A note on subsidy-free prices and scope economies

Abstract

The necessary admissible range of subsidy-free prices is bounded from above by the incremental scope economy measure for the service – the difference between total scope economies and the scope economies associated with the complement of the service. These incremental scope economy measures provide an alternative, though no less computationally burdensome, approach for deriving sufficient (necessary) conditions for subsidy-free prices.

Acknowledgements

I am grateful to Fred Kahn, Dale Lehman, Tim Tardiff and two anonymous referees for helpful comments. I thank Yuan Gao and Burak Onemli for expert research assistance.

Notes

¹Kahn (1970, 1971) had earlier explored the equity dimensions of stand-alone costs. To wit, no group of consumers should be required to pay more for a service than the cost of serving that group alone.

²See Faulhaber (1975, p. 968).

³That the are nonnegative is implied by Assumption 2.

⁴In general, for n > 2 services, the number of distinct measures of incremental scope economies is given by where is the number of services in the subset for which scope economies are defined.

⁵The phrase ‘necessary admissible range’ means that prices inside (outside) this range may (cannot) be subsidy-free.

⁶The alternative admissible revenue range, the complement of is given by

⁷The alternative admissible revenue range, the complement of is given by

⁸The alternative admissible revenue range, the complement of is given by

⁹It is straightforward to show that the error in the approximation of the admissible revenue range approaches zero as the price elasticity of demand approaches zero.

¹⁰I am grateful to anonymous referee for suggesting this interpretation.