Footloose Entrepreneurs, Taxes and Subsidies

Abstract

This paper challenges the robustness of policy propositions of the New Economic Geography. Simply altering the temporal framework of the Footloose Entrepreneur model implies that the system can exhibit periodic cycles, chaotic orbits or agglomeration. Minute changes in a tax or subsidy rate can have dramatic, unpredictable and/or irreversible repercussions on the spatial location of manufacturing industry and on social welfare. The complexity of the dynamics is likely to be exacerbated by competition between governments employing subsidies to attract or retain entrepreneurs. The possibility of complex dynamical behaviour is not eliminated by assuming that entrepreneurs are ‘rational’.

Abstract

Entrepreneurs libres, taux et subventions

Cette étude remet en question la vigueur des propositions de politiques de la Nouvelle Géographie Economique. Alterner simplement le cadre temporel du modèle d'Entrepreneur Libre implique que le système peut exposer des cycles périodiques, des orbites chaotiques ou une agglomération. Les changements de dernière minute pour un taux fiscal ou un taux de subvention peuvent avoir des répercussions dramatiques, imprévisibles et/ou irréversibles sur l'emplacement spatial du secteur secondaire et sur le bien-être collectif. La complexité de la dynamique est susceptible d’être exacerbée par la concurrence existante entre les gouvernements qui emploient des subventions afin d'attirer ou de retenir des entrepreneurs. La possibilité d'un comportement complexe dynamique n'est pas éliminée en assumant que les entrepreneurs sont ‘rationnels’.

Abstract

Empresarios móviles, impuestos y subsidios

Este estudio desafía la robustez de las proposiciones de políticas de la Nueva Geografía Económica. Si el marco temporal del empresario móvil se altera de manera simple, el sistema puede mostrar ciclos periódicos, órbitas caóticas o aglomeración. Cambios mínimos en una tasa de subsidio o impuesto pueden tener repercusiones dramáticas, impredecibles y/o irreversibles en la localización espacial de la industria manufacturera y en el bienestar social. Es probable que la complejidad de la dinámica sea exacerbada por la competencia entre gobiernos empleando subsidios para atraer o retener a los empresarios. La posibilidad de un comportamiento dinámico complejo no se ve eliminada al suponer que los empresarios son ‘racionales’.

Keywords:

• New Economic Geography
• Footloose Entrepreneurs
• taxation
• chaotic dynamics

Keywords:

• F20
• R1
• R12

Notes

1. See also Commendatore et al. (2007) concerning the footloose capital model.

2. For all bifurcation diagrams, the orbit is determined for 5,000 periods and, to identify long-term behaviour, the first 2,000 iterates are discarded.

3. See BFMOR (Ch. 4) for the general expressions for and for symmetric regions; for confirmation that ; and for the significance of the no-black-hole condition, .

4. Chapter 1 of Alligood et al. (1996) provides an excellent introduction to discrete-time dynamical systems and explains, in particular, the remarkable implications of the existence of a period-3 orbit.

5. The impact of a fall in N is equivalent to the impact of a fall in the migration speed. On the comparative dynamical effects of changes in and in a discrete-time core–periphery model, see Currie & Kubin (2006).

6. See also the argument in Currie & Kubin (2006, p. 259, fn. 6) that specifying migration processes in terms of the ratio of real incomes is more consistent with the essence of core–periphery models and that it avoids the use of standard normalizations that have caused some disquiet in the literature.

7. Specifically, Figure 10 assumes , which is a point on orbit A ₂.

8. Figure 11 assumes the same , , N and γ as in Figure 6.

9. See BFMOR's Result 15.2.

10. Baldwin & Krugman (2004), the basis of BFMOR's Chapter 16.6, use a similar Stackelberg-type sequence.

11. The impossibility of overshooting in one-dimensional continuous-time systems means that the range of possible behaviours is considerably circumscribed compared to one-dimensional discrete-time systems. For a continuous-time system, at least two dimensions are needed for closed orbits to arise; and at least three dimensions are required for chaotic trajectories.