Abstract
In this paper, we deal with a three-region new economic geography model. The dynamic law which governs the migration of the mobile factor – in our context, “footloose” entrepreneurs (Commendatore et al. (Spat Econ Anal 3(1):115–141, 2008); Forslid and Ottaviano (J Econ Geogr 3:229–240, 2003)) – across three identical regions is formulated in discrete time. The resulting dynamical model belongs to the class of two-dimensional noninvertible maps (Mira et al. (1996) Chaotic dynamics in two-dimensional noninverible maps. World Scientific, Singapore). We present the local stability analysis of the map’s fixed points, corresponding to long term stationary equilibria of the economic system, and a preliminary study of its global stability properties. Our results show that the presence of a third region matters and that there are crucial differences with respect to the symmetric two-region footloose entrepreneurs model: firstly, when the manufacturing sector is absent in one of the three regions, stable asymmetric equilibria may emerge; secondly, we detect complex/strange two-dimensional attractors that cannot exist in two-region new economic geography models, which are typically one-dimensional; finally, we highlight the complex self-similar structure of the basins of attraction of some of the two-dimensional attractors.
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Notes
- 1.
Fujita et al. (1999) examine also the case of a racetrack economy where, in a multiregional setting, the distance between any two regions is always the same, i.e. all the regions are placed along a circumference. However, a number of regions larger than three necessarily implies different transport costs for some regions when these costs are directly proportional to distance. Different regional transport costs can also emerge endogenously by explicitly modeling a transportation sector characterized by increasing returns (Krugman, 1993).
- 2.
Note that if one share M r becomes greater than + 1, at least another share M s has to be negative, where r, s = 1, 2, 3 and r≠s.
- 3.
This value of μ is close to the value that violates the sufficient non-full specialization condition \(\mu < \frac{\sigma } {3\sigma -2} = \frac{5} {11}\) but sufficiently distant from the necessary one \(\mu < \frac{2\sigma } {3\sigma -1} = \frac{10} {13}\).
- 4.
Figure 5 was produced with the software E&F Chaos, which is available at the CENDEF website. We discarded 5,000 initial iterations and plotted 500; and used the following initial values: \({\lambda }_{1} = 0.4,\,{\lambda }_{2} = 0.35,\,{\lambda }_{3} = 0.25\).
- 5.
This figure uses the same values for parameters and initial conditions as the figures above; 5,000 initial iterations are discarded and 15,000 points are plotted.
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Commendatore, P., Kubin, I. (2013). A Three-Region New Economic Geography Model in Discrete Time: Preliminary Results on Global Dynamics. 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_7
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DOI: https://doi.org/10.1007/978-3-642-29503-4_7
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