چگونه نابرابری درآمد ، نتایج بازار در بازارهای عمودی متفاوت را تحت تاثیر قرار می دهد ؟

The distribution of consumer incomes is a key factor in determining the structure of a vertically differentiated industry when consumer's willingness to pay depends on her income. This paper computes the Shaked and Sutton (1982) model for a lognormal distribution of consumer incomes to investigate the effect of inequality on firms' entry, product quality, and pricing decisions. The main findings are that greater inequality in consumer incomes leads to the entry of more firms and results in more intense quality competition among the entrants. More intense quality competition raises the average quality of products in the market as firms compete for the shrinking share of higher-income consumers. With zero costs of quality improvements and an upper bound on the top quality or when costs of quality are fixed and rise sufficiently fast, greater heterogeneity of consumer incomes also reduces firms' incentives to differentiate their products. Competition between more similar products tends to reduce their prices. However, when income inequality is very high, the top quality producer chooses to serve only the rich segment of the market and charges a higher price. The conclusion is that income inequality has important implications for the degree of product differentiation, price level, industry concentration, and consumer welfare.

In this paper I study decisions of firms operating in a vertically differentiated market. The products offered in such a market differ in quality. The consumers are perfectly informed of the products' characteristics and have the same ranking over the products, preferring higher quality products to inferior ones. Thus, if prices were the same, the consumers would all choose to buy the top quality good. In this type of market the demand is directly affected by the properties of consumers' income distribution. If consumers have different incomes and thus, different willingness to pay for higher quality products, firms can profitably split the market by offering products differentiated in qualities at different prices. Therefore, in vertically differentiated markets, income inequality among consumers becomes a key factor in determining the product varieties offered by the firms. The purpose of this paper is to study the effect of income inequality on market outcomes in vertically differentiated markets, with particular interest in the range of qualities on offer. Many countries have experienced significant increases in income inequality over the past several decades.2 The welfare implications of higher income inequality have been analyzed by looking at the consumer expenditures data and measuring the corresponding change in consumption inequality (Krueger and Perri, 2006 and Jappelli and Pistaferri, 2010). Data on expenditures do not take into account the changes in quality of products consumed, and these are endogenous to the consumer demand and depend on the distribution of consumer incomes. This paper uses a stylized model to demonstrate that firms' decisions on product characteristics are affected by the degree of inequality and these choices have important welfare implications. The line of research linking income distribution of the consumers to the industry structure dates back to Gabszewicz and Thisse (1979), and has been cultivated by them (Gabszewicz and Thisse, 1980) as well as by Shaked and Sutton, 1982, Shaked and Sutton, 1983 and Shaked and Sutton, 1987. These authors demonstrate that the interplay of the industry cost structure and demand conditions, which are the outcome of the underlying income distribution, determines the degree of concentration and the maximum number of firms in vertically differentiated markets (Shaked and Sutton, 1987). They have almost nothing to say, however, about what kind of products these firms would be producing. Endogenous quality choices in duopolies with uniform distributions of consumer preferences for quality are analyzed by Motta, 1993, Lehmann-Grube, 1997 and Aoki and Prusa, 1997. Motta (1993) studies two types of duopolistic markets, one with price and the other with quantity competition. He finds quality differentiation in equilibrium in both Bertrand and Cournot setting, with larger quality spreads under Bertrand. This result holds under two different cases of fixed and variable costs of quality improvement. Lehmann-Grube (1997) demonstrate that in duopolistic markets the top quality firm makes a higher profit for any convex fixed-cost function of quality, and under the scenarios of simultaneous or sequential choice of qualities. Aoki and Prusa (1997) study the effect of simultaneous versus sequential quality choices on the equilibrium quality levels under the assumption of quadratic fixed costs of quality. Multiproduct competition has been analyzed by De Fraja (1996), who considers a vertically differentiated industry with an exogenous number of firms that simultaneously choose both qualities and quantities of their products, and a general distribution function for consumer preferences with upper and lower bounds on incomes. Johnson and Myatt (2003) study optimal quality choices of a multiproduct monopoly in response to entry by another firm and how these choices are affected by the properties of the distribution of consumer