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Textbook wisdom says that competition yields lower prices and higher consumer surplus than monopoly. We show in two versions of a simple location-product differentiation model with and without endogenous choice of products that these two results have to be qualified. In both models, more than half of the reasonable parameter values lead to higher prices with duopoly than with monopoly. If the product characteristics are exogenous to the firms, consumers may even be be better off with monopoly in average.