Cournot competition on Hotelling line yields at most three varieties
Eric Langlais  1@  , Andreea Cosnita  1@  
1 : EconomiX, CNRS and university Paris-Nanterre
CNRS : UMR7235, Université Paris X - Paris Ouest Nanterre La Défense
Bat G 200 Avenue de la République 92001 NANTERRE CEDEX -  France

This paper reexamines the equilibrium product choices in a spatial Cournot n-oligopoly on the linear market by considering the case of output accidentally harming consumers and firms being subject to product liability. We characterize the resulting spatial pattern in terms of unicity and stability. For low levels of the unit cost of accident, central agglomeration is the unique and stable location equilibrium. For a high enough unit cost of accident, multiple equilibria exist, from central agglomeration to partial dispersion (both asymmetric and symmetric). In this case we show that asymmetric dispersion equilibria as well as symmetrical three-variety equilibria are unstable, whereas there always exists a symmetrical two-variety location equilibrium which is stable. Finally, complete dispersion appears as a very specific case limited to duopoly and tripoly: for markets with more firms, equilibrium product differentiation involves partial clustering on three varieties/locations.



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