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In models of product differentiation and location models it is implicitly assumed that consumers can afford to buy the differentiated goods in the market. I show that with income heterogeneity there are severe existence problems of a price equilibrium in models of horizontal product differentiation with unit demand because some consumers are income-constrained. The result generalizes to other models of product differentiation, search, and switching costs. I present an alternative specification of variable individual demand in which this kind of existence problem cannot arise.