of the number of broadcasters to steady state and the comparative statics of the steady state are analyzed.