Horizontal Differentiation Model Research Articles

Fare evasion in public transport: How does it affect the optimal design and pricing?

Fare evasion produces significant revenue losses in public transport systems. Recent research has found that low service quality and high prices are important determinants of fare evasion. However, the economic literature that studies the optimal public transport provision has overlooked the phenomenon. We develop a demand model of horizontal differentiation to investigate how fare evasion affects the design and pricing of public transport that maximizes utilitarian social welfare. We show analytically that fare evasion can create incentives to reduce public transport prices and improve service quality, putting upward pressure on its subsidization. We perform numerical simulations and sensitivity analysis to quantify the impact of these incentives on the public transport provision. These simulations confirm that the incentive to reduce fare evasion can lead to an optimal design and price that requires subsidies.

Intercity bus and rail services: Competition and welfare effects

We study the effects of the deregulation of intercity bus services in Europe on intermodal competition in long-distance land passenger transport and on social welfare. We consider a bus company with a flexible (Internet-based) business model and a rail operator with a rigid cost structure due to indivisibilities. We adjust the standard location model of horizontal differentiation to account for quality differences between modes, and for a bus capacity limit. We show that deregulation may turn the former rail monopoly on a route into a bus monopoly, particularly if bus quality is high enough and/or bus marginal cost is low enough. Since the bus is capacity constrained, then social welfare may be improved through a lump-sum transfer from bus to rail to restore competition and increase the number of travelers. Instead, we show that intermodal competition may reduce welfare (compared to rail monopoly) if the bus is inefficient and/or of low quality, so that bus services should be restricted by imposing quotas or even entry bans. Finally, we relax some assumptions and calibrate the model with data from the Genoa-Milan route in Italy. Numerical simulations confirm theoretical predictions and estimate annual welfare gains on the route under the compensation scheme.

Salience and horizontal differentiation

AbstractI study a horizontal differentiation model in which one of two attributes of a product, product fit and price, is more salient for a consumer than the other and different consumers can find a different attribute salient. The attribute that is more salient is determined by relative differences between the two products and is determined endogenously as a result of firms' pricing strategies. High (low) marginal costs soften (toughen) price competition between firms. Pass‐through rates are greater than 1 for some parameter values. Both industry‐ and firm‐level cost increases may be beneficial for firms.

A competitive analysis of information security investment: The role of hacker attacks

The role of hacker attacks on information security investment and firm profits is fundamental in information security economics, which, however, has not been fully examined yet. This paper builds a duopolistic horizontal differentiation model to study this issue and yields a series of interesting findings. First, we find that each firm may benefit from an increase of the probability of hacker attacks when it gains more from security differentiation and suffers less from investment competition. Second, when market competition becomes fiercer, each firm invests less in information security to maintain security differentiation. Third, each firm may benefit from an increase of consumer security loss because the resulting security investment can lead to a more desirable security differentiation. Finally, an increase of cost coefficient of security investment may be profitable to each firm in spite of an increase of security expenditure. This is because an increase of cost coefficient may facilitate security differentiation through discouraging security investment. Additionally, the model is extended to analytically and numerically check the robustness of the main results.

Designing subscription menu for software products: Whether to release a long-length option

An increasing number of information product vendors adopt a subscription-based business model and offer a menu of options with different subscription lengths for the same information product. This study adopts a horizontal differentiation model, wherein subscription options are differentiated only in the renewal lengths to make a comparison between the single- and two-option menus. The former offers one option only, whereas the latter offers both the short- and long-length options. Analytical results show that the basic value of the product and the unit misfit cost, which measures consumers’ disutility per unit distance between the actual and ideal subscription lengths, are critical factors in determining the optimal design of the subscription menu. The two-option menu dominates the single-option menu when the basic value and the unit misfit cost exceed certain thresholds. The impact of consumer churn rate on the design of the subscription menu is further examined. The two-option menu is more likely to be the dominant choice as the consumer churn rate increases. Moreover, the effect of the increase in the consumer churn rate on the pricing decision depends on the unit misfit cost. Given a higher consumer churn rate, only if the unit misfit cost is sufficiently low, vendors should improve the price for the short-length option and the price discount level for the long-length option; otherwise, the optimal pricing decision remains unchanged. After endogenizing the length of the long-length option, we discuss how the optimal number of periods of the long-length option varies with the product value, consumers’ cognitive cost, and unit misfit cost. The optimality of the multiple-option menu with more than two options is also explored.

