Abstract
Classical spatial economics as formulated by Johann Heinrich von Thünen and Wilhelm Launhardt in the nineteenth century dealt with economic geographical phenomena in the continuous two-dimensional plane. The present chapter explores to what extent their equilibrium outlook can be extended to deal with dynamic phenomena. Issues, such as spatial distributions of prices, land rents, and populations, along with flows – of traded commodities, migrants, and diffusion of non-material influences, such as economic growth or business cycles, definitely seem to call for such a dynamic perspective. In particular, it is argued that, even in motivating persistent equilibrium patterns, focus should be shifted from optimality to structural stability. Implicit is then that one considers topological properties rather than strictly geometrical ones. This in itself is a move towards more realism, as the extreme regularity inherent in the classical geometric models is so unconvincingly abstract. This reasoning is applied to two much discussed cases; the emergence of shapes of market areas, and the shapes of structurally stable flows of trade.
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Notes
- 1.
A wave with flat surfaces is not the only possibility for \({\nabla }^{2}Y = 0\); any surface satisfying Laplace’s differential equation (just stated) reduces the Laplacian to zero.
- 2.
Even if the gains from compatification in terms of the isoperimetric problem in applications to physics are notably larger than those in tre Löschian context, there is an interesting case discussed in Weyl’s delightful book Weyl (1952). It has been thought that rhombic dodecahera provide the closest packing of solids in three dimensions. These, by the way, are the shapes also found in beehives where the two layers of cells fit together back to back.
Fig. 5 
The rhombic dodecahedron, long thought to be the most compact shape in a close packing in terms of minimal surface area that separates cells of equal volume. Half of it with hexagonal crossection is found in the back of each layer of cells of a beehive, and it also turns up in experiment to compactify soft originally spherical cells under pressure. However, Lord Kelvin demonstrated that this is not the most compact shape. The shape he found, however, never turns up in practical experiment, as friction impedes the packing to obtain the final state of optimum
They also resulted from experiment, from the attempt by the priest who enclosed peas in a barrel and added water to make them swell, to the experiment of loading lead shot in a strong cylinder and then pushing a piston using explosives.
Yet, Lord Kelvin in his Barltimore Lectures proved that there existed a different shape with slightly curved edges which actually represented a better economy of surface area to enclosed volume. However, it never turned up in experiment. A likely hypothesis is that this was due to friction preventing the shapes to attain the slight final perfection.
- 3.
Professor Gardini, to whose honour this volume is dedicated, and her students created a node of extreme attraction at the small University of Urbino. The attraction is even so strong that Professor Gardini herself seldom leaves its gravity field, though, due to the scattering of her students, and the numerous published discoveries, it is fortunately not a black hole.
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Puu, T. (2013). Pattern Formation in Economic Geography. In: Bischi, G., Chiarella, C., Sushko, I. (eds) Global Analysis of Dynamic Models in Economics and Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29503-4_6
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