Toshihide Mizuno

"On the existence of a unique price equilibrium for models of product differentiation"
JEL codes: L13, D43, C62
Keywords: Bertrand equilibrium, existence, uniqueness, discrete choice model, representative consumer model

Abstract: We prove the existence of a unique price equilibrium for models of product differentiation. These models are characterized by demand functions that depend on differences in prices and have log-increasing differences in own price and other prices, which implies that best response correspondences are increasing. Many discrete choice models satisfy these conditions, including logit models and nested logit models, and the existence theorem can be applied directly. With the logarithmic transformation, the existence theorem can be extended to models with homogeneous demand functions, which characterizes representtive consumer models.

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