Franchise bidding with differences in demand

Abstract

With a given static market demand and given static cost functions of all potential suppliers as well as sufficient competition, Demsetz' (1968) concept of franchise bidding leads to the selection of the welfare-maximizing supplier. However, with differences in demand among bidders, franchise bidding may lead to an inefficient choice of supplier. If the bidder with the lowest bid were barred from the auction, total surplus might rise, even under economies of scale. This result does not hold, if demand is noncrossing and if bidders' cost functions are identical and exhibit economies of scale.

Acknowledgements

We are grateful to Franz Diboky, Sonja Remetic, Jo Voola, Klaus Zauner, participants at the 2004 Business & Economics Society International Conference, Rhodes, at the 2005 Annual Congress of the Verein für Socialpolitik, Bonn, at the 4th Conference on Applied Infrastructure Research, Berlin, at the 33rd Annual Conference of the European Association for Research in Industrial Economics, Amsterdam and many other colleagues for helpful comments. The usual caveat applies.

Notes

¹ For an overview of the efficiency properties of franchise bidding, see, e.g., Viscusi et al. (2005).

² We choose a second-price auction in order to exclude strategic behaviour.

³ The concept of (cost) economies of scale is described in Baumol et al. (1988).

⁴ Even if the private values assumption is violated, auction models can show in a variety of circumstances that a bidder's best response to rivals' strategies is to submit a bid at which she is indifferent between winning and losing (e.g., Milgrom, 1981; Levin and Harstad, 1986; Bikhchandani and Riley, 1991; Crew and Harstad, 1992).

⁵ Strictly speaking, there are two average cost prices for each of the inverse demand functions. Of course, only the lower one of these is relevant.