preferences for quality. The authors, however, do not endogenize the number of firms in the market. The paper most closely related to this one is Benassi et al. (2006). These authors analyze the effect of income concentration on product differentiation and obtain solutions for quality and pricing decisions of duopolistic firms. To obtain analytical results they assume that consumer incomes are distributed with a trapezoid distribution, and that the market is not covered. The authors find that more concentrated income distributions lead to more product differentiation. In this paper I propose to further this research agenda by modifying the existing models to make them applicable for studying the effects of changes in the consumers' income distribution on the firms' entry decisions and the optimal choices of product attributes and prices for a lognormal income distribution function. I solve the model numerically to obtain the equilibrium number of firms in the market, the qualities they produce, and the prices they charge. The baseline theoretical model is based upon Shaked and Sutton (1982). Firms compete in a three-stage non-cooperative game by making entry, product quality and pricing decisions. Each firm, if it enters, supplies a single product variety, and consumers can choose to purchase at most one good. The outputs of the model are the number of firms in the market, product qualities and prices, and the major input is the income distribution of the consumers. Shaked and Sutton (1982) assume that the income distribution is uniform and obtain analytical solution for a duopoly. Changes in the degree of income inequality can be modeled with a uniform distribution by shifting its endpoints. However, the support of the distribution would change, also altering the nominal scale of the market. Since the demand functions depend on nominal incomes, the uniform distribution cannot be used to analyze the purely redistributive effects of changes in income inequality on firms' decisions.3 This paper models the distribution of consumer incomes with a lognormal distribution, which has been found to provide an accurate fit of real-life income distributions among other candidates for parametric estimation (Pinkovskiy and Sala i Martin, 2009).4 The most valuable insight from the present analysis is that income inequality among consumers affects the intensity of competition. The result that greater income inequality enables more firms to enter the industry with positive market shares dates back to Gabszewicz and Thisse (1979) and has been replicated in most of the works that followed. In this paper I am also able to demonstrate that income inequality impacts the degree of product differentiation in the market. Low degree of heterogeneity in consumer incomes intensifies price competition in the last stage of the game, thus, in order to soften it, firms differentiate their products more when income inequality is lower. Greater inequality in consumer incomes reduces the incentive to differentiate and intensifies quality competition among firms for the shrinking middle and higher-income sections of the market. Thus, when income inequality is higher, firms locate their products in higher ranges of the quality spectrum, closer to each other, raising the average product quality and decreasing the degree of product differentiation. Competition between more similar products tends to reduce their prices. However, when income inequality is very high, the top quality producer chooses to serve only the rich segment of the market, and the low price elasticity of demand of these consumers allows him to charge a higher price. The model predicts that aggregate consumer welfare is higher in economies with greater income inequality. Higher intensity of quality competition in these economies induces lower-quality firms to raise the quality of their products and offer these products at lower prices. Thus, the majority of consumers are better off when income variability is high. Greater income inequality also decreases the degree of product differentiation; therefore, on a quality-adjusted basis, consumption inequality may be lower in economies with a higher degree of income inequality. The main results of the paper are derived under the assumption of the costless quality choice when there exists an upper bound on the best quality that can be produced. This simplifies the analysis and makes it possible to study product differentiation as the outcome of a purely demand-driven strategic behavior. However, this assumption is limiting since it makes the quality choice of the top quality producer trivial. Thus, I also compute the model for the case when the cost of quality improvement is fixed and quadratic and show that the results hold when the burden of quality improvement falls primarily on fixed costs and these costs rise sufficiently fast in quality. The assumption of quickly diminishing returns, especially at very high levels of quality, is realistic for many industries where quality improvements are achieved via investments in R & D.5 The paper is organized as follows. After describing the model in Section 2, I outline the solution method in Section 3. The discussion in this part also includes the issues of existence and uniqueness of equilibria. Section 4 of the paper gives the results of the model. Section 5 concludes.

