Examining Externality on Welfare and Market Access Arising from Consumer Heterogeneity

Abstract

This paper extends the literature on spatial price–quality competition by looking into the welfare impact of increased consumer heterogeneity. This is done by incorporating consumer heterogeneity into a model where firms compete simultaneously in price and quality within a circular market framework. Consumers are assumed to have either high or low willingness to pay for quality, thereby capturing both vertical and horizontal product differentiation in the model. The analysis establishes that as consumer heterogeneity increases, welfare for low-preference consumers follows an inverted-U pattern. Initially, greater heterogeneity enhances welfare by inducing firms to offer higher-quality products at higher prices. However, beyond a threshold, rising production costs and hence, price increases outweigh these benefits, leading to reduced welfare and access to the market for consumers with a low preference for quality. This finding highlights a crucial trade-off between quality improvement and affordability, and hence, in market access. This offers an important insight into framing policies that aim to promote inclusive market access and maintain balanced quality competition.

JEL Classifications: D21, D62, I31, D49

Keywords

Consumer heterogeneity externality welfare market access

Introduction

The main objective of this research is to investigate the impact of increased consumer heterogeneity with respect to preference for quality on market outcomes and, consequently, on the aggregate welfare of consumers who have lower preference parameters for quality. This investigation is conducted when consumers vary both with respect to their taste parameter (horizontal attribute) and their preference for quality (vertical attribute).

To answer this research question, this work integrates the vertical parameter, which represents preference for quality, into Salop’s circular city model. Each consumer is defined by their taste, captured by their location in the circular city, and their preference for quality (the vertical attribute). Depending on their preference for quality, each consumer is classified as one of two types—high (θ_H) or low (θ_L)—with each type being uniformly distributed around the city. Three key assumptions are made for the analysis. First, following Epple and Romano (1998), a higher preference parameter for quality implies that consumers with higher θ have higher marginal utility from quality improvements. Second, transportation costs are assumed to rise linearly with distance, capturing the idea that disutility increases linearly as the distance from the most preferred variety increases. Third, following Pires et al. (2024), it is assumed that the cost associated with quality improvement increases at an increasing rate, that is, the relationship is convex. The aim is to examine how increases in consumer heterogeneity arising from increasing θ_H affect both welfare and market access for consumers with low preference for quality.

The analysis yields a central result: greater consumer heterogeneity in preferences for quality has a non-monotonic effect on the welfare of low-preference consumers. As the willingness to pay for quality among high-preference consumers increases, firms optimally raise quality. Initially, this quality upgrading benefits all consumers, including those with low willingness to pay, leading to higher welfare. Beyond a threshold, however, further increases in quality raise production costs and prices and leads to reduced market access and welfare for low-preference consumers. As a result, welfare exhibits an inverted-U relationship with respect to preference heterogeneity.

The mechanism underlying this result operates through a preference externality. Although the preferences of low-preference consumers remain unchanged, their welfare depends on the preferences of high-preference consumers because firms’ quality and pricing decisions respond to the latter. In this sense, consumer heterogeneity generates external effects across consumer groups through endogenous quality choice. By comparing outcomes in a mixed-preference economy, where heterogeneous consumers coexist, with those in a segregated economy consisting of homogeneous consumers, the paper shows that heterogeneity can either enhance or reduce welfare for low-preference consumers depending on its magnitude.

This research makes the point that the policies and market environments that focus on and reward upgrades like high-end technologies may unintentionally exclude price-sensitive consumers. Therefore, it becomes significantly important for policymakers to understand the trade-off between heterogeneity and welfare for low-preference consumers while designing policies.

The paper makes three primary contributions. First, it establishes an inverted-U-shaped relationship between increased consumer heterogeneity arising from increases in θ_H and welfare for low-preference consumers—a pattern not previously recognized through market mechanisms. Second, this work formally endogenizes the market exclusion threshold beyond which increased heterogeneity causes a reduction in welfare. Third, it establishes that the extent to which the externality of high-preference consumers imposes on low-preference consumers varies depending on the relative differences in the preference parameter.

Empirical evidence also reinforces the importance of consumer heterogeneity in shaping market outcomes across diverse markets. Fan and Yang (2020) in smartphones, Kumar et al. (2024) and Choi et al. (2024) in electric vehicles, Flach and Janeba (2017) in export prices, Fajgelbaum et al. (2011) in international trade, and Vélez-Velásquez (2024) in telecommunications demonstrate that preference heterogeneity fundamentally shapes pricing strategies, product variety and market access. These findings justify explicit modelling of distinct consumer segments and analyzing how heterogeneity affects equilibrium outcomes.

