Approximation of Short-Run Equilibrium of the N-Region Core-Periphery Model in an Urban Setting
The purpose of this chapter is to give an approximation of short-run equilibrium of the N-region core-periphery model in an urban setting. The approximation is sufficiently accurate and expressed explicitly in terms of the distribution of workers that is
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Abstract The purpose of this chapter is to give an approximation of short-run equilibrium of the N-region core-periphery model in an urban setting. The approximation is sufficiently accurate and expressed explicitly in terms of the distribution of workers that is contained as known function in the model. Making use of this approximation, we can analyze the behavior of each short-run equilibrium. Keywords Discrete nonlinear equation · Krugman model · Spatial economics Mathematical Subject Classification 39B72 · 91B72
1 Introduction In natural and social sciences, a large number of discrete nonlinear equations (DNEs) are considered, and it is important to study them mathematically (see, e.g., [3, 4, 6, 10, 14]). However, if we attempt to conduct such studies, then we often encounter serious obstacles due to the lack of a general mathematical theory of DNEs (see, e.g., [11, pp. 13–15]). Hence, it is advisable and useful to study concrete and specific DNEs constructed in various sciences. Among such DNEs, we are concerned with ones in economics. In particular, noting that various new mathematical sciences (game theory, financial engineering, and so on) were born from Nobel Prize research in economics, we find it important to study DNEs constructed in a branch of economics for which the prize has been recently awarded. Hence, this chapter deals with DNEs in spatial economics.
M. Tabata (B) Department of Mathematical Sciences, Osaka Prefecture University, Osaka 599-8531, Japan e-mail: [email protected] N. Eshima Center for Educational Outreach and Admissions, Kyoto University, Kyoto 606-8501, Japan e-mail: [email protected] © Springer Nature Switzerland AG 2019 F. T. Smith et al. (eds.), Mathematics Applied to Engineering, Modelling, and Social Issues, Studies in Systems, Decision and Control 200, https://doi.org/10.1007/978-3-030-12232-4_17
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Spatial economics is an interdisciplinary field between economics and geography of which the purpose is to study the location, distribution, and spatial organization of economic activities. In about 1990, Krugman began to conduct seminal research by placing particular emphasis on the clustering of economic activities and the formation of economic agglomeration in this interdisciplinary area. Since then, his research has grown into one of the major branches of spatial economics, which is now known as the New Economic Geography (NEG). In 2008, Krugman was awarded the Nobel Memorial Prize in Economic Sciences for his great contribution to spatial economics (see, e.g., [8, 15, 17, 21]). A large number of interesting and impressive DNEs are constructed in the NEG, but many of them have not been studied fully in mathematics (see, e.g., [9, (7.1)– (7.8), (7.14)–(7.19), (15A.1)–(15A.10), (16.1)–(16.8)]). The DNEs in the NEG are promising objects for applied mathematics. Among such DNEs, the N-region coreperiphery model (NRCP model) is one of the most important models in the NEG, since many spatial-economic models are constructed as
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