SPATIAL STABILITY

We consider a continuous spatial economy consisting of pure exchange local economies. Agents are allowed to change their location over time as a response to spatial utility differentials. These spatial adjustments toward higher utility neighborhoods lead the spatial economy to converge to a spatially uniform allocation of resources, provided that the matrix of price effects is quasi-negative definite. Furthermore our model provides a real time interpretation of the tâtonnement story. Also, spatial fluctuations are shown to be damped at different rates according to their spatial scale.local markets, migration, spatial economy, convergence, stability, tâtonnement, normal modes.

THE CORE-PERIPHERY MODEL: EXISTENCE AND UNIQUENESS OF SHORT-RUN EQUILIBRIUM

We consider the core-periphery model by Krugman (1991). The nature and stability of the possible steady states of the model have been made progressively precise, see Fujita et al. (1999) and Baldwin et al. (2003). In that model as well as in all the new economic geography models that have been derived from it, the short-run (instantaneous) equilibrium is implicitly determined by the current labor distribution across regions. The numerical computations used so far to determine the short-run equilibrium, tend to suggest its existence. In this work, an existence and uniqueness proof of short-run equilibrium is provided.core-periphery, economic geography, fixed point F12, R12, R23, C62

On spatial equilibria in a social interaction model

Social interactions are at the essence of societies and explain the gathering of individuals in villages, agglomerations, or cities. We study the emergence of multiple agglomerations as resulting from the interplay between spatial interaction externalities and competition in the land market. We show that the geographical nature of the residential space tremendously affects the properties of spatial equilibria. In particular, when agents locate on an open land strip (line segment), a single city emerges in equilibrium. In contrast, when the spatial economy extends along a closed land strip (circumference), multiple equilibria with odd numbers of cities arise. Spatial equilibrium configurations involve a high degree of spatial symmetry in terms of city size and location, and can be Pareto-ranked.social interaction, multiple agglomerations, spatial economy

On spatial equilibria in a social interaction model

Social interactions are at the essence of societies and explain the gathering of individuals in villages, agglomerations, or cities. We study the emergence of multiple agglomerations as resulting from the interplay between spatial interaction externalities and competition in the land market. We show that the geographical nature of the residential space tremendously affects the properties of spatial equilibria. In particular, when agents locate on an open land strip (line segment), a single city emerges in equilibrium. In contrast, when the spatial economy extends along a closed land strip (circumference), multiple equilibria with odd numbers of cities arise. Spatial equilibrium configurations involve a high degree of spatial symmetry in terms of city size and location, and can be Pareto-ranked.social interaction, multiple agglomerations, spatial economy.

Existence and uniqueness of equilibrium for a spatial model of social interactions

We extend Beckmann’s spatial model of social interactions to the case of a two-dimensional spatial economy involving a large class of utility functions, accessing costs, and space-dependent amenities. We show that spatial equilibria derive from a potential functional. By proving the existence of a minimiser of the functional, we obtain that of a spatial equilibrium. Under mild conditions on the primitives of the economy, the functional is shown to satisfy displacement convexity, a concept used in the theory of optimal transportation. This provides a variational characterisation of spatial equilibria. Moreover, the strict displacement convexity of the functional ensures the uniqueness of spatial equilibrium. Also, the spatial symmetry of equilibrium is derived from that of the spatial primitives of the economy. Several examples illustrate the scope of our results. In particular, the emergence of multiple of equilibria in the circular economy is interpreted as a lack of convexity of the problem

The core-periphery model with three regions

We study a 3-region core-periphery model à la Krugman and compare our results with those of the standard 2-region model. The conditions for the stability of the dispersion and concentration configurations are established. Like in the 2-region model, dispersion and concentration can be simultaneously stable. We show that the 2- region (3-region) model favors the dispersion (concentration) of economic activity. Finally, we extend the core-periphery model to the case of n regions and show that stability of concentration with 2 regions implies stability of concentration with any even number of regions.new economic geography, core-periphery

Quality Differentiation and Spatial Clustering among Restaurants

To explore the relationship between spatial location and quality differentiation, we build a dataset of over 30,000 restaurants rated by TripAdvisor, across large UK cities. Whereas top-rated restaurants tend to locate closer to other top restaurants, bottom-rated restaurants tend to locate away from each other and closer to top ones. Our theoretical model can explain the main features of the observed spatial patterns. We find that an increase in the population density in the city center reduces the spatial dispersion of both top and bottom restaurants but the reduction is larger in magnitude for top restaurants. A larger quality difference between top and bottom restaurants increases both the absolute and relative dispersion of top restaurants

Urban Structures with Forward and Backward Linkages

We study urban structures driven by demand and vertical linkages in the presence of increasing returns to scale. Individuals consume local urban varieties and firms use these varieties to produce a national good. We prove the existence of a spatial equilibrium and obtain an invariance result according to which more intense demand or vertical linkages have the same effect on the urban structure as lower commuting costs. Various urban configurations can emerge exhibiting a monocentric, an integrated, a duocentric, or a partially integrated city structure. We discuss the role of commuting and transport costs, intensities of demand and vertical linkages, and urbanization in affecting these patterns. We show that multiple equilibria may arise in equilibrium involving the monocentric city and up to a couple of duocentric and partially integrated structures

The core-periphery model: existence and uniqueness of short-run equilibrium

We consider the core-periphery model by Krugman (1991). The nature and stability of the possible steady states of the model have been made progressively precise, see Fujita et al. (1999) and Baldwin et al. (2003). In that model as well as in all the new economic geography models that have been derived from it, the short-run (instantaneous) equilibrium is implicitly determined by the current labor distribution across regions. The numerical computations used so far to determine the short-run equilibrium, tend to suggest its existence. In this work, an existence and uniqueness proof of short-run equilibrium is provided