The remainder of the paper is organized as follows. The second section reviews the relevant literature. The third section presents the model and derives equilibrium quality and price. The fourth section examines the effects of increasing consumer heterogeneity on market access. The fifth section defines consumer welfare. The sixth section analyses the impact of increasing heterogeneity on the welfare of consumers with low preference for quality. The seventh section compares single-preference and mixed-preference societies. The eighth section concludes.

Literature Review

This paper integrates two major strands of literature: spatial competition and vertical differentiation. The spatial competition literature was initiated by Hotelling (1929). Salop (1979) later extended and simplified Hotelling’s analysis by introducing the circular city to avoid the ‘corner’ difficulties. This formed the foundation for modelling horizontal product differentiation. Anderson et al. (1992) and Tirole (1988), in their texts on industrial organization, further developed these models to analyze various competitive scenarios and examine how firms differentiate products to mitigate intense price competition.

The vertical differentiation literature emerged from the seminal work of Gabszewicz and Thisse (1979), who analyzed price competition in vertically differentiated industries arising from differences in willingness to pay for marginal quality increases. This work assumed exogenous quality levels. Shaked and Sutton (1982, 1983) extended the literature by endogenizing quality choices, demonstrating that firms have strategic incentives to vertically differentiate products to soften price competition.

Subsequent literature on vertically differentiated markets developed further by making varied assumptions about market coverage, cost structure and the number of dimensions. Some studies assumed partial market coverage (Benassi et al., 2006; Lambertini & Tampieri, 2012), while others exogenously assumed full market coverage. Benassi et al. (2006), in their work, allow consumers the non-purchase option. Wauthy (1996) was the first paper to make coverage endogenous. Later, Pires et al. (2024) also endogenized market configuration, allowing for both full and partial market coverage when marginal cost is quality-dependent.

Several papers have made significant advances in understanding vertical differentiation by moving beyond unidimensional models, including Vandenbosch and Weinberg (1995) and Garella and Lambertini (2014). Yurko (2011) further extended previous work on vertical differentiation by considering the effects of income distribution changes on firms’ entry decisions and optimal product attributes using numerical simulations. Gayer (2025) examines the impact of the curvature of the marginal cost function to determine how it influences outcomes under vertical consumer heterogeneity. Barigozzi and Ma (2018) characterized the equilibrium assuming that the unit cost of the product is increasing and convex in quality in a multistage game of vertical product differentiation.

This work extends the literature on horizontal and vertical product differentiation by integrating both these attributes in one framework. This modelling approach is similar to Neven and Thisse (1989) and Economides (1993), who allow consumers to vary both with respect to their taste for particular product attributes and their preference for quality. Degryse (1996) and Brekke et al. (2010) are closely related papers that examine the interplay between vertical and horizontal product differentiation and its impact on outcomes of interest. While Degryse (1996) analyses outcomes in the banking sector, Brekke et al. (2010) showed that the relationship between competition and quality critically depends on assumptions about the linearity of the utility function. A tangentially related paper by Saouma et al. (2024) examines incumbents’ incentives to enter an industry characterized by both horizontal and vertical product differentiation.

This paper aligns most closely with Gulati and Ray (2016), but with a key distinction: there is competition in both price and quality. This work allows quality choice to be endogenous and makes it a function of the average preference for quality. Also, this work clearly looks at the welfare of consumers with lower preference when they are living in a society with heterogenous preferences versus when they are in a homogenous society. Unlike Neven and Thisse (1989), and following Benassi et al. (2006), it allows the non-purchase option and examines how the cut-off level of preference for quality changes with heterogeneity. The utility specification pertaining to the preference for quality follows the standard vertical differentiation framework where high-θ consumers have a greater willingness to pay for quality. And, also like Barigozzi and Ma (2018), the marginal cost of the output is assumed to be increasing and convex in quality.

Several theoretical papers have examined the welfare implications of increased consumer heterogeneity within monopolistic competition frameworks, beyond standard price and quality outcomes. Kichko and Picard (2024) show how market enlargement increases product diversity in trade contexts, benefiting all individuals but particularly those with higher incomes. Tarasov (2009) looks at a general equilibrium model of monopolistic competition when consumers have identical but non-homothetic preferences and there is free entry. He shows that higher income inequality may benefit the poor. The mechanism that he explores is the trickle-down effect working through the market because of the free entry of the firms. Osharin and Verbus (2015) model the response of the price with the change in the number of firms in the short run and show that it can be both anti- and pro-competitive.