Vertical integration and input foreclosure in the Hotelling model of horizontal differentiation

Vertical integration and input foreclosure in the Hotelling model of horizontal differentiation

Privatization Policies by National and Regional Governments

In order to analyze the privatization policies undertaken by the national and regional governments, I consider a horizontal differentiation model with price competition in which a country consists of two regions of different sizes. I show that public-sector intervention by either the national or regional government is essential for achieving the social optimum. The preferences of consumers and firms about privatization policy are completely opposite: consumers prefer a regional public-sector intervention, while firms prefer a national public-sector intervention. Finally, I find that the preferences of the two regions about market structures are also opposite: the least populated region prefers the private duopoly, while the most populated region prefers a government intervention in the market.

Device-funded vs ad-funded platforms

We analyze device-funded and ad-funded platforms with differentiated ecosystems supporting apps provided under monopolistic competition. The incentives of a device-funded platform in investing in app curation, introducing its own apps and setting commissions on in-app purchases of external apps are largely aligned with those of consumers, while this is not necessarily the case for the ad-funded platform. In particular, consumers gain from a positive commission set by the device-funded platform because this implies a lower price of the device, and the platform’s apps are introduced and priced internalizing the impact on consumer welfare, perfectly in models of horizontal differentiation and partially in models of vertical differentiation.

Comment on “Strategic Information Management Under Leakage in a Supply Chain”

Anand and Goyal [Anand KS, Goyal M (2009) Strategic information management under leakage in a supply chain. Management Sci. 55(3):438–452] propose a horizontal differentiation model to study information leakage and demand signaling in a supply chain. The authors present a composite equilibrium consisting of separating and pooling outcomes in different parameter regions and claim that it satisfies the intuitive criterion. We show that their analysis for the pooling equilibrium has errors and also that all pooling outcomes are actually eliminated by the intuitive criterion. The positive note is that if the undefeated equilibrium or the lexicographically maximum sequential equilibrium refinement is adopted, a similar composite equilibrium will be achieved, which will lead to qualitatively the same results as in the original paper. This paper was accepted by Chris Forman, information systems.

R&D Concentration Under Endogenous Fixed Costs: Evidence from Genetically Modified Corn Seed

AbstractWe examine the role of fixed costs in research and development (R&D) in the market for genetically modified (GM) corn seed. In a mixed model of horizontal differentiation by genetic traits and vertical differentiation by productivity, we derive the empirically testable lower bounds to R&D concentration when R&D investments and market entry are jointly determined. When R&D investments translate into higher product quality, industries are said to be characterized by endogenous fixed costs such that the lower bound to R&D concentration increases with market size, but is less than the lower bound to market concentration based on sales. Using data on field trial applications of GM corn seed, we estimate the lower bound to R&D concentration, and find evidence of endogenous fixed costs with R&D concentration that is significantly greater than perfectly competitive levels. These endogenous fixed costs imply that concentration in the agricultural biotechnology industry is occurring due to the nature of R&D investment in product quality and not through anticompetitive practices. Adjusting for past merger and acquisition activity significantly raises the lower bound for infinitely‐sized markets, but has no impact upon current market sizes, implying the industry may still undergo additional consolidation.