In this paper I study how income inequality among consumers affects the decisions of firms operating in vertically differentiated industries. The model used to address this question makes the following important assumptions: a) each consumer chooses at most one good out of a variety of products differentiated in quality; b) consumers have different incomes, and richer consumers are willing to pay more for better products; c) the products are supplied by firms that compete by choosing qualities and prices in a non-cooperative three-stage game, with each firm supplying only one type of quality; and d) there are either no costs to producing higher quality products or these costs are fixed and quadratic. In order to study the effects of changes in income inequality on model outcomes, I assume a lognormal distribution for consumer incomes and solve the model numerically, holding the mean of the distribution constant while changing the variance. The lognormal distribution has been found to provide a good fit of real-life income distributions in many studies,20 and small variations in the shape of the distribution function should not significantly impact the conclusions of this study. The results demonstrate that income inequality impacts the degree of product differentiation in vertically differentiated markets. The industries in the economies with greater income inequality are characterized by a greater number of firms and more intense quality competition. The following results hold under the assumption of zero costs of quality and when costs of quality are fixed and quadratic: 1) the degree of product differentiation declines in inequality and 2) the average quality is higher in the economies with less equal distributions of income. The strictly convex fixed cost of quality function implies that developing a product of better quality is costly and increasingly so. This assumption may not be valid for some industries where the fixed costs of quality improvement are less steep. Intuitively, the second result should be robust to any specification of the fixed cost of quality function, since for lower-quality firms the incentive to attract higher-income consumers becomes stronger with higher income inequality while the incentive to differentiate their product weakens. However, when the fixed-cost function is not very steep, the top quality firm may choose very high quality when income distribution is unequal, differentiating itself strongly from the rivals, resulting in wider quality gap. Thus, both results will hold as long as the fixed costs of quality are sufficiently steep. The model also assumes zero variable costs to quality improvement. Shaked and Sutton (1987) show that when the burden of quality improvement falls primary on fixed costs, that is, the unit variable costs do not increase much with quality, then the number of firms in the market will be limited. This occurs because higher quality producers can use price competition to undercut their lower-quality rivals and possibly drive them out of the market entirely. When the variable costs rise sufficiently fast in quality, however, higher quality firms may no longer find it profitable to undercut lower-quality firms by lowering prices. Thus, more firms can survive in the market with positive market shares.21 The questions are 1) how would the number of firms be affected by the degree of consumer income inequality? and 2) which parts of the quality spectrum would fill up faster in the economies with varying degrees of consumer heterogeneity? While this paper does not aim to provide rigorous investigation of these issues, some hypotheses can be made. Convex variable unit costs of quality weaken the price competition, but do not eliminate it entirely. Thus, firms have the incentive to differentiate their products more in economies with lower degree of consumer heterogeneity when the costs of quality are variable and convex, and the number of firms is higher in economies with greater income inequality. What types of products would these firms chose to produce? Greater income inequality means more very poor and very rich consumers, and less consumers with the incomes in the middle range. Intuitively, sections of the market with relatively more consumers make it possible for more firms to survive even when prices are close to marginal costs. Thus, for two economies with the same average income and size of the market, we would expect to see greater concentration of products at the ends of the quality spectrum in the economy with higher inequality of consumer incomes. Whether the average quality on offer would decline or increase with inequality is unclear. The model assumes that consumers' preferences are represented by a Cobb–Douglas utility function. However, intuitively, as long as the preferences are such that consumers with higher incomes have higher willingness to pay for better products the qualitative predictions of the model should remain unaltered, for the logic behind them remains the same: when consumers' tastes for quality are more homogeneous the price competition is more intense. Thus, in order to weaken it, firms differentiate their products more, and fewer firms can survive in the market with positive market shares. Likewise, Benassi et al. (2006) use a quasi-linear utility function as in Mussa and Rosen (1978) and find that in a duopoly the quality spread is larger when the consumers are more homogeneous. Another result of the paper shows lower prices in the economies with higher levels of inequality. Lower degree of product differentiation leads to more intense price competition, pushing down the prices of all firms in the market. However, in the economies where income inequality is very high, the top quality producer chooses to serve only the rich consumers; their demand is more price inelastic, which enables him to charge a higher price. Also, market shares and profits of all firms are distributed more equally in less egalitarian economies, and the consumers are better of in terms of aggregate welfare.