Kokovin et al. (2024) examine horizontal consumer heterogeneity with vertical firm heterogeneity under monopolistic competition, finding that markups are highest in both the most and least populated niches due to firm-consumer heterogeneity interactions. Ghazzai et al. (2023) demonstrate a non-monotonic relationship between market competition and poverty, where outcomes critically depend on consumers’ sensitivity to quality changes. Klarl (2018) extends vertical product differentiation models by integrating willingness-to-pay and cost heterogeneity to re-evaluate the welfare implications of third-degree price discrimination.

Empirical research across diverse markets confirms that preference heterogeneity plays an important role in shaping market outcomes. Vélez-Velásquez (2024) found that the elimination of price discrimination in Colombia’s telecommunications industry will lead to substantially higher uniform prices that would harm lower-income consumers. Flach and Janeba (2017) showed that export prices in more unequal destinations are systematically higher. Pennerstorfer et al. (2025) demonstrated the influence of income distribution on product variety in Austria’s restaurant industry. In electric vehicle markets, Choi et al. (2025) documented adoption reluctance among disadvantaged groups, while Kumar et al. (2024) showed how preference heterogeneity shapes adoption patterns. Fan and Yang (2020) found that removing either high-end or low-end smartphone models significantly reduces consumer surplus. Waldfogel (1999) looks at the externality imposed by the difference in preference as the market size increases.

These findings consistently demonstrate that consumer welfare is impacted by the variation in consumers’ preference for quality and that it fundamentally shapes product variety, pricing strategies and quality levels. This empirical evidence showcases the need for building a theoretical framework that examines both vertical and horizontal dimensions of product differentiation, with model details and key assumptions presented in the following section.

The Model

To analyze the impact of consumer heterogeneity on the welfare of individuals with lower marginal willingness to pay, we extend the Salop (1979) model to incorporate two segments of consumers differing in their willingness to pay for quality, denoted by the parameters $θ_{H}$ for consumers with high willingness and $θ_{L}$ for those with low willingness. Consumers are uniformly distributed along the circumference of a circular market, where a proportion $f$ represents high-willingness consumers and ( $1 - f$ ) denotes low-willingness consumers.

The model is built upon the key assumption that consumers with higher preference parameters $(θ_{H})$ exhibit a greater willingness to pay for incremental increases in product quality while also incurring disutility from travelling to

acquire goods. The utility function for a consumer located at position $z$ with a preference parameter $θ_{i}$ when purchasing a product of quality $δ_{j}$ from firm $j$ located at $x_{j}$ can be expressed as:

U (z, θ_{i}, x_{j}) = θ_{i} δ_{j} - p_{j} - t |x_{j} - z|

(1)

where $θ_{i} δ_{j}$ represents the gross utility derived from the quality of the product, $p_{j}$ denotes the price of the product, and $t$ indicates the travel cost per unit distance to the firm. Our utility specification follows the standard vertical differentiation framework, where high-θ consumers have a greater willingness to pay for quality. This functional form satisfies the ‘single-crossing’ condition, ensuring that the indifference curves for consumers with higher willingness to pay intersect those with lower willingness from below, thereby maintaining a clear distinction between consumer types. Recent theoretical work confirms that such preferences generate market segmentation (Gayer, 2025; Klarl, 2018).

Firms operating within this model have a fixed production cost $F (δ_{j})$ , which is strictly increasing and convex in relation to product quality. We also characterize the marginal cost of production $c (δ_{j})$ as dependent on quality while being independent of output level.

It is assumed that higher quality entails higher production costs. Following the foundational work of Mussa and Rosen (1978), Barigozzi and Ma (2018) posit that a firm’s unit cost is increasing and convex in quality—an assumption adopted here to ensure interior optimal quality choices. This cost structure captures the reality that quality improvements require both greater upfront investments (fixed costs) and higher per unit expenses (marginal costs), as documented in healthcare (Chandra & Skinner, 2012). The above assumptions with respect to the cost function allow focusing only on the change in quality with a change in preference.

The profit function for firm $j$ , which charges a price $p_{j}$ for a product of quality $δ_{j}$ , can be formulated as follows:

π_{j} = [p_{j} - c (δ_{j})] D_{j} - F (δ_{j})

(2)

where $D_{j}$ is the demand faced by firm $j$ . Demand for each firm depends on the firm’s own strategic choices, ( $x_{j}, p_{j}, δ_{j}$ ), and on the strategic choices of the two adjacent firms, $(x_{j - 1}, p_{j - 1}, δ_{j - 1})$ and $(x_{j + 1}, p_{j + 1}, δ_{j + 1})$ . Each consumer buys either one unit of the product of quality $δ$ at price $p$ from their most preferred firm, or does not buy the product at all.

