Vertical Differentiation and the Distribution of Income

Abstract

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.

Product Differentiation with Multiple Qualities

“…5 The complication is that (8) sets up a function e v 1 that depends on N 1 continuous variables v k , k = 2; ::; N , and the quality vector (q; r), and this is to be determined simultaneously with the prices in (6) and (7).…”

“…Using the solution to (9), we can then proceed to solve for the equilibrium prices in (6) and (7). We are unaware 5 If we divide (6) by p A , it can easily be seen that the right-hand side is the inverse elasticity of demand, which is obtained from the demand…”

Beyond the Uniform Distribution: Equilibrium Prices and Qualities in a Vertically Differentiated Duopoly

“…Our exercise will focus on the effects of equal-mean, second-order stochastic-dominance shifts of the distribution, as this allows to consider how the firms' equilibrium choices react to a well-defined change in income dispersion. 5 The density of the Beta symmetric distribution over the unit interval…”

“…By using the Mussa and Rosen (1978) specification of the indirect utility function, the existence of a duopolistic equilibrium in prices has been proved by Furth (2011) under logconcave densities. The full solution has been developed only for two specific densities: Yurko (2011) develops an algorithm to solve numerically a oligopoly model of the ShakedSutton type (Shaked and Sutton, 1982) under a lognormal distribution of consumers, while Benassi et al (2006) offer an analytical solution of the price-quality game under a trapezoid distribution -clearly, for models of vertical differentiation with uncovered market there is still an open problem in terms of robustness, manageability and empirical relevance.…”

Environmental quality: impact of economic growth

“…More recently, Benassi et al (2006); Yurko (2011) and Chatterjee and Raychaudhuri (2004) have examined the effect of changes in income distribution on firms' choice of product quality. Benassi et al (2006) analytically analyze the effects of income concentration on the behavior of a duopoly with vertical product differentiation assuming a trapezoid distribution of income, costless quality and uncovered market.…”