Abstract
This work performs a comparative welfare analysis of two types of entry regulation in a duopolistic retail market: number of licenses and minimum distance between stores. In a linear (Hotelling) market we show that a minimum distance rule is beneficial for consumers and disadvantageous for the firms when demand is sufficiently inelastic. The distance rule that maximises social welfare is one quarter of the market under which firms will be located at the quartiles. Those locations are also optimal under regulated prices. Moreover, our model of two licenses with simultaneous entry is the first one that performs the horizontal product differentiation analysis using quadratic transportation costs and a binding reservation price. We find that a subgame perfect equilibrium exists for all the values of the reservation price and, for those values that induce a unique location equilibrium, the distance between the firms ranges from one half of the of the market to the whole market length.This analysis, which is not yet considered in the literature, is motivated by a change of entry regulation in the drugstore market in the Spanish region of Navarre. Since the demand in this market is quite inelastic, the minimum distance rule maybe socially more beneficial than the license rule.
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Notes
A license is a publicly allocated right to open and operate a pharmacy. Depending on the nature of regulation there are different additional and specific restrictions in different countries. In our model, a license allows the right to open a pharmacy.
An alternative approach is to consider that demand is elastic at every point of the demand curve, so that the quantity demanded is a continuous and decreasing function of price. Smithies (1941) introduced this approach by considering that each consumer has a demand function which is decreasing in price and showed that duopolists in equilibrium locate between the market centre and the quartiles. Rath and Zhao (2001) extend Smithies’ model by using quadratic, rather than linear, transportation cost, finding that a Nash equilibrium in prices exists for each possible pair of locations. Another functional form is the one used by Gu and Wenzel (2009) who follow Anderson and de Palma (2000) by considering a constant elasticity demand function.
Which follows the literature on first mover advantages, see Gal-Or (1985). Other works that analyse the earlier entrant advantages are Anderson (1987), analysing sequential moves in both location and price, Lambertini (2002), who considers an infinite time horizon, and Fleckinger and Lafay (2010), who consider sequential moves in a market where firms choose at the same time location and price.
For a formal definition of subgame perfect equilibrium see, for example, Fudenberg and Tirole (1991), p 74.
The corresponding calculations are available from the authors upon request.
For \(d \ge 0.5\), there is only one firm located in the market centre, and for \(d < 0.25\), there are more than two firms. Without minimum distance, this situation is analysed by Economides et al. (2004).
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Financial support from Ministerio de Ciencia e Innovación (ECO2010-18680 and ECO2012-34202) is gratefully acknowledged.
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Elizalde, J., Kinateder, M. & Rodríguez-Carreño, I. Entry regulation, firm’s behaviour and social welfare. Eur J Law Econ 40, 13–31 (2015). https://doi.org/10.1007/s10657-014-9471-y
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DOI: https://doi.org/10.1007/s10657-014-9471-y