The set-up is a three-stage game. In the first stage, firms decide whether to enter or not. The number of firms is not fixed; it is determined endogenously from a free entry and exit condition.¹ The entering firms choose locations in the second stage. We assume that $n$ firms are located equidistant from each other around the circle so that the distance between adjacent firms is $\frac{1}{n}$ . In stage 3, given entry and location decisions in the earlier stages, each firm decides its price and quality to maximize profit, $π_{j}$ . The equilibrium price, the number of firms equation and the quality equation are given by:

p^{*} = c (δ) + \sqrt{t F (δ)}

(3)

n^{*} = \sqrt{\frac{t}{F (δ)}}

(4)

c^{'} (δ) + F^{'} (δ) \sqrt{\frac{t}{F (δ)}} = f θ_{H} + (1 - f) θ_{L}

(5)

The details of the derivation of these key equations are given in Appendix A1. The equilibrium quality level $δ$ is determined implicitly in Equation ( $5$ ), which equates the marginal benefit from increasing quality to its marginal cost. The right-hand side of Equation (5) is a weighted average of the preference parameters of the two types of consumers. Imposing sufficient convexity on the cost structure, it is easy to verify that equilibrium quality $δ$ increases as either $θ_{H}, θ_{L}$ , or their weighted average increases.² Change in equilibrium product quality, $δ$ *, in turn affects the price and the number of firms. From Equation (3), it is clear that the price responds positively to changes in quality, as both fixed and marginal costs increase with quality, whereas the number of firms given by Equation $(4)$ negatively correlates with a higher preference for quality.

Market Coverage Condition

Before diving deeper, it is essential to identify the parameter range for $θ_{H}$ and $θ_{L}$ such that all the consumers are served. Let $\bar{θ}$ denote the cut-off parameter such that a consumer with $\bar{θ}$ , indifferent between firms $j$ and $j + 1$ at a distance $δ_{j, j + 1}$ , is also indifferent between buying and not buying:

\bar{θ} δ - p_{j} - \frac{t L}{2 n} = \bar{θ}

All consumers are served when:

θ_{H} > θ_{L} > \bar{θ} = \frac{c (δ) + \frac{3}{2} \sqrt{t F (δ)}}{(δ - 1)}

(6)

The level of quality $δ$ is given by Equation (5). The details of the derivation are given in Appendix A2. Together, Equations (5) and (6) describe the joint determination of equilibrium quality and the lower threshold for market participation.

The next section explores how changes in $θ_{H}$ —and hence consumer heterogeneity—affect this threshold, shaping market access and welfare for consumers with lower willingness to pay.

Consumer Heterogeneity and Market Access for Consumers with Lower Preference Parameters

Having established in the second section that equilibrium quality $δ^{*}$ increases with greater consumer heterogeneity $θ_{H}$ , we now explore how this relationship affects the market access of consumers with a lower willingness to pay for quality $θ_{L}$ . Specifically, we examine how variations in the higher preference parameter $θ_{H}$ , while keeping the lower preference parameter $θ_{L}$ constant, influence the threshold of θ—that is, $\bar{θ}$ , the point beyond which all low-θ consumers remain served in equilibrium.

The Mechanism Linking Heterogeneity to Market Access

Recall from Equation ( $5$ ) that equilibrium quality depends positively on the average preference parameter of consumers. As $θ_{H}$ increases, firms face stronger incentives to improve product quality, leading to higher equilibrium quality $δ^{*}$ . However, this improvement is accompanied by higher production costs and prices. Initially, as quality improves, consumers with a lower preference parameter gain access to better products at still manageable prices, enhancing welfare. But beyond a threshold level of $θ_{H}$ , further improvement in quality raises costs and prices disproportionately, making products less affordable. Consequently, both the number of firms and market access for low-θ consumers decline. Thus, while firms may initially capture both high- and low-θ consumers by offering better quality goods, rising prices eventually begin to exclude low-θ consumers, who become priced out of the market.

