publication . Preprint . Article . 2009

Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory

Wen-Tai Hsu; Thomas J. Holmes; Frank Morgan;
Open Access
  • Published: 01 Jan 2009
Abstract
Central place theory is a key building block of economic geography and an empirically plausible description of city systems. This paper provides a rationale for central place theory via a dynamic programming formulation of the social planner's problem of city hierarchy. We show that there must be one and only one immediate smaller city between two neighboring larger-sized cities in any optimal solution. If the fixed cost of setting up a city is a power function, then the immediate smaller city will be located in the middle, confirming the locational pattern suggested by Christaller [4]. We also show that the solution can be approximated by iterating the mapping ...
Subjects
free text keywords: Dynamic programming, Mathematical economics, Bellman equation, Hierarchy, Social planner, Fixed point, Central place theory, Recursion, Mathematical optimization, Mathematics, Fixed cost
Related Organizations
16 references, page 1 of 2

Beckmann, M. J. (1958), \City hierarchies and the distribution of city size," Economic Development and Cultural Change, Vol. 6, No. 3: 243-248. [OpenAIRE]

Berliant, M. and H. Watanabe (2007), \Explaining the size distribution of cities: X-treme economies," working paper, Washington University in St. Louis.

Berry, B. J. L, and William L. Garrison (1958a), \The functional base of the central place hierarchy," Economic Geography, 34 (2): 145-154.

Berry, B. J. L, and William L. Garrison (1958b), \A note on central place theory and the range of a good," Economic Geography, 34 (4): 304-311.

Black, D. and J. V. Henderson (2003), \Urban evolution in the USA," Journal of Economic Geography, 3 (4): 343-372.

Christaller, W. (1933), Central Places in Southern Germany, translated by Carlisle W. Baskin (1966), Englewood Cli®s, N.J. : Prentice-Hall.

C¶ordoba, J.-C. (2008), \On the distribution of city sizes," Journal of Urban Economics, 63: 177-197.

Cronon, W. (1991), Nature's Metropolis: Chicago and the Great West, New York, N.Y.: Norton.

Duranton, G. (2006), \Some foundations for Zipf's law: product proliferation and local spillovers," Regional Science and Urban Economics, 36(4): 543-563. [OpenAIRE]

Duranton, G. (2007), \Urban evolutions: the fast, the slow, and the still," American Economic Review, 97 (1): 197-221. [OpenAIRE]

Eaton, B. C. and R. G. Lipsey (1982), \An economic theory of central places," The Economic Journal, Vol. 92, No. 365: 56-72. [OpenAIRE]

Eeckhout, J. (2004). "Gibrat's law for (all) cities." American Economic Review, 94(5): 1429-1451. [OpenAIRE]

Fujita, M., P. Krugman, and T. Mori (1999), \On the evolution of hierarchical urban systems," European Economic Review, 43: 209-251. [OpenAIRE]

Fujita, M., P. Krugman, and A. J. Venables (1999), The Spatial Economy: Cities, Regions, and International Trade, The MIT Press.

Gabaix, X. (1999) \Zipf's law for cities: an explanation," The Quarterly Journal of Economics, Vol. 114, No. 3: 739-767 [OpenAIRE]

16 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue