Classic Spatial Models
In this chapter, we illustrate some classic spatial models. We provide a collection of the principal classic spatial models, by illustrating their characteristics and their main results. In particular, we discuss the Hotelling linear market and the Salop
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1.1
Introduction
In this chapter, we illustrate some classic spatial models. Starting from the seminal paper of Hotelling (1929), space has become a crucial variable in the economic analysis of oligopolistic models.1 The aim of this chapter is mainly pedagogical: we aim to provide a useful collection of the principal classic spatial models, by illustrating their characteristics and the main results. Indeed, classic spatial models are a flexible tool which adopts the
1 Obviously, the importance of the spatial dimension has been well recognized even before Hotelling.
For example, Thunen (1826), Launhardt (1885), Marshall (1890), and Weber (1909) developed relevant frameworks to understand the implications of space for consumers and firms’ behavior. However, none of these models has been used for plenty of applications as the Hotelling one and its epigones.
S. Colombo () Department of Economics & Finance, Università Cattolica del Sacro Cuore, Milano, Italy e-mail: [email protected] © The Author(s) 2020 S. Colombo (ed.), Spatial Economics Volume I, https://doi.org/10.1007/978-3-030-40098-9_1
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space dimension to model a wide array of economic questions, including industrial organization, regional science, and marketing. This is not an exhaustive review of spatial models. Indeed, hundreds and hundreds of spatial models have been developed by scholars; we have selectively chosen those contributions we believe represent the cornerstone of modern spatial economy, in order to provide a toolkit for those who are approaching this field for the first time. Before starting, we briefly put forward the common characteristic of classic spatial models: classic spatial models do not want to represent “stylized facts”, but, rather, to highlight and describe the forces that determine the choices of the firms or the consumers. Indeed, classic spatial models are often too simple to provide a good description for what happens in the real word, but they are sufficiently simple to capture which incentives are at work when the firms or the consumers take their decision. This is the main purpose of classic spatial models. The rest of the chapter proceeds as follows. In Sect. 1.2 we introduce and describe the linear model. In Sect. 1.3, we consider the circular model. In Sect. 1.4 we describe some spatial models adopting price discrimination, whereas in Sect. 1.5 we introduce elastic demand. In Sect. 1.6 we discuss the “barbell” model. In Sect. 1.7 we consider a spatial model of vertical differentiation. Section 1.8 concludes.
1.2
The Linear Model
In this section, we describe the linear model, which is based on the work of Hotelling (1929). The aim of the model consists in providing a simple framework to describe product differentiation, that is, a situation where a slight decrease of the price of one firm does not determine an abrupt increase of the demand of that firm, but rather a gradual shift of demand. In fact, Hotelling was rather skeptical about Bertrand’s (1883) criticism of Cournot (1838) equilibr
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