That the resulting relationship between $θ_{H}$ and the market-access threshold for low-θ consumers, denoted by $\bar{θ}$ , is U-shaped is established in Appendix A4. Initially, an increase in $θ_{H}$ lowers $\bar{θ}$ , expanding access. Beyond a critical point, however, further increases in $θ_{H}$ raise costs and prices enough to reverse this effect, causing $\bar{θ}$ to rise and market access to contract.

The above results can be attributed to the settings where the agents are heterogeneous with respect to their preferences compared to the benchmark homogeneous environment. In line with the recent work on heterogeneous consumers in spatial settings (Gayer, 2025; Kokovin et al., 2024), we find that higher average quality under heterogeneity does not necessarily translate into higher welfare for low-preference consumers. Instead, beyond a certain degree of heterogeneity, quality upgrading primarily targets high-preference consumers and can reduce access and surplus for the low types.

These theoretical results provide a mechanism for ‘too much quality’ from the perspective of some consumers, which is consistent with empirical findings in quality-intensive markets such as electric vehicles and smartphones. Studies of EV adoption (Couture et al., 2025; Jenn et al., 2020; Kumar et al., 2024; Pennerstorfer et al., 2025; Vyas & Kushwah, 2023) and smartphones (Fan & Yang, 2020) document strong sorting of high-income or high-valuation consumers into high-quality products, while lower-income groups may be priced out or remain with lower-quality alternatives. Our model rationalizes how such patterns can arise even in otherwise symmetric spatial environments once preferences for quality become sufficiently dispersed.

Economic Implications

These examples illustrate how moderate consumer heterogeneity can encourage inclusive market outcomes by stimulating innovation and qualitative improvement, while an excess of heterogeneity can create exclusionary effects. When the competition involves both pricing and qualitative dimension, the balance between innovation incentives and affordability becomes critical.

Thus, the model underscores an important policy insight: promotion of competitive entry and innovation, which focuses on cost reduction, is extensively important to preserve the market access for low- $θ$ consumers even when there is an improvement in quality. Measures such as research and development (R&D) subsidies for low-cost production, technology diffusion incentives or price regulation in essential markets can help mitigate the negative effects of excessive heterogeneity

Consumer Surplus

It will also be insightful to see how the welfare of the consumers, particularly with lower preference to quality, changes as consumer heterogeneity increases because of the increase in $θ_{H}$ . To answer this, we begin by calculating the aggregate consumer surplus for individuals with a preference for quality given by $θ$ . The surplus for a consumer with preference parameter $θ$ , located at a distance $x$ from the firm from which they are purchasing, can be expressed as:

Surplus = θ δ - p - t x, where the reservation utility is θ

Given that there are $n$ firms, each with market coverage of $\frac{L}{2 n}$ on either side of its location, the aggregate consumer surplus for consumers with low preference for quality can be computed as:

C S_{θ_{L}} = 2 n \int_{0}^{\frac{1}{2 n}} [θ_{L} (δ - 1) - p - t x] d x = [θ_{L} (δ - 1) - p - \frac{t}{4} (\frac{1}{n})]

Similarly, the aggregate consumer surplus for consumers with a high preference parameter is given by:

C S_{θ_{H}} = 2 n \int_{0}^{\frac{1}{2 n}} [θ_{H} (δ - 1) - p - t x] d x = [θ_{H} (δ - 1) - p - \frac{t}{4} (\frac{1}{n})]

As expected, consumer surplus increases with ( $θ_{H}$ ), quality of the product $(δ)$ , and number of firms $(n)$ , and decreases with travel cost $(t)$ and price $(p)$ .

The aggregate consumer surplus derived reflects not just the immediate benefits enjoyed by consumers but also encompasses the broader implications of consumer heterogeneity in the market. The preference parameter ( $θ_{H}$ ) plays a critical role in determining consumer surplus for those consumers with a lower preference parameter $θ_{L}$ .

An increase in $θ_{H}$ directly correlates with a higher consumer surplus for high preference consumers, indicating that a greater willingness to pay for quality yields better market outcomes, enhancing their overall utility from consumption.

Additionally, the number of firms ( $n$ ) in the marketplace is a significant factor that influences consumer surplus. As the number of firms decreases, prices increase because of decreased competition among firms. However, it also causes decreased product availability. This competitive environment means that consumers cannot find products that meet their needs easily, thereby reducing their consumer surplus.

In contrast, travel costs ( $t$ ) negatively affect consumer surplus. As travel costs increase, the effective utility consumers derive from their purchases decreases. Higher travel costs may deter consumers, particularly those with lower purchasing power, from accessing markets, leading to a decline in their surplus. The travel cost here can be interpreted as the disutility from consuming the product for which the consumers have low preference. This may happen because of the fall in the number of firms. Similarly, higher prices $(p)$ directly detract from consumer surplus—when production costs rise, the prices of goods increase, which subsequently reduces the effective surplus for consumers.

