Optimal Control of Broadcasting Spectrum with a Variety-Reception Tradeoff and Consumers’ Income Sensitivity

A socially desirable number of royalties-paying users of a state-owned broadcasting spectrum is derived within an optimal control framework where the adjustment of the number of users to above-normal profits is adversely affected by sunk costs. The optimal control takes into account the tradeoff between the benefits from higher variety and royalties’ revenues and the costs of the intensified interferences associated with entry. It also considers the positive information-dissemination effect and the negative effort-diversion effect of broadcasts on aggregate income. The broadcasting industry’s optimal steady state is identified and its stability is analyzed.