The paper analyses the effects of income concentration on the behaviour of a duopoly with vertical product differentiation and uncovered market. By using a trapezoid distribution, we solve explicitly for market equilibrium as a function of a mean preserving spread of the income distribution. We show that overall more concentrated incomes imply stronger product differentiation, as the presence of a large share of middle-income consumers stimulates a price competition, whose effects are dampened through an enlargement of the quality spread. While the high-quality advantage and market coverage increase unambiguously in the degree of income concentration, the behaviour of prices is non-monotone in the distribution parameter.

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In the framework of a vertically differentiated mixed duopoly, with uncovered market and costless quality choice, we study the existence of a price equilibrium when a welfare-maximizing public firm producing low quality goods competes against a profit-maximizing private firm producing high quality goods. We show that a price equilibrium exists if the quality spectrum is wide enough visà vis a measure of the convexity of the distribution of the consumers' willingness to pay, and that such equilibrium is unique if this sufficient condition is tightened. Logconcavity of the income distribution is inconsistent with the existence of equilibrium.JEL classification: D43, L13, L51.

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