Since the price and number of firms are endogenous, substituting their equilibrium values from Equations (3) and (4), the expression for aggregate consumer surplus of consumers with a high preference parameter for quality solely in terms of the parameters of the model will be:

C S_{θ_{H}} = [θ_{H} (δ - 1) - c (δ) - \frac{5}{4} \sqrt{t F (δ)}]

(7)

Similarly, consumer surplus for those with a low preference parameter is given by:

C S_{θ_{L}} = [θ_{L} (δ - 1) - c (δ) - \frac{5}{4} \sqrt{t F (δ)}]

(8)

where $δ$ denotes the equilibrium quality of the product and t denotes the transportation cost per unit distance.

Consumer Heterogeneity and Change in Consumer Surplus for Those with Lower Preference Parameters

Now, we specifically turn to the impact of an increase in the preference parameter $θ_{H}$ , (i.e., consumers with a high preference for quality) on the welfare of consumers with a low preference for quality. The consumer surplus expression is given by Equation (8), and the level of quality is determined by Equation (5).

It is interesting to see how the consumer surplus of those with a lower preference for quality changes with the change in $θ_{H}$ . It is shown in Appendix A5 that the same convexity condition on the cost structure that generates an inverted-U-shaped relationship between $\bar{θ}$ and $θ_{H}$ leads to an inverted-U-shaped relationship between $C S_{θ_{L}}$ and an increase in $θ_{H}$ . The reason is the tension between the cost effect and the valuation effect.

Detailed Discussion of Consumer Surplus and Its Dynamics

The relationship between consumer heterogeneity and welfare for low-θ consumers follows an inverted-U shape. When heterogeneity is small—that is, when differences between high-θ and low-θ consumers are limited—firms have modest incentives to improve product quality. In this region, an increase in heterogeneity encourages firms to raise quality, which benefits all consumers, including those with low willingness to pay. The quality upgradation enhances the utility component, while price increase remains moderate due to healthy competition.

However, as heterogeneity widens further, the dynamics shift. High-θ consumers drive firms to produce substantially higher-quality goods, leading to increased fixed and marginal costs. Prices p∗ begin to rise faster because of increased quality and a reduction in the number of firms. At this stage, the cost effect dominates the valuation effect, causing the overall welfare of low-θ consumers to decline. This trade-off—between improved product quality and reduced affordability—is the central mechanism generating the inverted-U relationship observed in both theoretical and real-world markets. This inverted - U shape relationship between quality and consumer surplus is illustrated in the Figure 1.

In shaping this dynamic, the existing gap between high preference ( $θ_{H}$ ) and low preference parameters ( $θ_{L}$ ) plays a critical role. A narrow gap encourages more inclusive market strategies that benefit lower preference individuals. Conversely, a widening gap can lead to increased marginalization of these consumers, reducing their access to higher-quality products and significantly affecting their overall welfare.

Figure 1.

Relationship Between Consumer Surplus and Quality.

To summarize, from a welfare perspective, the shape of the relationship is governed by two opposing forces:

Quality effect: As heterogeneity increases initially, competition drives firms to enhance quality. This raises consumer satisfaction and expands welfare.

Cost effect: Beyond a critical point, the higher cost of producing superior goods and decline in the number of firms translates into higher prices, which low-θ consumers cannot fully offset through increased utility. Welfare therefore declines.

Illustrative Example

Consider again the smartphone market. When consumer preference for technology features began to diverge, firms introduced higher quality devices at varying price points. Initially, even budget buyers benefited from access to improved models. But as innovation accelerated and production costs increased—due to advanced processors, cameras and materials—prices escalated, excluding lower-income consumers from the high-quality segment. The welfare pattern of low-θ consumers thus mirrors the inverted-U predicted by the model: first rising with technological diffusion, then declining as cost and price pressures intensify.

Comparing a Single-preference Economy with a Mixed-preference Economy

It has already been shown in the third section that equilibrium quality, $δ$ , increases as $θ_{H}$ increases; it follows that there is, in general, an inverted-U-shaped relationship between $θ_{H}$ and aggregate consumer surplus of those consumers with low preference for quality. What happens to the aggregate consumer surplus of consumers with low preference parameter as the gap between $θ_{H}$ and $θ_{L}$ increases depends on the existing consumer preference heterogeneity; that is, it is the existing consumer preference heterogeneity that determines which side of the inverted-U we begin with.