Hotelling Models with Price-Sensitive Demand and Asymmetric Transport Costs: An Application to Public Transport Scheduling

We formulate a horizontal differentiation model with price-sensitive demand and asymmetric transport costs, in the context of transport scheduling. Two competitors choose fares and departure times in a fixed time interval. Consumers are distributed uniformly along the interval; their location indicates their desired departure time. In a standard Hotelling model, locations are chosen before prices. In our context, the opposite order is also conceivable, but we show that it does not result in a Nash equilibrium; the same is true for a game in both variables are chosen simultaneously. We also discuss Stackelberg game structures and second-best regulation.We conclude that the addition of price-sensitive demand results in equilibria in the traditional Hotelling model with price setting; there, services are scheduled closer together than optimal. We also show that it is possible to include asymmetric schedule delay functions. Our results show that departure times can be strategic instruments. Optimal regulatory strategies depend on the value of schedule delay, and on whether the regulator can commit.

Comment on 'Strategic Information Management Under Leakage in a Supply Chain'

Anand and Goyal (2009) propose a horizontal differentiation model to study information leakage and demand signaling in a supply chain. The authors present a composite equilibrium consisting of separating and pooling outcomes in different parameter regions and claim that it satisfies the Intuitive Criterion. We show that their analysis for the pooling equilibrium has errors and also that all pooling outcomes are actually eliminated by the Intuitive Criterion. The positive note is that if the undefeated equilibrium or lexicographical maximum sequential equilibrium (LMSE) refinement is adopted, a similar composite equilibrium will be achieved, which will lead to qualitatively the same results as in the original paper.

NESTING VERTICAL AND HORIZONTAL DIFFERENTIATION IN TWO‐SIDED MARKETS

ABSTRACTWe merge the two‐sided markets duopoly model of Armstrong (2006) with the nested vertical and horizontal differentiation model of Gabszewicz and Wauthy (2012), which consists of a linear city with different consumer densities on the left and on the right side of the city. In equilibrium, the high‐quality platform sells at a higher price and captures a greater market share than the low‐quality platform, despite the indifferent consumer being closer to the high‐quality platform. The difference between market shares is lower than socially optimal. A perturbation that introduces a negligible difference between the consumer density on the left and on the right side of the city may disrupt existence of equilibrium in the model of Armstrong (2006).

Product Repositioning in the UK Newspaper Industry

This paper investigates the alleged predatory behaviour in the UK quality newspaper industry in the 1990s in terms of product repositioning using a horizontal differentiation model and industry data. It supports the call for an “effects based” approach to competition law by showing that non-price conduct can be a critical and less visible, complementary means to achieve a predatory goal than mere price cuts.

The economics of eco-labeling: Standards, costs and prices

The existing eco-label landscape is fragmented because of the presence of numerous labels with different standards and is a pre-competitive environment for firms to play in with many unanswered questions. Different standards – eco-labels are built around – have different effects on credibility and legitimacy, costs and benefits, and ability to achieve sustainability goals of eco-labeling. Focusing on eco-label standards and using a Hotelling-type horizontal differentiation model, we identify standards-specific issues for and characterize primary barriers to eco-labeling. Some of the major findings are as follows: (1) More rigorous environmental standards enforced by higher-integrity labels do not necessarily translate into higher selling prices; (2) Higher prices commanded by labeled products do not guarantee that a firm will derive higher profits from eco-labeling; (3) Auditing fees paid per product unit being inspected for ensuring compliance with an eco-label standard (rather than participation fees paid up front) is the primary de facto barrier to business involvement in eco-labeling; and (4) Customers׳ willingness to pay price premiums for eco-labeled products is not a sufficient condition to generate a premium in the market.

Information and quality with an increasing number of brands

We analyze the potential trade-off between product variety and consumer information and the implications this trade-off has for product quality. We introduce a simple information accumulation process in a horizontal differentiation model with unobservable quality. As the number of brands increases, per-brand consumer information decreases, which leads to lower average quality. Eventually, the reduction in quality can outweigh the marginal welfare benefits of greater product variety. Thus, the continuous increase in the number of brands requires a parallel improvement in consumer information mechanisms. It remains to be answered how efficiently new information mechanisms respond to this requirement in each market.

