Vertical differentiation with non-uniform consumers' distribution

This note explores a vertical differentiation model with a continuous non-uniform consumers' distribution. First, a result concerning the finiteness property obtained with uniform consumers' distribution is generalized. Second, we prove an existence result of price equilibrium when the distribution is concave. Finally, we exhibit a counter-example to the existence of price equilibrium to show that the concavity assumption is not superfluous.     

Brand familiarity and product knowledge in customization

I adopt Hotelling's model with two firms. Each consumer has a most preferred variety and possesses a certain level of category‐specific knowledge. When a firm offers customization, consumers must interact with the firm to create their products. Consumers familiar with the brand can do this seamlessly, whereas consumers unfamiliar with the brand have difficulty expressing their individual needs (the difficulty decreases with consumers' knowledge). The firms first simultaneously decide whether to customize, then engage in price competition. Although customization makes the products less differentiated, the frictions caused by consumer co‐design activities relax price competition. Customization by one of the firms occurs in equilibrium.     

Quality and Quantity Competition in a Multiproduct Duopoly

This article proposes a Cournot model of two‐stage competition to examine the patterns of vertical product differentiation in a multiproduct duopoly. Firms simultaneously choose the number of products and their qualities at the first stage and compete in quantities at the second stage. We show that when the fixed setup cost of a product is high enough to result in a monopoly outcome, the monopolist always sells a single product. Moreover, in any equilibrium of a multiproduct duopoly, quality differentiation between them will develop into a nonsegmented pattern because each firm desires to avoid a strong effect of cannibalization. The set of equilibria reveals the properties of quality differentiation between multiproduct firms. In a multiproduct duopoly, the profit from a high‐quality product can be lower than that from a low‐quality product. This finding sharply contrasts with the literature on single‐product firms, which finds the high‐quality advantage.     

Bifurcation and sunspots in the continuous time equilibrium model with capacity utilization

In the present paper, we construct a continuous time model of economic growth with positive externalities and with variable capacity utilization, and study the global equilibrium paths in this model. If there is a homoclinic orbit or a periodic solution in this model, equilibrium is globally indeterminate. We show that positive externalities can yield multiple steady states, a one-parameter family of homoclinic orbits, and a two-parameter family of periodic solutions. It is also shown that there exists a sunspot equilibrium in this model.     

No-arbitrage condition and existence of equilibrium in asset markets with a continuum of traders

In the present paper, we prove that a no-arbitrage condition (à la Werner) is necessary and sufficient for the existence of an equilibrium with a continuum of traders and a finite number of assets. As in Aumann (1966) , Hildenbrand (1974) and Schmeidler (1969) , preferences are not assumed to be convex. We do not use Fatou's Lemma and do not assume that the consumption sets are compact.