To answer that and to get a perspective, we compare the welfare of the consumers who have lower preference for quality in two scenarios. One, when there is no heterogeneity in preference. They reside in a single preference economy. So, a single preference economy is one where each consumer has the same preference parameter, which is given by $θ_{L} .$ It is also assumed that the preference parameter $θ_{L} > \bar{θ}$ , where $\bar{θ}$ is given by Equation (6).

θ_{L} > \bar{θ} = \frac{c (δ) + \frac{3}{2} \sqrt{t F (δ)}}{(δ - 1)} .

And, the level of quality in the single preference economy, represented by $δ_{S}$ is determined from Equation (5). Given that all the consumers have the same preference parameter given by $θ_{L}$ , the right-hand side of Equation (5) is given by:

c^{'} (δ_{S}) + \sqrt{t} \cdot \frac{F^{'} (δ_{S})}{\sqrt{F (δ_{S})}} = θ_{L}

(9)

The consumer surplus for those with a low preference for quality is given by Equation (8).

C S_{θ_{L}} = [θ_{L} (δ_{S} - 1) - c (δ_{S}) - \frac{5}{4} \sqrt{t F (δ_{S})}]

(10)

It is shown in Appendix B, specifically by Equation $(A 12),$ that aggregate consumer surplus for consumers with a lower preference for quality in a single preference economy is maximized at $δ_{W_{θ_{L}}},$ which is determined from the following equation:

c^{'} (δ_{W_{θ_{L}}}) + \frac{5}{8} \sqrt{t} \cdot \frac{F^{'} (δ_{W_{θ_{L}}})}{\sqrt{F (δ_{W_{θ_{L}}})}} = θ_{L}

(11)

Compared to a single-preference economy, a mixed-preference economy is the one that we have looked at so far, where at each point of the city, $f$ proportion of consumers have a high preference for quality and $(1 - f)$ proportion of consumers have a low preference for quality. Since all consumers are served, the aggregate consumer surplus of those with low preference for quality is given by:

C S_{θ_{L}} = [θ_{L} (δ_{M} - 1) - c (δ_{M}) - \frac{5}{4} \sqrt{t F (δ_{M})}]

In the mixed-income economy under consideration, the quality level (call it $δ_{M}$ ) is determined from Equation (5):

c^{'} (δ_{M}) + \sqrt{t} \cdot \frac{F^{'} (δ_{M})}{\sqrt{F (δ_{M})}} = f θ_{H} + (1 - f) θ_{L}

(12)

The equations for the purpose of analysis in this section are (9), (10), (11) and (12). Given the assumption on the cost structure, it follows that $δ_{W_{θ_{L}}} > δ_{S}$ , and $δ_{M} > δ_{S}$ . But the comparison between $δ_{M}$ and $δ_{W_{θ_{L}}}$ depends on the extent of the existing preference gap. This is illustrated in Figures 2 and 3. Figure 2 illustrates the case where the starting heterogeneity in preference is not very high, resulting in $δ_{M} < δ_{W_{θ_{L}}}$ . In this case, as $θ_{H}$ increases, the aggregate consumer surplus of consumers with a low preference increases in the beginning, reaches a maximum and then starts falling. On the other hand, Figure 3 illustrates the case where the starting heterogeneity in preference is high enough so that $δ_{M} > δ_{W_{θ_{L}}}$ . In this case, the aggregate consumer surplus of the consumers with a low preference for quality steadily declines as $θ_{H}$ increases.

Figure 2.

Low Gap in Preference: $δ_{M} < δ_{W_{δ_{L}}}$ .

Figure 3.

High Gap in Preference: $δ_{M} > δ_{W_{δ_{L}}}$ .

The comparison of welfare in the single preference economy with welfare in the mixed preference economy is an interesting exercise. It gives key insights into the externality by showing that each consumer’s welfare is not solely a function of their own preferences. Rather, it depends on how their preference interacts with the market and leads to an outcome that may either decrease or increase their welfare, depending on where they stand on the preference landscape in conjunction with others.

Conclusion

This paper investigates the impact of increased consumer heterogeneity in preference for quality on market outcomes and welfare, extending Salop’s spatial competition model to incorporate vertical differentiation. The analysis reveals a novel inverted-U-shaped relationship: as preference heterogeneity increases, welfare for low-preference consumers initially rises due to quality improvements, but then falls as rising costs and prices exclude them from the market.

