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.
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.
References
Allen, R. G. D. (1956). Mathematical economics. London: Macmillan.
Angel, S., & Hyman, G. M. (1976). Urban fields – a geometry of movement for regional science. London: Pion Ltd.
Ball, P. (1999). The self-made tapesrtry – pattern formation in nature. Oxford: Oxford University Press.
Beckmann, M. J. (1952). A continuous model of transportation. Econometrica,20, 642–660.
Beckmann, M. J. (1953). The partial equilibrium of a continuous space economy. Weltwirtschaftliches Archiv,71, 73–89.
Beckmann, M. J. (1968). Location theory. New York: Random House.
Beckmann, M. J. (1976). Equilibrium and stability in a continuous space market. Operations Research Verfahren,14, 48–63.
Beckmann, M. J., & Puu, T. (1985). Spatial economics: Potential, density, and flow. Amsterdam: North-Holland.
Beckmann, M. J., & Puu, T. (1990). Spatial structures: Vol. 1. Advances in spatial and network economics. Heidelberg: Springer.
Bos, H. C. (1965). Spatial dispersion of economic activity. Rotterdam: Rotterdam University Press.
Bunge, W. (1962). Theoretical geography. Lund: Gleerup.
Christaller, W. (1933). Die zentralen Orte in Süddeutschland. Jena: Fischer.
Commendatore, P., & Kubin, I. (2012). A three-region new economic geography model in discrete time: Preliminary results on global dynamics. In G. I. Bischi, C. Chiarella, & I. Sushko (Eds.), Global analysis of dynamic models in economic and finance: Essays in honour of Laura Gardini. pp. 133–158.
Fujita, M., Krugman, P., & Venables, A. J. (1999). Cities, regions, and international trade. Cambridge, MA: MIT Press.
Gumowski, I., & Mira, C. (1980). Dynamique chaotique. Toulouse: Editions Cépadues.
Harrod, R. F. (1948). Towards a dynamic economics. London: Macmillan.
Henle, M. (1979). A combinatorial introduction to topology. San Francisco: Freeman.
Hotelling, H. (1921, 1978). A mathematical theory of migration, Technical report, MA Thesis, University of Washington. Reprinted in Environment and Planning A 10, 1223–1239.
Hotelling, H. (1929). Stability in competition. Economic Journal,41, 41–57.
Kaashoek, J. F., & Paelinck, J. (1994). Potentialized partial differential equations in theoretical spatial economics. Chaos, Solitons & Fractals,4, 585–594.
Launhardt, W. (1885), Mathematische Begründung der Volkswirtschaftslehre. Leipzig: Teubner.
Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences,20, 130–293.
Lösch, A. (1940). Die räumliche Ordnung der Wirtschaft. Jena: Fischer.
Mira, C., Gardini, I., Barugola, A., & Cathala, J. C. (1996). Chaotic dynamics in two-dimensional noninvertible maps. Singapore: World Scientific.
Mosler, K. C. (1987). Continuous location of transportation networks. Berlin: Springer.
Okubo, A. (1980). Diffusion and ecological problems. Heidelberg: Springer.
Palander, T. F. (1935). Beiträge zur Standortstheorie. Uppsala: Almqvist & Wiksell.
Peixoto, M. M. (1977). Generic properties of ordinary differential equations. In J. Hale (Ed.), Studies in ordinary differential equations: Vol. 14. MAA studies in mathematics (pp. 52–92). Washington: Mathematical Association of America.
Phillips, A. W. (1954). Stabilization policy in a closed economy. Economic Journal,64, 290–323.
Ponsard, C. (1955). Économie et Espace. Paris: Sedes.
Poston, T., & Stewart, I. (1978). Catastrophe theory and its applications. London: Pitman.
Puu, T. (1979). The allocation of road capital in two-dimensional space. Amsterdam: North-Holland
Puu, T. (1997, 2003b), Mathematical location and land use theory; an introduction. Berlin: Springer.
Puu, T. ( 2000, 2003a). Attractors, bifurcations, & chaos – nonlinear phenomena in economics. Berlin: Springer.
Puu, T. (2005). The genesis of hexagonal shapes. Networks and Spatial Economics,5, 5–20.
Puu, T., & Beckmann, M. J. (1999, 2003). Continuous space modelling. In R. Hall (Ed.), Handbook of transportation science (pp. 269–310). Norwell, MA: Kluwer.
Samuelson, P. A. (1947). Foundations of economic analysis. Cambridge, MA: Harvard University Press.
Samuelson, P. A. (1952). Spatial price equilibrium and linear programming. American Economic Review,42, 283–303.
Skellam, J. G. (1951). Random dispersal in theoretical populations. Biometrika,38, 196–218.
Tobler, W. R. (1961). Map transformations of geographic space. Ph.D. thesis, University of Washington, Seattle, Wash. Ph.D. diss.
Tromba, A. (1985). Mathematics and optimal form. New York: Scientific American Books.
Vaughan, R. (1987). Urban spatial traffic patterns. London: Pion Ltd.
von Stackelberg, H. (1938). Das brechungsgesetz des verkehrs. Jahrbücher für Nationalökonomie und Statistik,148, 680–696.
von Thünen, J. H. (1826). Der isolierte Staat in Beziehung auf Landwirtschaft und Nationalökonomie. Hamburg: Perthes.
Wardrop, J. G. (1969). Minimum-cost paths in urban areas. Strassenbau-und Strassenverkehsrtechnik,86, 184–190.
Weyl, H. (1952). Symmetry. New Jersey: Princeton University Press.
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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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