We study a two-period model of spatial competition with two symmetric firms where firms learn customers' preferences from the first-period purchase, which they use for personalized pricing in the second period. With product choice exogenously fixed with maximal differentiation, we show that there exist two asymmetric equilibria and customer switching is only from one firm to the other unless firms discount future too much. Firms are worse off with such personalized pricing than when they use pricing at higher levels of aggregation. When product choice is also made optimally, there continue to exist two asymmetric equilibria given sufficiently small discounting, none of which features maximal differentiation. More customer information hurts firms, and more so when they make both product choice and pricing decisions.

We investigate a mixed duopoly, where a state-owned welfare-maximizing public firm competes against a profit-maximizing private firm. We use a Hotelling-type spatial model which represents product differentiation. We endogenize production costs by introducing cost-reducing activities. We show that the private firm's cost becomes lower than the public firm's because the private firm engages in excessive strategic cost-reducing activities. Even though each firm's cost is heterogeneous, the locations of the firms are socially efficient, given the cost differentials. Privatization of the public firm would improve welfare because it would mitigate the loss arising from excessive cost-reducing investments.

We investigate a mixed market where a state-owned welfare-maximizing public firm competes against profit-maximizing private firms. We use a circular city model with quantity-setting competition. In contrast to a pure market case discussed by Pal (1998a), spatial agglomeration of private firms always appears in equilibrium. All private firms locate at the same point, and the public firm locates at the opposite side. We also find that this equilibrium pattern of the location is second best provided that output of each private firm cannot be controlled by the social planner. JEL Classification: H42, L13Oligopole mixte et agglome´ration spatiale. Les auteurs examinent un marche´mixte ouù ne entreprise publique posse´de´e par l'É tat et cherchant a`maximiser le niveau de bieneˆtre est en concurrence avec des entreprises prive´es qui cherchent a`maximiser leurs profits. On utilise un mode`le de cite´circulaire ou`la concurrence se fait en choisissant la quantite´produite. En contraste avec le cas du marche´parfait discute´par Pal (1998a), l'agglome´ration spatiale des entreprises prive´es paraıˆt eˆtre en e´quilibre. Toutes les entreprises prive´es se localisent au meˆme point, et l'entreprise publique se localise du coˆte´oppose´. Il appert que ce pattern d'e´quilibre de localisation est un e´quilibre de second ordre compte tenu du fait que la production de chaque entreprise prive´e ne peut eˆtre controˆle´e par le planificateur social.We are grateful to Koichi Futagami, Shingo Ishiguro, Yasushi Iwamoto, Murdoch MacPhee, Yoshiyasu Ono, Akihisa Shibata, Hiroki Yoshino, and participants of the seminars at Shinshu University and University of Tokyo, and Macroeconomics workshop for their helpful comments and suggestions. We are also indebted to two anonymous referees for their precious and constructive comments and suggestions. Needless to say, we are responsible for any remaining errors.

Two models of competition between high-end and low-end products benefiting the high-end firms are presented. One is a quantity competition model, and the other is a price competition model with product differentiation. The key factor is the existence of two heterogeneous consumer groups: those who demand only high-end (name-brand) products and those who care little whether products are high or low end. We show that, under certain conditions, the profits of firms in the high-end market are larger when there are firms producing low-end products than when there are not. The existence of price-sensitive consumers who care little about product quality intensifies competition among the high-end firms. The existence of low-end firms functions as a credible threat, which induces the high-end firms not to overproduce because price-sensitive consumers buy products from the low-end firms. The result provides a new theoretical mechanism concerning the profitability and pricing of national brand firms after the entry of private labels. It has an implication for pricing and marketing strategies: Established firms should not decrease their prices after the entry of nonestablished firms.marketing strategy, pricing research, product positioning, game theory