The key insight is that moderate heterogeneity can positively influence welfare by stimulating innovation, while excessive heterogeneity creates negative exclusionary effects. This trade-off is clearly visible when one compares mixed societies (with heterogeneous preferences) to segregated societies (with homogeneous preferences), highlighting important externalities arising from consumer heterogeneity.

These theory-driven results directly contribute to policy debates in markets where quality is both essential and expensive. In healthcare markets, Brekke et al. (2010) show that competition and technological progress influence quality, access and waiting times in complex ways. In transport and mobility, studies document how policy incentives shape heterogeneous adoption of higher-quality options such as electric vehicles (Couture et al., 2025; Kumar et al., 2024).

The mechanism emphasized in our model suggests that governments should carefully weigh policies that reward quality enhancements without addressing affordability—such as untargeted subsidies, generous incentives that more often benefit high-valuation users, or unregulated premium upgrades. These policies may unintentionally exclude consumers with lower preferences or lower ability to pay for quality from the market.

While this model prioritizes externalities from high- to low-preference consumers, as an extension, exploring the reverse path may provide a more comprehensive understanding as an increase in the density of low-preference consumers would optimally make firms choose lower quality at lower prices, potentially benefiting high-preference consumers through reduced costs but harming them on the qualitative front.

Another important avenue for future research is to empirically measure preference parameters (θ) across different markets and track their evolution over time. This would allow researchers to test the theoretical predictions of the model regarding the relationship between consumer heterogeneity and market outcomes in terms of variety, price and quality.

Footnotes

Declaration of Conflict of Interests

The author declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author received no financial support for the research, authorship and/or publication of this article.

Notes

ORCID iD

Namrata Gulati

Appendix A

In this appendix, detailed derivations of the demand functions, calculations of equilibrium conditions and sensitivity analyses based on consumer preferences and production costs are given.

Appendix B: Comparison of the Homogenous Preference Parameter With the Heterogenous Preference Parameter

Key Equations

The following are the key equations relevant to our analysis:

1. The aggregate consumer surplus of the consumers with low preference for quality is given by: (A13)

C S_{θ_{L}} = [θ_{L} (δ - 1) - c (δ) - \frac{5}{4} \sqrt{t F (δ)}]

2. The condition for maximizing aggregate consumer surplus of those with preference parameter $θ_{L}$ is given by: (A14)

c^{'} (δ_{W_{θ_{L}}}) + \frac{5}{8} \sqrt{t} \cdot \frac{F^{'} (δ_{W_{θ_{L}}})}{\sqrt{F (δ_{W_{θ_{L}}})}} = θ_{L}

3. In an economy where there are consumers with preference $θ_{L}$ , the quality level is determined by: (A15)

c^{'} (δ_{S}) + \sqrt{t} \cdot \frac{F^{'} (δ_{S})}{\sqrt{F (δ_{S})}} = θ_{L}

4. The quality level in an economy with heterogeneous preferences is assessed as follows:

c^{'} (δ_{M}) + \sqrt{t} \cdot \frac{F^{'} (δ_{M})}{\sqrt{F (δ_{M})}} = f θ_{H} + (1 - f) θ_{L}

These equations underpin the findings of our analysis, emphasising the intricate relationship between consumer preferences, market dynamics and welfare outcomes for individuals with lower preference parameters.

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Examining Externality on Welfare and Market Access Arising from Consumer Heterogeneity

Abstract

Keywords

Introduction

Literature Review

The Model

Market Coverage Condition

Consumer Heterogeneity and Market Access for Consumers with Lower Preference Parameters

The Mechanism Linking Heterogeneity to Market Access

Economic Implications

Consumer Surplus

Consumer Heterogeneity and Change in Consumer Surplus for Those with Lower Preference Parameters

Detailed Discussion of Consumer Surplus and Its Dynamics

Relationship Between Consumer Surplus and Quality.

Illustrative Example

Comparing a Single-preference Economy with a Mixed-preference Economy

Low Gap in Preference: δ M < δ W δ L .

High Gap in Preference: δ M > δ W δ L .

Conclusion

Footnotes

Declaration of Conflict of Interests

Funding

Notes

ORCID iD

Appendix A

Appendix B: Comparison of the Homogenous Preference Parameter With the Heterogenous Preference Parameter

References

Low Gap in Preference: $δ_{M} < δ_{W_{δ_{L}}}$ .

High Gap in Preference: $δ_{M} > δ_{W_{δ_{L}}}$ .