Portal de Periódicos da CAPES

Predation in Space

2012; Routledge; Volume: 8; Issue: 1 Linguagem: Inglês

10.1080/17421772.2012.722667

1742-1780

Stefano Colombo,

Economics of Agriculture and Food Markets

In a spatial economic context, we analyse the incentive to prey of an incumbent facing the potential entrance by a rival. We show that the existence of space modifies the incentive to prey of the incumbent and the resulting equilibrium. RÉSUMÉ Dans un contexte économique spatial, nous analysons l'incitation pour exploiter un titulaire affrontant l'entrée potentielle par un rival. Nous démontrons que l'existence de la dimension spatiale modifie l'incitation d'exploiter le titulaire et l’équilibre résultant. EXTRACTO En un contexto económico espacial, analizamos el incentivo de cazar de un titular que se enfrenta a la entrada en potencia de un rival. Mostramos que la existencia de una dimensión espacial altera el incentivo de cazar de un titular y el equilibrio resultante. Keywords: Predationspatial marketsJEL CLASSIFICATION: D43L11 Acknowledgments I would like to thank the Editor, Bernard Fingleton, and an anonymous referee for useful comments. I am also grateful to Valentina Bertani and Roberta Bertani for helpful assistance. Any errors are my own. Notes 1. See Bolton et al. (Citation2000) for a comprehensive survey of the notion of predation. 2. See for instance Bolton et al. (Citation2000). 3. One exception is Colombo (Citation2011), whose analysis focuses on the interrelation between taxes and predatory prices in a spatial context. 4. See for example Isard (Citation1949) and Fujita (Citation2010). 5. The Hwang & Mai (Citation1990) model has been considered by, among others, Gross & Holahan (Citation2003), Liang et al. (Citation2006), Colombo (Citation2011) and Andree (Citation2011). 6. As shown by Liang et al. (Citation2006), maximal distance between the firms is the unique locational equilibrium in the Hwang & Mai (Citation1990) model. Moreover, in the case of different market sizes, the incumbent locates in the most profitable market, which in our set-up is market 1. 7. It can be shown (details available) that the results are qualitatively the same if a T-period model is considered instead of a three-period model. 8. The results are qualitatively the same in the case of positive entrance costs of Firm B (see later). 9. Things do not change if Firm B has a limited access to credit, provided that Firm A has better access to credit than the rival. For the asymmetry in the disposal of credit, see for example Bolton et al. (Citation2000). 10. Note that Firm A would not want to deviate from its predatory quantities. In fact, even if Firm B sells zero, Firm A cannot decrease its output to the monopoly quantities if Firm B is active: the only way for Firm A to induce Firm B to sell zero (and then to force it to leave the market) is to sell the predatory quantities. In a word, if both firms are active, only two situations are possible: both firms set the duopolistic quantities, or one firm preys on the other. A situation where one firm sells zero and the other sets the monopolistic quantity cannot constitute an equilibrium situation if both firms are active. On the contrary, monopolistic quantities represent an equilibrium situation if Firm B is out. 11. Note that Π A,P might be negative. 12. Note that in equilibrium a predatory behaviour never arises: if predation is a credible threat, Firm B stays out, and Firm A is a monopolist in both periods; if predation is not a credible threat, Firm B enters, and there is a duopolistic equilibrium in both periods. 13. Clearly, when δ *∉ [0,1], any variation of δ * has no impact on the likelihood of the monopolistic equilibrium: when δ *≤0 a monopoly always arises in equilibrium, whereas when δ *≥1 a duopoly always arises in equilibrium. Note the similarity between δ * and the critical discount factor in the collusion literature (Friedman, Citation1971). In both cases, the critical discount factor provides a measure of the sustainability of a certain scenario in equilibrium: in the collusion literature, it refers to the sustainability of a cartel in equilibrium, whereas in this article it refers to the sustainability of the threat of predation in equilibrium. 14. In Figure 1, we set γ=0.3. 15. A remark is worthwhile. We have assumed that Firm B does not sustain entrance costs. If Firm B sustains positive entrance costs, say K>0, it leaves the market at the end of period 1 when its profits are lower than K, instead than lower than zero. Therefore, predation is less costly for the incumbent and a monopolistic scenario is more likely to arise in equilibrium. In a word, the parameter space under which the threat of predation is credible in equilibrium is larger the higher K is. 16. Obviously, this case is relevant only for the parameter set where . A sufficient condition for to be positive everywhere is that γ≥0.072. 17. and . 18. There is also a third case, where . In this case, a duopoly always arises, as the threat of predation is never credible in equilibrium. Therefore, this case is less relevant to the implications of t and it can be excluded from the analysis. 19. It should be noted that Figure 3 is not exhaustive of all the possible relations between the thresholds t 1 and t 2, and the minimum of PS D . To save on space, the remaining cases are omitted and are available upon request. However, the shape of the profits within each scenario as well as the sign of the jump at t 1 and t 2 are fully characterized in the text. 20. The second-order condition shows that t * is a minimum, as expected. 21. We report only the conclusions of our analysis. The complete analysis of the impact of parameter γ over consumer surplus, profits and welfare is available upon request. 22. . The uniqueness of the root comes directly from the fact that δ * strictly increases with γ (see Section 3). 23. The proof consists in noticing that the following inequality always holds: W D (γ 1)>W M (γ 1). 24. Note that this last possibility is excluded in the two-market model adopted in this article.