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Abstract
This paper provides a unifying framework to analyze whether a monopoly transit provider will under or over-supply frequency. To this end we couch the problem in term of Spence [(1975). Monopoly, quality and regulation. The Bell Journal of Economics, 6, 417–429] who analyzed the incentives to provide quality by a monopolist. We show that all of the results of a recent academic exchange discussing this topic are special cases of Spence [(1975). Monopoly, quality and regulation. The Bell Journal of Economics, 6, 417–429], albeit with an adjustment in order to take into account the cost structure of frequency provision in the case of public transport. In theory then, there are cases when a monopolist may offer optimal or above optimal levels of frequency without requiring subsidies. However, public transport is rarely provided by an unregulated monopolist. Rather, these services are usually provided either by an exclusive operator under regulated fares or by a group of competing operators, with or without fare regulation. We show that in the first case frequency will always be below the social optimal level.
Acknowledgements
I would like to thank Anna Matus and conference participants for useful comments received during the “Primer Encuentro de Economía de Transportes”, FEDEA, Madrid, March 14th, 2011. I would also like to thank seminar participants in the Engineering Faculty and the Economics Department of the University of Chile and in the 2013 Annual Conference of ITEA, Chicago, July 2013, as well as the comments by four anonymous referees. The usual disclaimers apply.
Notes
1. An analogous effect is present when higher demand density implies a geographically denser route structure thereby reducing access time for all users of public transport. A countervailing force is present when higher demand increases boarding and alighting times. This last case was analyzed by Turvey and Mohring (Citation1975) and generates a negative externality among transit users.
2. Savage and Small (Citation2010) make the same point regarding Van Reeven (Citation2008).
3. Sheshinski (Citation1976) is attributed to have developed the same analysis independently of Spence (Citation1975) and some authors refer to the Spence–Sheshinski model.
4. See also Else (Citation1985) for a related contribution.
5. However, he did understand the consequences of Spence's analysis for this particular case. See page 72 of Frankena's paper.
6. But, of course, monopolists typically restrict output to maximize profits, so a monopolist and a social-welfare maximizing firm will generally not produce the same supply level. The effects of differing supply levels on quality provision are examined further below.
7. See Appendix.
8. Note that this cost function implies that there are economies of scale in bus capacity.
9. Also, as mentioned in Jara-Díaz and Gschwender (Citation2009), it is also the assumption made in some classic papers in the transport literature such as Jansson (Citation1980) and Mohring (Citation1972). Costs proportional to frequency was also assumed by Brueckner and Zhang (Citation2001) in their model of the airline industry.
10. Most of these more complex cost functions have a component linear in demand and another linear in frequency or fleet size. However, it must be borne in mind that some extensions may add a cross effect between demand and frequency, that would complicate the following analysis. This would happen, for example, if there are economies of scale in frequency at the route level in addition to economies in bus size. As noted in the conclusions, further research should explore the consequences of these more complex cost functions on the results.
11. Van Reeven (Citation2008) assume that r < t because waiting at the bus stop is more expensive than waiting at home or work in the case of scheduled services. However, this is not relevant for the results.
12. There seems to be a typo in Van Reeven (Citation2008) as the X term is in the denominator of the expression for d while the correct expression has this variable in the numerator.
13. In the next section we analyze the effects of introducing heterogeneity in other variables such as the marginal utility of income or the value of time.
14. Without loss of generality we follow Karamychev and Van Reeven (Citation2010) and assume . We also assume X = 1.
15. Except for the inclusion of a travel time cost ― which for the present discussion is not relevant ― Brueckner and Zhang's (2001) demand structure is identical to equation (19). As mentioned in footnote 9 their cost assumption is identical to Equation (10) with c 1 = 0.
16. The inverse demand function is almost identical to Equation (28) except that the last term is divided by 4 instead of 2.
17. For ease of exposition we normalize X to 1 in what follows.
18. Heterogeneity in the marginal utility of income is equivalent to having heterogeneity in reservation utility and in the value of time simultaneously.
19. The model presented here is related to the airline competition literature initiated by Panzar (Citation1979). See Brueckner (Citation2010) for a recent contribution. However, the demand structure is different from our model. They assume models of monopolistic competition, fares are endogenous and there is free entry. Panzar (Citation1979) finds that the Nash equilibrium results in over-provision of frequency while Brueckner (Citation2010) finds the opposite effect in his model.
20. We could add a restriction that demand per bus has to be below bus capacity. However, this would not add much intuition to the model.
21. If there are diseconomies of scale in providing frequency, then it would be more efficient to have many small firms rather than a monopolist, and an oligopolistic industry would certainly supply more frequency than a monopolist.