Welfare, competition, specialization and growth

In this paper we consider a model of horizontal differentiation with a quite general production function and derive the closed form solutions for the level of the variables in the decentralized economy and in the social planner case. This enables us to analyze how consumers’ welfare varies in terms of the degree of competition and the degree of returns to specialization. We find that welfare is increasing in the degree of returns to specialization both in the market economy and in the centralized economy and the decentralized economy's welfare is a bell-shaped function of the degree of competition.

A Competitive Analysis of Web 2.0 Communities: Differentiation with User-Generated Content

This paper studies the competition between Web 2.0 communities in a game theoretic framework. We model three important features of these institutions: (i) firms' content is usually user-generated; (ii) consumers' content preferences are governed by local network effects, and (iii) consumers have strong tendencies to multi-home. Our analyses reveal that ex-ante identical community sites can acquire differentiated market positions that spontaneously emerge from user-generated content. Moreover, sites may obtain unanticipated and sometimes ambiguous market positions, wherein one site simultaneously attracts distinct and isolated consumer segments that seldom interact. Spontaneous differentiation reduces firm competition but may imply too much consumer segregation and lower social welfare. In most equilibria, a subset of consumers multi-home. We show that the degree of spontaneous differentiation increases in the localness of network effects. Interestingly, more multi-homing consumers imply reduced differentiation and intensify site competition. In one extension, we show that market growth tends to lead to lower market concentration, in contrast to the prediction by the classical horizontal differentiation model. We also study competing sites' community design strategies and provide conditions under which sites reduce or enhance user connectivity within their communities, leading to maximal and minimal spontaneous differentiation respectively.

Kinked-Demand Equilibria and Weak Duopoly in the Hotelling Model of Horizontal Differentiation

The Hotelling model with finite consumer reservation price is, in its various forms, perhaps the canonical model of horizontal product differentiation. Yet the following key aspects of this model are little understood: (i) the existence of asymmetric price equilibria when consumers have unit demands and (ii) for a very broad set of model specifications, the non-monotonicity of price as a function of consumers' transportation cost, i.e., the degree of product differentiation in the market. We provide a complete characterization of the asymmetric equilibria, show that they exist for a comparatively "wide" range of markets, and argue that their existence is robust to various extensions of the prototype model. Introducing elasticity into consumer demands suppresses the kink in the firms' demand functions and ensures the uniqueness (and symmetry) of the price equilibrium. However, the key perverse comparative static of the symmetric kinked equilibrium, decreasing price as a function of transport cost, survives relaxation of the unit-demand assumption. Indeed the symmetric kinked equilibrium of the unit-demand case is a special case of a general but largely unexplored set of equilibria in the Hotelling model we call weak duopoly. Weak-duopoly equilibria exist for intermediate values of transportation cost for a very broad class of consumer demands. They occupy a comparatively wide range of the model parameter space, and firm behavior in weak duopoly differs fundamentally from that which occurs for lower values of the transportation cost, or when consumers have no reservation price.

Is Conformism Desirable? Network Effects, Location Choice, and Social Welfare in a Duopoly

In this paper we study a duopoly where the network e¤ect is nonmonotone and the network can be overloaded. The firms choose prices and locations endogenously, and the agent's utility is influenced by the number of people patronizing the same firm she does. We determine the market equilibrium, and we study how the network effect influences social welfare. We compare this setting with the standard horizontal differentiation model with no network effects to understand whether and how conformism is socially desirable. The results show that whether network effects are desirable depends on how people are conformist, and whether overloading is feasible. If overloading is not possible (in either of the firm's network), and the total consumers' mass is sufficiently high, a network effect which is slightly concave increases social welfare. By contrast, if overloading is feasible, and the total consumers' mass is sufficiently small, social welfare is increased if the network effect is more concave than in the previous case.